Test Bank for Precalculus 4th Edition by Cynthia Young

Test Bank for Precalculus, 4th Edition by Test BankCynthia for Y. Young Precalculus, 4th Edition(Young) Chapter 1-11

Chapter 1 1.1

Functions and Their Graphs

Functions

1) Classify the following relationship as a function or not a function. {(-17, 20), (17, 20), (-12, 20), (1, 20)} A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 2) Classify the following relationship as a function or not a function. {(9, -18), (9, -2), (9, 15), (9, -3)} A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 3) Classify the following relationship as a function or not a function. {(15, 10), (-10, -20), (-20, -16), (-14, 1), (-12, -14)} A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 4) Classify the following relationship as a function or not a function. {(4, 10), (18, -2), (12, 2), (4, 16)} A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01

1

5) Determine if the equation x = A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 6) Determine if the equation 8 + 4 A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 7) Determine if the equation x = variable y.

A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01

is a function.

= 4 is a function.

is a function with independent variable x and dependent

8) Given the function f (x) = 5x - 4, evaluate f (x + 10).

A) 5x + 46 B) 5x - 46 C) 5 + 46 D) 5x + 6 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 9) Given the function f (x) = - 3x + 2, evaluate f (x) - f (6).

A) - 3x + 18 B) - 3x - 20 C) - 3x - 18 D) x - 6 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01

2

10) Given the function H(x) = 1 A) -4 B) -4 + 10x C) -24 + 7x D) -4 - x Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01

, evaluate H(x - 5).

11) Given the function G(x) = 6 - 4x, evaluate G(4x + 2).

A) -16 + 16x + 12 B) -16 + 2 C) -16x - 14 D) -16x - 2 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 12) Given the function G(x) = -7 - 6x, evaluate G(4).

A) 17 B) 31 C) -31 D) 4x - 7 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 13) Given the function f (x) =

- 5x - 15, evaluate

A) 2x + h - 5 B) C) 2x + h + 5 D) 1 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01

3

.

14) Given the function f (x) = -7 - 5x, evaluate

.

A) 5 B) -5 C) D) 1 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01 15) Given the function G(t) =

- 7t + 3, evaluate

.

A) h + 17 B) h - 17 C) h D) h - 12 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01 16) Given the function G(t) =

, state the domain in interval notation.

A) [10, ∞) B) (-∞, 10) ∪ (10, ∞) C) (-∞, ∞) D) (-∞, -10) ∪ (10, ∞) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 17) Given the function f (x) =

, state the domain in interval notation.

A) (-∞, -8] ∪ [8, ∞) B) (-∞, -8) ∪ (8, ∞) C) [-8, 8] D) (-∞, -64] ∪ [64, ∞) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01

4

18) Given the function h(t) =

, state the domain in interval notation.

A) (-∞, 8] B) (8, ∞) C) (-∞, ∞) D) (-∞, 8) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 19) Determine if the equation 11x2 + 18 Answer: Not a function Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 20) Given the function G(t) = Answer: [-6, 6] Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01

= 10 is a function of x.

, state the domain in interval notation.

21) A projectile is fired straight up from an initial height of 230 feet, and its height is a function of time, h(t) = -16 + 128t + 230 where h is the height in feet and t is the time in second with t = 0 corresponding to the instant it launches. What is the height 4 seconds after launch?

Answer: 486 feet Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 22) Use the given graph to evaluate the functions. y = r(x)

a. r(-4) b. r(-3) Answer: a. -36 b. -8 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 5

23) Let f (x) = 2x - 21 A) {3/4, -7/2, 11/4} B) {-3/4, 7/2, 11/4} C) {-3/4, 7/2} D) {21/2, 11/4} Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01

and find the values of x that corresponds to f (x) = 0.

24) Use the vertical line test to determine if the graph below defines a function.

Answer: is not a function Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 25) Use the vertical line test to determine if the graph below defines a function.

A) is a function B) is not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01

6

26) Classify the following relationship as a function or not a function.

A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01

7

Precalculus, 4e (Young) Chapter 1 Functions and Their Graphs 1.2

Graphs of Functions

1) Determine if the function in the graph is even, odd, or neither:

A) neither even nor odd B) odd C) even Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 02 2) Determine if the function h(x) = 7 A) even B) odd C) neither even nor odd Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 02

+ 6 is even, odd, or neither even nor odd.

8

3) Determine if the function g(x) = 3 + x is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 4) Determine if the function h(t) = 2 A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

- 9 is even, odd, or neither even nor odd.

5) Determine if the function f (x) = A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

- 10 is even, odd, or neither even nor odd.

6) Determine if the function f (t) = 4|t| + A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

is even, odd, or neither even nor odd.

7) Determine if the function h(x) = 7|x + 10| is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 8) Determine if the function h(x) = 7|x| + 17 is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 9

9) Determine if the function f (x) = A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

is even, odd, or neither even nor odd.

10) Determine if the function f (x) = A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

is even, odd, or neither even nor odd.

11) Determine if the function h(t) = |6t| is even, odd, or neither even nor odd.

Answer: even Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 12) Determine if the function f (x) = A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

is even, odd, or neither even nor odd.

13) The cost of Internet access in a hotel is $18 for the first 25 minutes and $0.07 per minute for each additional minute. Write a function describing the cost of the service as a function of minutes used online.

Answer: C(x) = Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02

10

14) State (a) the domain, (b) the range, and (c) the x-intervals where the function is increasing, decreasing, and constant. Find the values of f (0) and f (1).

Answer:

f (0) = not defined, f (1) = 0 Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 15) Find the difference quotient

for the function.

f (x) = -9 + 15x - 11 Answer: -18 + 15 - 9h Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

11

16) Graph the piecewise-defined function. State the domain and range in interval notation.

Determine the intervals where the function is increasing, decreasing, or constant.

A)

B)

12

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02

13

17) Graph the piecewise-defined function. State the domain and range in interval notation.

Determine the intervals where the function is increasing, decreasing, or constant.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 18) Graph the piece-wise defined function.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 14

19) Match the graph of the piece-wise function.

A)

B)

C)

15

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 20) State the domain and range for the given graph of the piece-wise function.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02

16

21) (a) Graph the piece-wise function. (b) State the domain and range in interval notation.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 22) Given the graph of the piece-wise function, (a) state the domain and range in interval notation and (b) determine the intervals when the function is increasing, decreasing, or constant.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02

17

23) (a) Graph the piece-wise function. (b) State the domain and range in interval notation. (c) Determine the intervals when the function is increasing, decreasing, or constant.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 24) Find the difference quotient

for the function.

f (x) = 11x + 18 Answer: 11 Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 02 25) Find the average rate of change for the function f (x) = 2

+7

over the range x = 5 to x = 10.

Answer: 3750 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 26) Find the average rate of change for the function f (x) = over the range x = -2 to x = 1. Round the answer to 3 decimal places if necessary.

Answer: -4.333 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 18

27) Find the average rate of change for the function f (x) = over the range x = 3 to x = 7. Round the answer to 3 decimal places if necessary.

Answer: 0.424 Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 19

Chapter 2 2.1

Polynomial and Rational Functions

Quadratic Functions

1) Rewrite the quadratic equation in standard form by completing the square. y= - 8x + 19 A) y = +3 B) y = +3 C) y = + 35 D) y = + 35 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 2) Rewrite the quadratic equation in standard form by completing the square. y= + 4x - 20 A) y = + 16 B) y = - 24 C) y = - 16 D) y = - 24 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 3) Rewrite the quadratic function in standard form by completing the square. y = - - 14x + 3 A) y = - 46 B) y = + 21 C) y = + 52 D) y = - 46 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

20

4) Rewrite the quadratic equation in standard form by completing the square. y= - 1x A) y = - 1/4 B) y = C) y = - 1/4 D) y = + 1/4 Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 5) Find the vertex of the parabola associated with the quadratic function. y= + 23 A) (-1, -23) B) (1, -23) C) (-1, 23) D) (1, 23) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 6) Find the vertex of the parabola associated with the quadratic function. y= + 10 A) (8, -10) B) (-8, -10) C) (8, 10) D) (-8, 10) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 7) Find the vertex of the parabola associated with the quadratic equation. y= -3 A) (-1/2, -3) B) (1/2, -3) C) (-1/2, 3) D) (1/2, 3) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01

21

8) Find the vertex of the parabola associated with the quadratic function. y = -5 +8 A) (14, -8) B) (14, 8) C) (-14, 8) D) (-5, 8) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 9) Find the vertex of the parabola associated with the quadratic function. y= + 6x + 22 A) (3, -13) B) (-3, -13) C) (-3, 13) D) (3, 13) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 10) Find the vertex of the parabola associated with the quadratic function. y = - + 4x + 6 A) (-2, 34) B) (2, 10) C) (2, 34) D) (-2, 10) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 11) Find the standard form of the equation of a parabola whose vertex is (2, 9) and passes through the point (7, -116).

A) y = -5 +9 B) y = -

-9

C) y = -

+9

D) y = -

-9

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

22

12) Find the general form of the equation of a parabola whose vertex is (7, -7.1) and passes through the point (-2, 146.8).

A) y = 1.9 - 26.6x + 86 B) y = 1.9 - 26.6x - 86 C) y = -1.9 + 26.6x + 86 D) y = -1.9 + 26.6x - 86 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 13) A rancher has 3000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides.

What is the maximum area of each pasture?

A) 187,500 square feet B) 15,000 square feet C) 375,000 square feet D) 360,000 square feet Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 14) Rewrite the quadratic function in standard form by completing the square. y = 4 - 48x + 130 Answer: y = 4 - 14 Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 15) Find the vertex of the parabola associated with the quadratic function. y = -4 + 76x - 370.5 Answer: (9.5, -9.5) Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 16) A rancher has 1800 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides.

What is the maximum area of each pasture?

Answer: 67,500 square feet Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 17) Find the standard form of the equation of a parabola whose vertex is (5, 10) and passes through the point (3, 30).

Answer: y = 5 + 10 Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 23

18) Find the standard form of the equation of a parabola whose vertex is (8, 4.1) and passes through the point (-2.5, 158.45).

Answer: y = 1.4 - 22.4x + 93.7 Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 19) Graph the quadratic function given in standard form.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

24

20) Graph the quadratic function given in standard form.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

25

21) Graph the quadratic function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

26

22) Graph the quadratic function.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

27

23) Match the quadratic function to an equation in standard form.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 24) Rewrite the quadratic function in standard form by completing the square.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 25) A person standing near the edge of a cliff 150 feet above a lake throws a rock upward with an initial speed of 40 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time and is described by h(t) = -16 + 40t + 150 a. How many seconds will it take until the rock reaches its maximum height?

What is that height? b. At what time will the rock hit the water? Round to two decimal places.

Answer: Part A: 1.25 seconds 175 feet Part B: 4.56 seconds Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01

28

26) The concentration of a drug in the bloodstream, measured in parts per million, can be modeled with a quadratic function. In 67 minutes the concentration is 49.266 parts per million. The maximum concentration of the drug in the bloodstream occurs in 300 minutes and is 375 parts per million. a. Find a quadratic function that models the concentration of the drug as a function of time in minutes. b. In how many minutes will the drug be eliminated from the bloodstream?

Answer: Part A: C(t) = -0.006 + 375 Part B: 550 minutes Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

29

27) Graph the quadratic function. y=

-1

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

30

28) Graph the quadratic function. y= + 2x + 4

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 31

Chapter 2 2.2

Polynomial and Rational Functions

Polynomial Functions of Higher Degree

1) Determine if the function f (x) = 21 degree.

A) Not a polynomial B) a polynomial of degree 21 C) a polynomial of degree 42 D) a polynomial of degree 4 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02

+ 30

- 30

+ 49 is a polynomial. If it is, state the

2) Determine if the function f (x) =

+ 38

- 25 is a polynomial. If it is, state the degree.

A) Not a polynomial B) a polynomial of degree 17 C) a polynomial of degree 39 D) a polynomial of degree -39 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 3) Determine if the function f (x) = 7 degree.

A) Not a polynomial B) a polynomial of degree 18 C) a polynomial of degree 7 D) a polynomial of degree 25 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02

(x + 31) is a polynomial. If it is, state the

4) Find all the real zeros (and state their multiplicity) of the polynomial function. y = 2 (x + 7)(x - 1) A) 0, -7, 1 B) -7, 1 C) 0 (multiplicity 4), -7, and 1 D) 0 (multiplicity 4), 7, and -1 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02

32

5) Find all the real zeros (and state their multiplicity) of the polynomial function. y=x A) 0, 1 (multiplicity 2) B) 0, -1, (multiplicity 2) C) 1, 1, (multiplicity 2), 20 (multiplicity 2) D) 0, 1 (multiplicity 2), Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 6) Find all the real zeros (and state their multiplicity) of the polynomial function. y= - 16 + 64 A) 0, 8 B) 0 (multiplicity 4), 8 (multiplicity 2) C) 8 (multiplicity 2) D) 0 (multiplicity 6), 8 (multiplicity 2) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02 7) Find a polynomial of minimum degree with zeros 4, -3 and 5 (of multiplicity 2).

A) y = + 11 + 23 - 95x - 300 B) y = - 6 - 7x + 60 C) y = + 13 - 25x -300 D) y = - 11 + 23 + 95x - 300 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02 8) Find a polynomial of minimum degree that has zeros -9, 0 (multiplicity 2) and 7.

A) y = + 2 - 63 B) y = - 2x - 63 C) y = - 2 - 63 D) y = + 2x - 63x Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02

33

9) Find a polynomial of minimum degree with zeros 0, 10 +

, and 10 -

.

A) y = - 20x + 90 B) y = + 20 + 90x C) y = - 20 + 90x D) y = + 20x + 90 Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 02, Sec 02 10) Find a polynomial of minimum degree that has the zeros (with multiplicity 2).

A) f (x) = + 10 + 25 B) f (x) = - 10 + 25

(with multiplicity 2) and -

C) f (x) = + 25 D) f (x) = + 10x + 25 Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 02, Sec 02 11) For the polynomial function y = (x - 12) or crosses at the x - intercept (-16, 0).

A) crosses the y - axis at (-16, 0) B) touches the y - axis at (-16, 0) C) crosses the x - axis at (-16, 0) D) touches the x - axis at (-16, 0) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02

(x - 14), determine whether the graph touches

12) For the polynomial function f (x) = or crosses at the x-intercept (0, 0).

A) touches the x-axis at (0, 0) B) crosses the x-axis at (0, 0) C) touches the x-axis at (14, 0) D) neither Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02

(x - 14), determine whether the graph touches

34

13) For the polynomial function f (x) = x A) (1, 0) B) (-1, 0) C) (0, 0) D) (0, 1) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02

(x - 1), find the y-intercept.

14) For the polynomial function f (x) = (x - 6)(x + 4) A) (0, -48) B) (0, -96) C) (0, 48) D) (0, 2) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 15) Determine if the function f (x) = 7 degree.

Answer: polynomial of degree 14 Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02

, find the y-intercept.

(x - 7) is a polynomial. If it is, state the

16) Find all the real zeros (and state their multiplicity) of the polynomial function. ](x - 20) f (x) = Answer: 0 (multiplicity 3), 5 (multiplicity 10), -16 (multiplicity 2), 20 (multiplicity 1) Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 17) Find a polynomial of minimum degree that has the zeros (with multiplicity 2).

Answer: y = -4 +4 Diff: 4 Var: 1 Chapter/Section: Ch 02, Sec 02

35

(with multiplicity 2) and -

18) Sketch the graph of the polynomial function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 19) Sketch the graph of the polynomial function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02

36

20) Match the polynomial function with its graph.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02

37

21) Match the polynomial function with its graph.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02

38

22) Match the graph to the polynomial function.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 23) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

Answer:

(e)

Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02

39

24) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

Answer:

(e)

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 25) For the given graph: (a) list each real zero and its smallest possible multiplicity; (b) determine whether the degree of the polynomial is even or odd; (c) determine whether the leading coefficient of the polynomial is positive or negative; (d) find the y-intercept; (e) write an equation for the polynomial function (assume the least degree possible).

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02 40

26) Graph the function by transforming a power function y = xn. f (x) = 2 + 3 Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) Chapter 3 Exponential and Logarithmic Functions 41

3.1

Exponential Functions and Their Graphs

1) Approximate the number . Round your answer to two decimal places.

A) 1.59 B) 11,585.24ȝ C) 64.00 D) 1.26 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 2) Approximate the number . Round your answer to two decimal places.

A) 0.58 B) 1.73 C) -1.73 D) -0.58 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 3) Approximate the number . Round your answer to two decimal places.

A) 9.42 B) 1.05 C) 31.54 D) 0.95 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 4) Approximate the number . Round your answer to two decimal places.

A) 31.54 B) 9.42 C) 5.32 D) 7.01 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

42

5) Approximate the number . Round your answer to two decimal places.

A) 22.27 B) 10.39 C) 216.00 D) 4.24 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 6) Given f (x) = , evaluate f (1.8). Round your answer to two decimal places.

A) 2.40 B) 2.30 C) 27.86 D) 0.60 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 7) Given f (x) =

, evaluate f (-0.1). Round your answer to two decimal places.

A) -0.20 B) 0.57 C) 0.87 D) 2.30 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 8) Find the y-intercept for the exponential function f (x) = A) (0, 3) B) (0, -3) C) (0, 4) D) (0, 5) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

+ 4.

9) Find the y-intercept for the exponential function f (x) = A) (0, 12) B) (0, -8) C) (0, -4) D) (0, -7) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

- 8.

43

10) Find the y-intercept for the exponential function f (x) = A) (0, 5) B) (0, -1) C) (0, 7) D) (0, 13) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

+ 6.

11) If Gabriel deposits $18,500 in a savings account that earns 3.1% interest per year compounded quarterly, how much money can he expect to be in the account in 2 years? Round your answer to two decimal places.

A) $19,647.00ȝ B) $1,822,882.13 C) $19,678.60ȝ D) $17,383.63ȝ Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 12) If Ashley deposits $10,500 into a savings account that earns 2.7% interest per year compounded monthly, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

A) $11,384.86ȝ B) $11,350.50ȝ C) $9682.15 D) $884.86 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 13) If Vu deposits $13,500 in a savings account that earns 1.5% interest per year compounded quarterly, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

A) $14,107.50ȝ B) $620.19 C) $12,904.87ȝ D) $14,120.19ȝ Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

44

14) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: 3 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 15) Given f (x) = , find f (3.81). Round your answer to two decimal places.

Answer: 8476.40 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 16) If Alicia deposits $1250 in a savings account that earns 5.4% interest per year compounded annually, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

Answer: $1463.63 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 17) Graph the exponential function. f (x) = Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

45

18) Use transformation to find the y-intercept and horizontal asymptote and to graph the exponential function. f (x) = -1 Answer: y-intercept: (0, -2) horizontal asymptote is y = -1

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

46

19) Graph the exponential function. f (x) = A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

47

20) Match the graph to the exponential function.

A) f (x) = -

+1

B) f (x) = +1 C) f (x) = +1 D) f (x) = -1 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 21) A radioactive isotope of indium-111, In, used as a diagnostic tool for locating tumors associated with prostate cancer, has a half-life of 2.807 days. If 100 milligrams are given to a patient, how many milligrams will be left after 4 days?

Answer: 37 milligrams Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 22) If you put $34,100 in a savings account that pays 3.8% a year compounded continuously, how much will you have in the account in 11 years?

A) $22,450.15ȝ B) $51,794.07ȝ C) $51,795.19ȝ D) $389,628.09 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 23) Approximate the number . Round your answer to two decimal places.

A) 0.12 B) -5.71 C) -0.12 D) 8.17 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01

48

24) Approximate the number . Round your answer to two decimal places.

A) 4.48 B) 4.71 C) 5.65 D) 10.04 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

25) Approximate the number . Round your answer to two decimal places.

A) 2.49 B) 1.01 C) 1.56 D) 1.45 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

26) Approximate the number . Round your answer to two decimal places.

A) 21.20 B) 2.04 C) 1.94 D) 4.06 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 27) For the exponential function f (x) = 1 + decimal places.

A) (0, 21.09) B) (0, 2) C) (0, 1.05) D) (0, -2) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

, state the y-intercept. Round your answer to two

49

28) For the exponential function f (x) = 1 decimal places.

A) (0, -1.72) B) (0, 0) C) (-1.72, 0) D) (0, 0.63) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

,state the y-intercept. Round your answer to two

29) For the exponential function f (x) = 1 decimal places.

A) (0, -1.72) B) (0, 25.46) C) (-1.72, 0) D) (0, 0) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

, state the y-intercept. Round your answer to two

30) For the exponential function f (x) = 6 decimal places.

A) (0, 3.28) B) (0, 5) C) (0, 8.72) D) (3.28, 0) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

, state the y-intercept. Round your answer to two

31) If Juan deposits $4200 in a savings account that earns 2.3% compounded continuously, how much money should he expect to be in the account in 3 years? Round your answer to two decimal places.

A) $300.03 B) $4500.03 C) $4489.80 D) $12,889.80ȝ Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

50

32) If Diane deposits $16,713 in a savings account that earns 3.5% interest per year compounded continuously, how much money should she expect to be in the account after 13 years?

A) $24,317.42ȝ B) $316,126.40 C) $26,342.59ȝ D) $9629.59 Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

33) Approximate the number Answer: 0.43 Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

. Round your answer to two decimal places.

34) If Vanessa deposits $4500 in a savings account that earns 3.25% interest per year compounded continuously, how much money should she expect to be in the account in 10 years?

Answer: $6228.14 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 35) State the y-intercept and horizontal asymptote, then graph the exponential function. Round the answer for the y-intercept to three decimal places. f (x) = Answer: y-intercept: (0, 1) horizontal asymptote: y = 0

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

51

36) Graph the exponential function. f (x) = 2 Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

52

37) Match the graph with the function. f (x) = A)

B)

C)

D)

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01

53

38) Match the graph to the exponential function.

A) f (x) =

-3

B) f (x) = -3 C) f (x) = -3 D) f (x) = -3 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 39) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 40) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01

54

41) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: 1 Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 42) State the domain and range for the function. Express in interval notation. f (x) = +7 Answer: Domain: (-∞, ∞) Range: (7, ∞) Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 43) State the domain and range for the function. Express in interval notation. f (x) = -4 Answer: Domain: (-∞, ∞) Range: (-∞, -4) Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 44) State the domain and range for the function. Express in interval notation. f (x) = -9 Answer: Domain: (-∞, ∞) Range: (-9, ∞) Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 45) State the domain and range for the function. Express in interval notation. f (x) = -9 Answer: Domain: (-∞, ∞) Range: (-∞, -9) Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) Chapter 3 Exponential and Logarithmic Functions 55

3.2

Logarithmic Functions and Their Graphs

1) Write the logarithmic equation in its equivalent exponential form.

25 = -2 A) = 1/5 B) = 25 C) = 25 D) = 25 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 2) Write the logarithmic equation in its equivalent exponential form.

32 = 5 A) =2 B) = 32 C) = 32 D) =2 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 3) Write the logarithmic equation in its equivalent exponential form. log 1000 = 3 A) = 1000 B) = 1000 C) = 1000 D) = 10 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

56

4) Write the logarithmic equation in its equivalent exponential form. log 0.01 = -2 A) = 0.01 B) = 0.01 C) = 0.01 D) = 10 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 5) Write the exponential equation in its equivalent logarithmic form.

5= A) ln 125 = 5 B)

= 125

C)

125 = 5

D)

5=

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 6) Write the exponential equation in its equivalent logarithmic form. = 625 A) ln 625 = 4 B) 625 = 4 C)

4=5

D) log 625 = 4 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

57

7) Write the exponential equation in its equivalent logarithmic form. = A)

=4

B)

=4

C) log

=4

D)

=4

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 8) Evaluate the logarithm exactly.

1 A) 1 B) 37 C) 0 D) undefined Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 9) Approximate the common logarithm using the calculator. Round your answer to two decimal places. log 838 A) 2.92 B) 8380 C) 6.73 D) 2277.92 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

58

10) Approximate the common logarithm using the calculator. Round your answer to two decimal places. log 0.0101 A) -4.60 B) -2.00 C) 0.03 D) 0.101 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 11) Approximate the natural logarithm using a calculator. Round your answer to two decimal places. ln 33 A) 1.52 B) 89.70 C) 3.50 D) 330 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 12) Approximate the natural logarithm using a calculator. Round your answer to two decimal places. ln 0.0084 A) -2.08 B) 0.08 C) 0.02 D) -4.78 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 13) State the domain of the logarithm function f (x) = A) (10, ∞) B) (-∞, 10) C) (-∞, 10] D) (0, ∞) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

59

(10 - x) in interval notation.

14) State the domain of the logarithm function f (x) =

.

A) (-∞, ∞) B) (-3, 3) C) (0, ∞) D) (-∞, -3) ∪ (-3, ∞) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 15) State the domain of the logarithm function f (x) =

.

A) (0, ∞) B) [- 4, 4] C) (- 4, 4) D) (-∞, 4) ∪ ( 4, ∞) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 16) Write the logarithmic equation in its equivalent exponential form.

21.11 = 2.2 Answer: = 21.11 Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 17) State the domain of the logarithmic function f (x) =

(47 - x) in interval notation.

Answer: (-∞, 47) Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 18) Write the exponential equation in its equivalent logarithmic form. = 3.48 Answer: 1.8 = 2 Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

60

19) Graph the logarithmic function. f (x) = (3 - x) Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 20) Graph the logarithmic function using transformation techniques. f (x) = (2 - x) Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02

61

21) Match the graph with the logarithmic function. f(x) = (3 - x) A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02

62

22) Match the graph to the logarithmic function.

A)

f (x) =

(x + 1) - 1

B)

f (x) =

(x - 1) - 1

C)

f (x) =

(x - 1) + 1

D)

f (x) =

(x + 1) + 1

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 23) A city experienced a major earthquake. The energy released measured Calculate the magnitude of the earthquake using the Richter scale.

A) 11.3 B) 7.5 C) 17.4 D) 13.4 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 24) A substance has an approximate hydrogen ion concentration of about 3.89 × Calculate its pH value.

A) 12.1 B) 25.1 C) -12.1 D) 10.9 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02

63

.

25) Evaluate the logarithm exactly.

161,051 A) 1 B) 11 C) 5 D) undefined Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 26) Evaluate the logarithm exactly.

- 243 A) 1 B) 3 C) 5 D) undefined Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02

64

27) Graph the logarithmic function. f (x) = +1

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02

65

28) Graph the logarithmic function. f (x) = (x + 5)

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02

66

29) Graph the logarithmic function. f (x) = -3 x

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02

67

30) Graph the logarithmic function on a logarithmic scale. f (x) = -3 x

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 68

Chapter 4 4.1

Trigonometric Functions of Angles

Angle Measure

1) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 7 mm.

A) 0.9 radians B) 1.2 radians C) 42.0 radians D) 1.0 radians Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 2) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 4.7 cm.

A) 1.7 radians B) 3.5 radians C) 38.5 radians D) 0.6 radians Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 3) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 2 ft.

A)

radians

B) 4 radians C)

radians

D)

radians

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 4) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length 7 mm. Round your answer to two decimal places.

Answer: 0.88 radians Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 5) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius 69

and arc length 1.6 yds. Round your answer to two decimal places.

Answer: 0.22 radians Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 6) Find the measure (in radians) of a central angle, θ, that intercepts an arc on a circle with radius and arc length Answer:

m.

radians

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 7) Convert 212 degrees to radians.

A) 3.70π radians B) 0.85π radians C) 1.18π radians D) 2.67π radians Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 8) Convert 344 degrees to radians. Round numbers to two decimal places and leave the answer in terms of π.

Answer: 1.91π radians Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 9) Convert

π radians to degrees.

A) 90.0° B) 0.5° C) 1.8° D) 360.0° Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 10) Convert

π radians to degrees. Round the answer to one decimal place.

Answer: 90.0° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 11) Convert 12.7 radians to degrees.

70

A) 44.53° B) 39.90° C) 0.66° D) 727.66° Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 12) Convert 12.6 radians to degrees. Use 3.14 for π and round the answer to the nearest hundredth of a degree.

Answer: 722.29° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 13) Convert 118.8° to radians.

A) 1.38 radians B) 2.38 radians C) 4.15 radians D) 2.07 radians Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 14) Convert 236.9° to radians. Round your answer to 3 significant digits.

Answer: 4.13 radians Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 15) Find the reference angle for A)

radians, 40°

B)

radians, 40°

C)

radians, 80°

D)

radians, 80°

in terms of both radians and degrees.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 16) Find the reference angle for

in terms of both radians and degrees.

71

Answer:

radians, 20°

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 17) Find the exact value of sin

.

A) 1 B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 18) Find the exact value of csc

.

A) - 2 B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

72

19) Find the exact value of cot

.

A) B) C) D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 20) Find the exact value of cos

.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 21) Find the exact value of csc

.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 22) Find the exact value of tan

.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

73

23) Electronic Signals. Two electronic signals that cancel each other out are said to be 180° out of phase, or the difference in their phases is 180°. How many radians out of phase are two signals whose phase difference is 132°?

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 24) Architecture. A citrus fruit stand in California is in the shape of an orange that is cut in half. If a wedge or sector of the orange has a central angle of 255°, how many radians does this represent?

A)

radians

B)

radians

C)

radians

D)

radians

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 25) Fruit. When a grapefruit is cut in half, wedges or sectors are visible. If the central angle of a sector is 55°, how many radians does this represent?

Answer:

radians

Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 26) Clock. How many radians does the second hand of a clock sweep through in 8 A) 9π radians B) 16π radians C) 25π radians D) 17π radians Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

74

minutes?

27) Clock. How many radians does the second hand of a clock sweep through in 6

minutes?

Answer: 13π radians Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 28) Stratosphere Tower. The Stratosphere Tower in Las Vegas dominates the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated in 98 minutes?

A)

radians

B)

radians

C)

radians

D)

radians

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 29) Stratosphere Tower. The Stratosphere Tower in Las Vegas dominates the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated in 78 minutes?

Answer:

radians

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 30) Sprinkler: A sprinkler is set to reach an arc of 47 feet, 19 feet from the sprinkler. Through how many radians does the sprinkler rotate?

A) B) 893 C) 142 D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 75

31) Sprinkler: A sprinkler is set to reach an arc of 15 feet, 9 feet from the sprinkler. Through how many radians does the sprinkler rotate?

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 32) Electronic Signals. Two electronic signals that cancel each other out are said to be 180° out of phase, or the difference in their phases is 180°. How many radians out of phase are two signals whose phase difference is 27°?

A) B) 21π C) 20π D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 33) Convert -

π radians to degrees.

A) -112.5° B) -0.2° C) 4.5° D) -288.0° Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 34) Convert -87.1° to radians.

A) 1.52 radians B) -3.25 radians C) -3.04 radians D) -1.52 radians Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01

76

35) Find the reference angle for Answer:

in terms of both radians and degrees.

radians, 40°

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 36) State in which quadrant the terminal side of a 1202° angle in standard position lies.

A) QII B) QI C) QIV D) QIII Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 37) State on what axis the terminal side of a 90° angle in standard position lies.

A) Negative x-axis B) Negative y-axis C) Positive y-axis D) Positive x-axis Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 38) State in which quadrant the terminal side of a -156° angle in standard position lies.

A) QIII B) QII C) QI D) QIV Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 39) State on what axis the terminal side of a -990° angle in standard position lies.

A) Negative x-axis B) Negative y-axis C) Positive y-axis D) Positive x-axis Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

77

40) What angle is coterminal to 585°?

A) 1125° B) 855° C) 1665° D) 405° Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 41) Name the angle that is coterminal with 280° after making 3 rotations in the counterclockwise direction.

Answer: 1360° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 42) Determine the angle of the smallest possible positive measure that is coterminal with 1219°.

A) 162 B) 139 C) 115 D) 104 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 43) Determine the angle of the smallest possible positive measure that is coterminal with 1159°.

Answer: 79° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 44) Clock. What is the measure of the angle an hour hand on a clock makes if it starts at 3:00 am on Tuesday and continues until 3:00 am on Thursday?

A) -720° B) 1440° C) 720° D) -1440° Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 45) Clock. What is the measure of the angle an hour hand on a clock makes if it starts at 3:00 am on Monday and continues until 8:00 pm on Tuesday?

Answer: -1230° Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

78

46) Satellites. Two satellites orbiting the Earth are travelling on the same path but in opposite directions. If they start at the same spot and then sweep through angles of -425° and 2095° before stopping, will they end up at the same spot? Assume they don't collide when they meet on the path.

A) Yes B) No C) Not enough information Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 47) Electrons. Two electrons orbiting an atom's nucleus are travelling on the same path but in opposite directions. If they start at the same spot and then sweep through angles of -812° and 2763° before stopping, will they end up at the same spot? Assume they don't collide when they meet on the path.

Answer: No Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 48) Kite. Henry is flying a kite on the beach. He lets out 68 feet of string and has it flying at an angle of 30° to the ground. How far is the kite extended horizontally and vertically from Henry?

Give the exact answer.

Answer: 34 feet horizontal and 34 feet vertical Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 49) Ferris Wheel. If the Ferris Wheel is centered at the origin and travels in a counterclockwise direction. A car starts at (0, -100) and before completing 4 rotations it is stopped at Through what angle has the car rotated?

Answer: 1290° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 50) Ferris Wheel. If the Ferris Wheel is centered at the origin and travels in a counterclockwise direction. A car starts at (0, -100) and before completing 3 rotations it is stopped at Through what angle has the car rotated?

A) 1200° B) 870° C) 930° D) 1230° Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

79

51) Sketch the angle with the measurement of 1200° in standard position.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

80

52) Find the exact length of the arc subtended by a central angle of θ = 16 on a circle with radius A) 176 cm B)

cm

C)

cm

D) 27 cm Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 53) Find the exact length of the arc subtended by a central angle of θ =

on a circle with radius

19 yds.

A) 39 yds B)

yds

C)

yds

D) 380 yds Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 54) Find the exact length of the arc subtended by a central angle of θ = 100° on a circle with radius A) 25 m B)

m

C)

m

D) 100 m Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 55) Find the exact length of the arc subtended by a central angle of θ = 11 radians on a circle with radius 23 m.

Answer: 253 m Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 81

56) Find the exact length of the arc subtended by a central angle of θ =

Answer:

on a circle with radius

cm

Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 57) Find the exact length of the arc subtended by a central angle of θ = 1800° on a circle with radius Answer: 90 yds Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 58) Find the exact length of the radius of a circle given arc length s =

A)

m

B)

m

C)

m

D)

m

m and central angle

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 59) Find the exact length of the radius of a circle given arc length s =

Answer:

mi

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

82

mi and central angle

60) Find the exact length of the radius of a circle given arc length s =

A)

m

B)

m

C)

m

D)

m

m and central angle

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 61) Find the exact length of the radius of a circle given arc length s =

Answer:

ft and central angle

ft

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 62) Use a calculator to approximate the length of the arc on a circle with central angle radians and radius r = 6 yds.

A) 0.50 yds B) 18.00 yds C) 2.00 yds D) 9.00 yds Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 63) Use a calculator to approximate the length of the arc on a circle with central angle θ = radius r = 2.5 ft.

A) 2.4 ft B) 24 ft C) 6.5 ft D) 11 ft Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 83

and

64) Use a calculator to approximate the length of the arc on a circle with central angle and radius A) 17 cm B) 13 cm C) 22 cm D) 6 cm Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 65) Use a calculator to approximate the length of the arc on a circle with central angle θ = 0.7 radians and radius r = 9.8 in. Round your answer to two significant digits.

Answer: 6.86 in Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 66) Use a calculator to approximate the length of the arc on a circle with central angle θ =

and

radius r = 3.9 in. Round your answer to two significant digits.

Answer: 4.6 in Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 67) Use a calculator to approximate the length of the arc on a circle with central angle θ = 334° and radius r = 30 mm. Round your answer to the nearest integer.

Answer: 175 mm Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 68) Find the area of the circular sector with a radius r = 1.7 in and central angle θ = A) 6.7 B) 13.4 C) 2.1 D) 3.9 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

84

.

69) Find the area of the circular sector with a radius r = 5.4 ft and central angle θ =

.

Answer: 10.2 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 70) Find the area of the circular sector with a radius r = 4.7 in and central angle θ = 135°.

A) 26.0 B) 52.0 C) 8.3 D) 5.5 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 71) Find the area of the circular sector with a radius r = 2.9 mm and central angle θ = 140°.

Answer: 10.3 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 72) Low Earth Orbit Satellites. A low earth orbit (LEO) satellite is traveling in an approximately circular orbit 100 km above the surface of the Earth. If a ground station tracks the satellite when it is within a 72° cone above the tracking antenna (directly overhead), how many kilometers does the satellite travel during the ground station track? Assume the Earth has a radius of 6,400 km.

A) 8042 km B) 2600 km C) 8168 km D) 5445 km Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 73) Low Earth Orbit Satellites. A low earth orbit (LEO) satellite is traveling in an approximately circular orbit 100 km above the surface of the Earth. If a ground station tracks the satellite when it is within a 59° cone above the tracking antenna (directly overhead), how many kilometers does the satellite travel during the ground station track? Assume the Earth has a radius of 6,400 km.

Answer: 6693 km Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

85

74) Clock Tower. The Metropolitan Life Insurance Company tower in New York City has clocks on all four sides. If each clock has a minute hand that is 13.25 feet in length, how far does the tip of each hand travel in 25 minutes?

A) 34.7 feet B) 11.6 feet C) 17.3 feet D) 23.1 feet Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 75) Big Ben. The Big Ben clock tower in London has clocks on all four sides. If each clock has a minute hand that is 11.5 feet in length, how far does the tip of each hand travel in 34 minutes?

Round to the nearest integer.

Answer: 41 feet Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 76) Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions.

The smaller (pinion) gear has a radius of and the larger (spur) gear has a radius of If the pinion gear rotates 88°, how many degrees will the spur gear rotate?

A) 8° B) 161° C) 48° D) 96° Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 77) Gears. Two gears have interlocking teeth, which cause them to rotate in opposite directions.

The smaller (pinion) gear has a radius of and the larger (spur) gear has a radius of If the pinion gear rotates 88°, how many degrees will the spur gear rotate?

Answer: 70° Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 78) Windshield Wipers. A windshield wiper that is 11 inches long (blade and arm) rotates 67°.

If the rubber part is 7 inches long, what is the area cleared by the wiper? Round to the nearest square inch.

Answer: 61 square inches Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

86

79) Use a calculator to approximate the length of the radius of a circle with central angle θ = 64° and arc length s = 37 in. Round your answer to the nearest integer.

Answer: 33 in Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 80) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s = 256 inches in time t = 50 hours.

A) 5.12 inches/hour B) 12,800.00ȝ inches/hour C) 0.20 inches/hour D) 8.12 inches/hour Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 81) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s = 26.4 feet in time t = 24.7 days.

A) 4.07 feet/day B) 652.08 feet/day C) 0.94 feet/day D) 1.07 feet/day Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 82) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s =

feet in time t = 18 days.

A) 252 feet/day B)

feet/day

C)

feet/day

D) 428 feet/day Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 83) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s = 26 meters in time t = 47 hours. Round your answer to two decimal places.

Answer: 0.55 meters/hour Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 87

84) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s = 13.7 centimeters in time t = 7.7 days. Round your answer to two decimal places.

Answer: 1.78 centimeters/day Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 85) Find the linear speed of a point that moves with constant speed in a circular motion if the point travels along the circle an arc length s =

yards in time t = 58 years. Give the answer as a

fraction.

Answer:

yards/year

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 86) Find the distance (arc length) a point travels around a circle if it moves with constant speed in time A) 0.540983607 kilometers B) 1.8 kilometers C) 20.1 kilometers D) 40.3 kilometers Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 87) Find the distance (arc length) a point travels around a circle if it moves with constant speed in time A) 0.2 kilometers B) 5.1 kilometers C) 328.0 kilometers D) 656.0 kilometers Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 88) Find the distance (arc length) a point travels around a circle if it moves with constant speed in time Round your answer to the nearest integer.

Answer: 572 miles Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01

88

89) Find the distance (arc length) a point travels around a circle if it moves with constant speed in time Round your answer to one decimal place.

Answer: 85.9 kilometers Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 90) Find the angular speed, ω, associated with rotating a central angle

in time

A) B) C) D) 390π Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 91) Find the angular speed, ω, associated with rotating a central angle Express your answer in radians/second.

in time

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 92) Find the angular speed, ω, associated with rotating a central angle

A) B) C) 480 D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 89

in time

93) Find the angular speed, ω, associated with rotating a central angle

in time

A) B) C) 600 D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 94) Find the angular speed, ω, associated with rotating a central angle Give the answer as a fraction

in time

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 95) Find the angular speed, ω, associated with rotating a central angle Give the answer as a fraction.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

90

in time

96) Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius r = 48 feet and angular velocity ω = A)

feet/sec

B)

feet/sec

C)

feet/sec

D)

feet/sec

.

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 97) Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius r = 23 feet and angular velocity ω = Answer:

. Give the exact answer.

feet/sec

Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 98) Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius r = 18 yards and angular velocity ω = Answer:

. Give the exact answer.

yards/sec

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 99) Find the linear speed of a point traveling at a constant speed along the circumference of a circle with radius r = 26 kilometers and angular velocity ω = 26.7 decimal place.

Answer: 694.2 kilometers/sec Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01

91

. Round the answer to the 1

100) Find the distance, s, a point travels along a circle over time t = 20 seconds, given the angular speed ω =

and the radius r = 2 yards.

A)

yards

B)

yards

C)

yards

D)

yards

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 101) Find the distance, s, a point travels along a circle over time t = 8 seconds, given the angular speed ω =

and the radius r = 39 centimeters.

Answer:

centimeters

Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 102) Find the distance, s, a point travels along a circle over time t = 16 seconds, given the angular speed ω =

and the radius r = 6 inches.

Answer: 8π inches Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 103) Find the distance, s, a point travels along a circle over time t = 13 minutes, given the angular speed ω = 5 rotations per second and the radius r = 6 inches. Express your answer in miles A) 0.5 miles B) 27.8 miles C) 4.4 miles D) 2.3 miles Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

92

104) Find the distance, s, a point travels along a circle over time t = 13 minutes, given the angular speed ω = 8 rotations per second and the radius r = 3 inches. Express your answer in miles and round your answer to one decimal place.

Answer: 1.9 miles Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 105) Find the distance a point travels along a circle in 30 minutes, if r = 31 m, and ω = 4 revolutions per second.

Round your answer to one decimal place.

Answer: 1,401,696.0 m Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 106) Bicycle. A bicyclist is traveling at an angular speed of 3 radians per second. How fast is he traveling in miles per hour if his tires are 25 inches in diameter?

A) 13.4 mph B) 6.7 mph C) 2.1 mph D) 80.3 mph Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 107) Bicycle. A bicyclist is traveling at an angular speed of 3 radians per second. How fast is she traveling in miles per hour if her tires are 25 inches in diameter? Round your answer to one decimal place.

Answer: 6.7 mph Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 108) Electric Motor. A 3-inch diameter pulley is being driven by an electric motor that is running at 1400 revolutions per minute. If it is connected by a belt to a 13-inch diameter pulley that is driving a drill bit, what is the speed of the drill bit in revolutions per minute (rpm)?

A) 6067 rpm B) 2200 rpm C) 323 rpm D) 2204 rpm Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

93

109) Electric Motor. A 3-inch diameter pulley is being driven by an electric motor that is running at 1400 revolutions per minute. If it is connected by a belt to a 15-inch diameter pulley that is driving a drill bit, what is the speed of the drill bit in revolutions per minute (rpm)? Round your answer to the nearest whole number.

Answer: 280 rpm Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 110) Carousel. A boy wants to jump onto a playground carousel that is spinning at the rate of 23 revolutions per minute. If the carousel is 18 feet in diameter, how fast must the boy run, in feet per second, to match the speed of the carousel and jump on? Round to two decimal places.

Answer: 21.68 feet per second Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 111) Carousel. A boy wants to jump onto a playground carousel that is spinning at the rate of 8 revolutions per minute. If the carousel is 21 feet in diameter, how fast must the boy run, in feet per second, to match the speed of the carousel and jump on?

A) 17.59 feet per second B) 8.80 feet per second C) 1.40 feet per second D) 527.79 feet per second Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 112) Gravitron. To achieve similar weightlessness as that on NSA's centrifuge, ride the Gravitron at a carnival or fair. The Gravitron has a diameter of 18 meters, and in the first 20 seconds it achieves zero gravity and the floor drops. If the Gravitron rotates 25 times per minute, find the linear speed of the people riding it in meters per second.

A) 47.12 feet per second B) 23.56 feet per second C) 3.75 feet per second D) 1413.72 feet per second Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

94

113) Gravitron. To achieve similar weightlessness as that on NSA's centrifuge, ride the Gravitron at a carnival or fair. The Gravitron has a diameter of 18 meters, and in the first 20 seconds it achieves zero gravity and the floor drops. If the Gravitron rotates 29 times per minute, find the linear speed of the people riding it in meters per second.

Answer: 27.33 feet per second Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01

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Precalculus, 4e (Young) 95

Chapter 4 4.2

Trigonometric Functions of Angles

Right Triangle Trigonometry

1) Specify the measure of the angle in degrees with a 2/5 rotation counterclockwise, to the nearest whole degree.

A) 144° B) 216° C) 59° D) 281° Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 2) Specify the measure of the angle in degrees with a 4/9 rotation clockwise, to the nearest whole degree.

A) -160° B) 200° C) 110° D) 160° Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 3) Specify the measure of the angle in degrees with a 1/7 rotation clockwise, to the nearest whole degree.

Answer: -51° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 4) Specify the measure of the angle in degrees with a 2/9 rotation counterclockwise, to the nearest whole degree.

Answer: 80° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 5) Find the complement of an angle that measures 70 degrees.

A) 25° B) 110° C) 160° D) 20° Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02

96

6) Find the complement of an angle that measures 65 degrees.

Answer: 25° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 7) Find the supplement of an angle that measures 120 degrees.

A) 300° B) 67° C) 60° D) 210° Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 8) Find the supplement of an angle that measures 14 degrees.

Answer: 166° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 9) Find the measure of each angle to one decimal place if angle A measures (10x)° and angle B measures (13x)°.

Answer: 39.1°, 50.9° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 10) Find the measure of each angle to one decimal place if angle A measures (17x)° and angle B measures (14x)°.

Answer: 98.7°, 81.3° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

97

11) If the measure of angle α = 108° and the measure of angle β = 2°, find the measure of angle γ.

Answer: 70° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 12) If the measure of angle α = 114° and the measure of angle β = 30° find the measure of angle γ.

A) 96° B) 126° C) 36° D) 99° Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 13) If β = γ and α = 3β, find all three angles.

A) 1°, 1°, 178° B) 25°, 25°, 130° C) 40°, 40°, 100° D) 36°, 36°, 108° Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

98

14) If β = 6γ and α = 13γ , find all three angles.

Answer: 9°, 54°, 117° Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 15) Find two supplementary angles with measures (9x)° and (9x)°. Write your answer to one decimal place.

Answer: 90°, 90° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 16) If d = 4, and e = 7, find f. Express the length exactly.

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 17) If d = 5, and e = 12, find f . Express the length exactly.

Answer: f = 13 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02

99

18) If d = 7, and e = 22, find f in the following right triangle. Write your answer to two decimal places.

Answer: 23.09 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 19) If the hypotenuse of a 45° - 45° - 90° triangle has a length of

, how long are the legs?

Answer: 16 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 20) If the longer leg of a 30° - 60° - 90° triangle has a length of

, how long is the hypotenuse?

Answer: 18 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 21) Clock. What is the measure (in degrees) of the two angles between the hour hand and minute hand on a clock when the time is exactly 2:22? Assume the hour hand points to 2:00.

A) 120°, 240° B) 72°, 288° C) 132°, 228° D) 12°, 348° Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

100

22) Clock. What is the measure (in degrees) of the two angles between the hour hand and minute hand on a clock when it is exactly 4:33? Assume the hour hand points to 4:00.

Answer: 78°, 282° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 23) Ferris Wheel. The Ferris Wheel was an amusement park ride that was invented by bridge builder George W. Ferris, and unveiled at the 1889 Paris Exhibition. The wheel had a diameter of 250 feet, a circumference of 825 feet, and a maximum height of 264 feet. If the Ferris Wheel made one rotation in 40 minutes, what was the measure of the angle (in degrees) that a cart on the Wheel would rotate in 26 minutes?

A) 260° B) 234° C) 208° D) 182° Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 24) Ferris Wheel. The Ferris Wheel was an amusement park ride that was invented by bridge builder George W. Ferris, and unveiled at the 1889 Paris Exhibition. The wheel had a diameter of 250 feet, a circumference of 825 feet, and a maximum height of 264 feet. If the Ferris Wheel made one rotation in 40 minutes, what was the measure of the angle (in degrees) that a cart on the Wheel would rotate in 15 minutes?

Answer: 135° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

101

25) Roof Truss. A roofing contractor is building triangular trusses with a pitch of 45 degrees. If the hypotenuse of the trusses is 101 feet, what is the number of linear feet of board required to build each truss (to the nearest foot)?

101 ft A) 244 linear feet B) 276 linear feet C) 143 linear feet D) 387 linear feet Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 26) Roof Truss. A roofing contractor is building triangular roof trusses with a pitch of 45 degrees.

If the hypotenuse of the trusses is 141 feet, what is the number of linear feet of board required to build each truss (to the nearest foot)?

141 ft Answer: 340 linear feet Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 27) A rope is to be tied from the top of a tent 8 feet high to a stake in the ground. If the angle between the ground and the rope is to be 31°, how far from the base of the tent should the rope be staked? (Round to two decimal places.)

A) 9.33 feet B) 13.31 feet C) 4.12 feet D) 15.53 feet Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 28) If a revolving restaurant can rotate 40° in 45 minutes, how long does it take for the restaurant to make a complete revolution?

Answer: 405 minutes Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

102

29) Name the trigonometric function that has a value of

.

A) cot 45° B) tan 45° C) sin 45° D) sec 45° Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 30) Name the two trigonometric functions that have a value of

on the interval 0° < x < 90°.

Answer: cos 30° and sin 60° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 31) Use the trigonometric ratio identity tan θ =

to calculate tan 60°.

A) B) 1 C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 32) Use the reciprocal identity cot θ =

to calculate cot 45°.

A) B) 2 C) 1 D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

103

33) Use a calculator to approximate the sin 49° to three decimal places.

A) 0.656 B) 0.869 C) 0.755 D) 1.325 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 34) Use a calculator to approximate the cos 27.5° to three decimal places.

A) 0.887 B) 1.921 C) 0.462 D) 2.166 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 35) Use a calculator to approximate the sec 73.9° to three decimal places.

A) 0.277 B) 3.606 C) 0.961 D) 1.041 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 36) Use a calculator to approximate the tan 43.9° to three decimal places.

A) 0.721 B) 1.039 C) 0.693 D) 0.962 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 37) Use a calculator to approximate the csc 1.5° to three decimal places.

A) 1.000 B) 38.188 C) 0.026 D) 38.202 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

104

38) Use a calculator to approximate the cot 0.9° to three decimal places.

A) 1.000 B) 63.657 C) 0.016 D) 63.665 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 39) Use a calculator to approximate the sin 4.7° to three decimal places.

Answer: 0.082 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 40) Use a calculator to approximate the cos 48.9° to three decimal places.

Answer: 0.657 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 41) Use a calculator to approximate the tan 83.2° to three decimal places.

Answer: 8.386 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 42) Use a calculator to approximate the csc 66.5° to three decimal places.

Answer: 1.090 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 43) Use a calculator to approximate the sec 3.1° to three decimal places.

Answer: 1.001 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 44) Use a calculator to approximate the cot 20.6° to three decimal places.

Answer: 2.660 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 45) Calculate ∠ A + ∠ B if ∠ A = 39° 15' 2" and ∠ B = 34° 1' 12" Answer: 73° 16' 14" Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02

105

46) Calculate ∠ A + ∠ B if ∠ A = 33° 49' 3" and ∠ B = 71° 28' 28" Answer: 105° 17' 31" Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 47) Calculate ∠ A + ∠ B if ∠ A = 84° 22' 19" and ∠ B = 75° 2' 20" Answer: 159° 24' 39" Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 48) Calculate 180° - ∠ B if ∠ B = 66° 29' 27" Answer: 113° 30' 33" Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 49) Calculate ∠ A - ∠ B if ∠ A = 85° 50' 31" and ∠ B = 26° 33' 7" Answer: 59° 17' 24" Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 50) Convert 6° 22' 48" to decimal degrees. Round your answer to the thousandths place.

Answer: 6.380 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 51) Convert 53° 46' 55" to decimal degrees. Round your answer to the thousandths place.

A) 54.683 B) 53.919 C) 53.782 D) 154.000 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 52) Convert 60.188° from decimal degrees to degrees-minutes-seconds. Round to the nearest second.

Answer: 60° 11' 17" Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

106

53) Convert 76.204° from decimal degrees to degrees-minutes-seconds. Round to the nearest second.

A) 76° 12' 14" B) 76° 20' 4" C) 274,334" D) 76° 12' Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 54) Convert 17.252° from decimal degrees to degrees-minutes-seconds. Round to the nearest minute.

Answer: 17° 15' Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 55) Evaluate sin(69° 40'). Round answers to 3 decimal places.

Answer: 0.938 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 56) Evaluate cos(41° 47'). Round answers to 3 decimal places.

Answer: 0.746 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 57) Evaluate tan(47° 8'). Round answers to 3 decimal places.

Answer: 1.077 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 58) Evaluate csc(77° 54' 20"). Round answers to 3 decimal places.

Answer: 1.023 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 59) Evaluate sec(61° 8' 7"). Round answers to 3 decimal places.

Answer: 2.071 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 60) Evaluate cot(38° 49' 20"). Round answers to 3 decimal places.

Answer: 1.243 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

107

61) Evaluate sin(15° 3' 25"). Round answers to 3 decimal places.

Answer: 0.260 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 62) Evaluate cos(66° 59' 42"). Round answers to 3 decimal places.

Answer: 0.391 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 63) Evaluate tan(87° 48' 14"). Round answers to 3 decimal places.

Answer: 26.077 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 64) Light bends as it travels from one medium to another according to Snell's Law: sin( ) =

sin( )

where: is the index of refraction of the medium (usually air) the light ray is leaving is the incident angle of the light ray (perpendicular to the boundary between the two mediums) is the index of refraction of the medium the light ray is entering is the refractive angle of the light ray (perpendicular to the boundary between the two mediums) Calculate the index of refraction incident angle

of a substance if air has an index of refraction

= 42°, and the refractive angle

places.

A) 0.608 B) 1.076 C) 1.645 D) 0.262 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 108

= 1.00, the

= 24°. Round your answer to 3 decimal

65) Light bends as it travels from one medium to another according to Snell's Law: sin( ) =

sin( )

where: is the index of refraction of the medium (usually air) the light ray is leaving is the incident angle of the light ray (perpendicular to the boundary between the two mediums) is the index of refraction of the medium the light ray is entering is the refractive angle of the light ray (perpendicular to the boundary between the two mediums) Calculate the index of refraction incident angle

of a substance if air has an index of refraction

= 42°, and the refractive angle

= 1.00, the

= 22°. Round your answer to 3 decimal

places.

Answer: 1.786 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 66) The pitch of a staircase is given as 41° 49' 3". Write the pitch in decimal degrees. Round your answer to three decimal places.

Answer: 41.818° Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 67) The height, measured in feet, of a certain staircase is given by the formula h = 18tan θ, where θ is the pitch of the staircase. What is the height of a staircase with a pitch of 42° 55' 37". Round your answer to one decimal place.

Answer: 16.7 feet Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02

109

68) The height, measured in feet, of a certain staircase is given by the formula h = 22tan θ, where θ is the pitch of the staircase. What is the height of a staircase with a pitch of 36° 19' 46".

A) 16.2 feet B) 13.0 feet C) 17.7 feet D) 22.7 feet Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 69) Determine the number of significant digits corresponding to the angle 62.71°.

A) 3 B) 4 C) 5 D) 1 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 70) Determine the number of significant digits corresponding to the length measurement A) 3 B) 4 C) 5 D) 1 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 71) Use the right triangle diagram below and the information given to find the indicated measure.

β = 19°, c = 29 in, find a. Round your answer to two decimal places.

A) 9.44 in B) 27.42 in C) 9.99 in D) 6.19 in Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

110

72) Use the right triangle diagram below and the information given to find the indicated measure.

α = 33°, b = 26 yd, find a. Round your answer to two decimal places.

A) 14.16 yd B) 21.81 yd C) 40.04 yd D) 16.88 yd Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 73) Use the right triangle diagram below and the information given to find the indicated measure.

β = 18°, a = 2 cm, find c. Round your answer to two decimal places.

A) 2.10 cm B) 1.90 cm C) 0.65 cm D) 6.47 cm Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

111

74) Use the right triangle diagram below and the information given to find the indicated measure.

α = 40°, a = 85 ft, find c. Round your answer to two decimal places.

Answer: 132.24 ft Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 75) Use the right triangle diagram below and the information given to find the indicated measure.

β = 43°, b = 19 cm, find a. Round your answer to two decimal places.

Answer: 20.38 cm Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 76) Use the right triangle diagram below and the information given to find the indicated measure.

α = 35°, c = 34 km, find b. Round your answer to two decimal places.

Answer: 27.85 km Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

112

77) Use the right triangle diagram below and the information given to find the indicated measure.

α = 38° 39', b = 25.6 cm, find a. Round your answer to two decimal places.

A) 20.47 cm B) 19.99 cm C) 15.99 cm D) 32.01 cm Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 78) Use the right triangle diagram below and the information given to find the indicated measure.

β = 19° 27', c = 1650 ft, find b. Round your answer to the nearest integer.

Answer: 549 ft Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 79) Use the right triangle diagram below and the information given to find the indicated measure.

a = 10 cm, c = 15 cm, find b. Round your answer to two decimal places.

Answer: 11.18 cm Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

113

80) Use the right triangle diagram below and the information given to find the indicated measure.

a = 70 mi, b = 61 mi, find c. Round your answer to two decimal places.

Answer: 92.85 mi Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 81) Use the right triangle diagram below and the information given to find the indicated measure.

a = 21 m, c = 69 0, find α. Round your answer to two decimal places.

Answer: 17.72° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 82) Use the right triangle diagram below and the information given to find the indicated measure.

a = 48 in, b = 69 in, find a. Round your answer to two decimal places.

Answer: 34.82° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

114

83) Height of a building. The angle of elevation of a stake in the ground to the top of a building is 31°. What is the height of the building if the distance from the stake to the base of the building is Round your answer to one decimal place.

A) 26.0 ft B) 30.3 ft C) 43.2 ft D) 97.9 ft Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 84) Height of a cliff. The angle of elevation of a point on the ground to the top of a cliff is What is the height of the cliff if the distance from the point on the ground to the base of the cliff is Round your answer to one decimal place.

A) 59.5 ft B) 104.7 ft C) 70.9 ft D) 151.7 ft Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

115

85) Altitude of a hot air balloon. The angle of depression θ from a hot air balloon to the recovery vehicle in the valley below is 52°. What is the height of the balloon above the valley floor if the distance from the recovery vehicle to a point on the ground directly below the balloon is Round to the nearest whole number.

Answer: 297 m Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 86) Altitude of an airplane. The angle of depression θ? from an airplane to the control tower at an airport is 75° 38'. What is the height of the airplane above the ground if the distance from the control tower to a point directly below the airplane is 204 m? Round your answer to the nearest whole number.

Answer: 796 m Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02

116

87) Distance across a lake. Steve can determine the distance across a lake without physically measuring it. He marks off a right triangle on dry land and calculates the distance across the lake using a trigonometric function. If Steve determines that one of the acute angles of the right triangle is 79°, and the side adjacent to the angle is 944 ft, what is the distance across the lake? Round your answer to one decimal place.

A) 183.5 ft B) 180.1 ft C) 4947.4 ft D) 961.7 ft Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 88) Distance across a pond. Stefanie can determine the distance across a pond without physically measuring it. She marks off a right triangle on the edge of the pond and calculates the distance across it using a trigonometric function. If Stefanie determines that one of the acute angles of the right triangle is 55°, and the side adjacent to the angle is 303 m, what is the distance across the pond? Round your answer to one decimal place.

Answer: 528.3 m Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

117

89) Height of a redwood tree. Redwood trees are the tallest trees in the world and are found in California. They have a diameter of up to 22 ft and grow to a maximum height of 367 ft. A conservationist wants to determine the height of a redwood tree without having to climb to the top of it. She measures the length of the tree's shadow and determines the angle of elevation from the tip of the shadow to the top of the tree. Using this information and a trigonometric function, the conservationist can calculate the height of the tree. What is the height of a tree if its shadow is 159 ft long and the angle of elevation is 40°? Round your answer to one decimal place.

A) 133.4 ft B) 102.2 ft C) 121.8 ft D) 247.4 ft Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 90) Height of a sequoia tree. Sequoias are among the longest living trees in the world. They can grow to a maximum height of 311 ft and can live up to 3,200 years. A park ranger wants to determine the height of a sequoia tree without having to climb to the top of it. He measures the length of the tree's shadow and determines the angle of elevation from the tip of the shadow to the top of the tree. Using this information and a trigonometric function, the park ranger can calculate the height of the tree. What is the height of a tree if its shadow is 345 ft long and the angle of elevation is 34°? Round your answer to one decimal place.

Answer: 232.7 ft Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

118

91) Glide slope of an airplane. The glide slope of an airplane is the angle between the flight path approaching the runway and the ground. An airliner approaches a runway on a glide slope of approximately 3°. How high is an airplane above the ground if the distance from the runway to a point on the ground directly below the airplane is 3360 feet? Round your answer to the nearest whole foot.

A) 176 ft B) 1680 ft C) 3355 ft D) 528 ft Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 92) Glide slope of an airplane. The glide slope of an airplane is the angle between the flight path approaching the runway and the ground. An airliner approaches a runway on a glide slope of approximately 3°. How long is the flight path of an approaching airliner if its height above the ground is 1069 feet? Round your answer to the nearest whole foot.

Answer: 20,426 ft Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02

119

93) Police spotlight. A police helicopter hovers above a crime scene at night. The pilot shines a light downward that has a field of view θ = 28°. What is the diameter of the circle that is illuminated on the ground if the helicopter is hovering 140 ft above the ground? Round your answer to one decimal place.

A) 34.9 ft B) 74.4 ft C) 69.8 ft D) 148.9 ft Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 94) Stage spotlight. A stage spotlight shines on an actor in a play. The light shines downward with a field of view θ = 38°. What is the diameter of the circle that is illuminated on the stage if the light is placed 140 in. above the stage? Round your answer to one decimal place.

Answer: 96.4 in.

Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02

120

95) Solve right triangle ABC if A = 71° and c = 23.6 yd. Round lengths to one decimal point.

A) a = 7.7 yd, b = 22.3 yd, B = 19° B) a = 22.3 yd, b = 7.7 yd, B = 19° C) a = 22.3 yd, b = 68.5 yd, B = 109° D) a = 68.5 yd, b = 7.7 yd, B = 109° Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 96) Solve right triangle ABC if A = 11° and c = 20 m. Round lengths to one decimal place.

Answer: a = 3.8 m, b = 19.6 m, B = 79° Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 97) Golf If the flagpole that a golfer aims at on a green measures 4 feet from the ground to the top of the flag and a golfer measures a 3.5° angle from top to bottom of the pole, how far (in horizontal distance) is the golfer from the flag? Round to the nearest foot.

Answer: 65 feet Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02

121

98) Midair Refueling Below is an enactment of the mid-air military aircraft refueling scenario.

Assume the elevation angle that the hose makes with the plane being fueled is θ = 45°. If the hose is 150 feet long, what should be the altitude difference a between the two planes? Round to the nearest foot.

Answer: 106 feet Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 99) Midair Refueling Below is an enactment of the mid-air military aircraft refueling scenario.

Assume the elevation angle that the hose makes with the plane being fueled is θ = 46°. If the smallest acceptable altitude difference a between the two planes is 250 feet, how long should the hose be? Round to the nearest foot.

Answer: 348 feet Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 100) Search and Rescue The illustration below shows a search and rescue helicopter with a 24° field of view with a search light. If the search and rescue helicopter is flying at an altitude of 640 feet above sea level, what is the diameter of the circle illuminated on the surface of the water?

A) 136 feet B) 570 feet C) 272 feet D) 285 feet Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 122

101) Search and Rescue The illustration below shows a search and rescue helicopter with a 37° field of view with a search light. If the search and rescue helicopter is flying at an altitude of 265 feet above sea level, what is the diameter of the circle illuminated on the surface of the water?

Answer: 177 feet Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 102) Glide Path of a Commercial Jet Airliner. If a commercial jetliner is at an altitude of 500 feet when it is 7500 feet from the runway, what is the glide slope angle? will the pilot see white lights, red lights, or both? Round to tenth of a degree.

Answer: 3.8° and white lights Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 103) Bearing (Navigation). If a plane takes off bearing N 38° W and flies 15 miles and then makes a right turn (90°) and flies 8 miles further, what bearing will the traffic controller use to locate the plane?

Answer: N 10° W Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02

123

104) Bearing (Navigation). If a plane takes off bearing N 32° W and flies 7 miles and then makes a right turn (90°) and flies 28 miles further, what bearing will the traffic controller use to locate the plane?

A) N 44° W B) N 44° E C) N 76° W D) N 76° E Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 124

Chapter 5 5.1

Trigonometric Functions of Real Numbers

Trigonometric Functions: the Unit Circle Approach

1) Find the exact value of sin

using the unit circle.

A) B) C) D) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 2) Find the exact value of sin

using the unit circle.

A) B) C) D) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01

125

3) Find the exact value of tan

using the unit circle.

A) B) C) D) - 1 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 4) Find the exact value of sin

using the unit circle.

A) B) C) 0 D) 1 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 5) Find the exact value of sec

using the unit circle.

A) B) C) D) 1 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01

126

6) Find the exact value of csc

using the unit circle.

A) B) C) D) -2 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 7) Find the exact value of cos

using the unit circle.

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 8) Find the exact value of csc

using the unit circle. Rationalize the denominator, if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 9) Find the exact value of tan

using the unit circle.

Answer: 1 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 10) Find the exact value of csc

using the unit circle. Rationalize the denominator, if

necessary.

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01

127

11) Find the exact value of tan 150° using the unit circle. Rationalize the denominator, if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 12) Find the exact value of sec 135° using the unit circle.

A) B) C) D) -1 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 13) Find the exact value of cos(90°) using the unit circle.

A) B) C) 0 D) 1 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 14) Find the exact value of sec (300°) using the unit circle. Rationalize the denominator, if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

128

15) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos

.

A) B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 16) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos

.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

129

17) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos

.

A) B) C) D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 18) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos (-225°).

A) B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 19) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos

.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

130

20) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of sin

.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 21) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos (-300°).

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 22) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos (-135°).

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 23) Use the unit circle and the fact that the sine is an odd function and the cosine is an even function to find the exact value of cos

.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

131

24) Use the unit circle to find all the exact values of θ that make cos θ =

A)

,

B)

,

C)

,

D)

,

in the interval

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 25) Use the unit circle to find all the exact values of θ that make sec θ =

A)

,

B)

,

C) D)

, ,

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

132

in the interval

26) Use the unit circle to find all the exact values of θ that make cot θ =

A) B)

, ,

C) D)

in the interval

, ,

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 27) Use the unit circle to find all the exact values of θ that make sin θ = -

Answer:

in the interval

,

Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 28) Use the unit circle to find all the exact values of θ that make csc θ = -

Answer:

in the interval

,

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 29) Use the unit circle to find all the exact values of θ that make cot θ = Answer:

,

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01

133

in the interval

30) Atmospheric Temperature. The average daily temperature in Peoria, Illinois, can be approximated by the equation

where x is the number of days since

December 31 of the previous year (Ex: January 1, x = 1; Mar 1, x = 60), and T is in degrees Fahrenheit. What is the expected temperature on November 25th, assuming it is not a leap year?

A) 36.5° B) 38.6° C) 39.9° D) 32.4° Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 31) Atmospheric Temperature. The average daily temperature in Peoria, Illinois, can be approximated by the equation

where x is the number of days since

December 31 of the previous year (Ex: January 1, x = 1; Mar 1, x = 60), and T is in degrees Fahrenheit. What is the expected temperature on July 4th, assuming it is not a leap year? Round your answer to one decimal place.

Answer: 74.7° Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 32) Body Temperature. The human body temperature normally fluctuates during the day. If a person's body temperature can be modeled by the formula

where x is the

number of hours since midnight and T is in degrees Fahrenheit, the what is a person's temperature at 3:00 pm?

A) 97.86° B) 98.88° C) 98.28° D) 97.38° Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 33) Body Temperature. The human body temperature normally fluctuates during the day. If a person's body temperature can be modeled by the formula

where x is the

number of hours since midnight and T is in degrees Fahrenheit, the what is a person's temperature at 5:00 am?

Answer: 99.05° Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 134

34) Body Temperature. The human body temperature normally fluctuates during the day. If a person's body temperature can be modeled by the formula

where x is the

number of hours since midnight and T is in degrees Fahrenheit, the what is a person's temperature at 7:00 pm?

A) 99.26° B) 98.94° C) 98.63° D) 99.30° Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 135

Chapter 5 5.2

Trigonometric Functions of Real Numbers

Graphs of Sine and Cosine Functions

1) State the amplitude and period of the sinusoidal function. y = -5 cos 15 x Amplitude is ________ Period is ________ Answer: Amplitude is 5 Period is 2π/15 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 2) State the amplitude and period of the sinusoidal function. y=-

sin 10 x

Amplitude is ________ Period is ________ Answer: Amplitude is Period is Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 3) State the amplitude and period of the sinusoidal function. y = 6cos

x

Amplitude is ________ Period is ________ Answer: Amplitude is 6 Period is 14 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02

136

4) State the amplitude and period of the sinusoidal function. y=

sin

x

Amplitude is ________ Period is ________ Answer:

Amplitude =

Period =

π

Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 5) State the amplitude and period of the sinusoidal function. y = 6 sin

x

Amplitude is ________ Period is ________ Answer: Amplitude is 6 Period is 6 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 6) Graph the function y = -5 sin x over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

137

7) Graph the function y = sin 8x over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 8) Graph the function y = -cos

over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 9) Graph the function y =

over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 138

10) Find an equation of the graph.

A) y = 2.5 cos B) y = -2.5 cos C) y = 2.5 sin D) y = 2.5 sin Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 11) Graph the function y = -2.5 sin

over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

139

12) Graph the function y = 2 cos

over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 13) Graph the function y = -4 sin

over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 14) Graph the function y = -4.5 cos (2πx) over one period.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 140

15) Graph the function y = -cos

over the interval [-8π?, 8π?].

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 16) Graph the function y = -6 cos

over the interval [-16, 16].

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 17) Graph the function y = -sin(5π) over the interval [-0.8, 0.8].

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 141

18) Graph the function y = -cos(7x) over the interval [-4π/7, 4π/7] where 2π/7 is the period of the function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 19) Find the cos equation of the graph.

Answer:

y = 1.5 cos

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

142

20) Find the sin equation of the graph.

A) y = 2 sin B) y = -2 sin C) y = 2 cos D) y = 2 cos Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 21) Find the cos equation of the graph.

Answer:

y = 3 cos

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

143

22) Find an equation of the graph.

A) y = sin B) y = -sin C) y = cos D) y = cos Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 23) Find the cos equation for the graph.

Answer:

y = -3 cos

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

144

24) Find an equation for the graph.

A) y = -2.5 cos B) y = 2.5 cos C) y = 2.5 sin D) y = 2.5 sin Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 25) Find an equation of the graph.

Answer:

y = -sin

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

145

26) Find an equation of the graph.

A) y = -1.5 sin B) y = 1.5 sin C) y = -1.5 cos D) y = -1.5 cos Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 27) Find an equation for the graph.

Answer: y = -3.5 cos (2πx) Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

146

28) Find an equation for the graph.

A) y = 4 cos (2πx) B) y = 4 sin (2πx) C) y = -4 cos (2πx) D) y = 4 sin Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 29) What is the frequency for the oscillation modeled by y = 8.5 cos

Frequency is ________ cycles per second Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 30) What is the frequency for the oscillation modeled by y = 6 cos Frequency is ________ cycles per second A) Frequency is

cycles per second

B) Frequency is 18π cycles per second C) Frequency is

cycles per second

D) Frequency is 9π cycles per second Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02

147

31) If a sound wave is represented by y = 0.005 cos

, what is amplitude and frequency?

Amplitude is ________ cm Frequency is ________ hertz Answer: Amplitude is 0.005 cm Frequency is 523 hertz Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 32) If a sound wave is represented by y = 0.009 cos 750πt, what is the frequency?

A) Frequency is 375 hertz B) Frequency is 750 hertz C) Frequency is 375π hertz D) Frequency is 750π hertz Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 33) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the plane is flying at Mach 2.4? Round to the nearest meter.

Speed of the plane is ________ m/sec.

Answer: 792 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 34) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the plane is flying at Mach 2.8?

Speed of the plane is ________ m/sec.

A) Speed of the plane is 924 m/sec.

B) Speed of the plane is 118 m/sec.

C) Speed of the plane is 0.008 m/sec.

D) Speed of the plane is 92.4 m/sec.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 148

35) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the mach number if the plane is flying at 726 m/sec.?

Answer: 2.2 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 36) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the Mach number if the plane is flying at 495 m/sec.? mach number is ________.

A) Mach number is 1.5 B) Mach number is 0.15 C) Mach number is 15 D) Mach number is0.67 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 37) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the cone angle is 40°. Round to the nearest whole number.

Speed of the plane is ________ m/sec.

Answer: Speed of the plane is 965 m/sec.

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

149

38) When an airplane flies faster than the speed of sound, the sound waves that are formed take on a cone shape, and where the cone hits the ground, a sonic boom is heard. If θ is the angle of the vertex of the cone, then sin

=

=

where V is the speed of the plane and M is the

Mach number, then what is the speed of the plane if the cone angle is 45°. Round to the nearest whole number.

Speed of the plane is ________ m/sec.

A) Speed of the plane is 862 m/sec.

B) Speed of the plane is 467 m/sec.

C) Speed of the plane is 126 m/sec.

D) Speed of the plane is 281 m/sec.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 39) A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple harmonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

where A is the amplitude, t is the time in seconds, m is

the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if

Amplitude: ________ cm.

Mass: ________ g.

Answer: Amplitude: 11 cm.; mass: 47.61 g.

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

150

?

40) A weight hanging on a spring will oscillate up and down about its equilibrium position after it's pulled down and released. This is an example of simple hormonic motion. This motion would continue forever if there wasn't any friction or air resistance. Simple harmonic motion can be described with the function

where A is the amplitude, t is the time in seconds, m is

the mass and k is a constant particular to that spring. If a spring is measured in centimeters and the weight in grams, then what are the amplitude and mass if y = 5.5cos (1.2t )?

Amplitude: ________ cm.

Mass: ________ g.

A) Amplitude: 5.5 cm.; mass:

g.

B) Amplitude: 5.5 cm.; mass:

g.

C) Amplitude: 30.25 cm.; mass:

g.

D) Amplitude: 30.25 cm.; mass: 1.44 g.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 41) State the amplitude, period, and phase shift of the function. y = 5sin(πx + 1) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 5 Period = 2 Phase Shift = Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02

151

42) State the amplitude, period, and phase shift of the function. y = 3sin(πx - 6) A) Amplitude = 3; period = 2π; phase shift = B) Amplitude = 3; period = 2; phase shift = C) Amplitude = 3; period = 2π; phase shift = D) Amplitude = 3; period = 2, phase shift = 6 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 43) State the amplitude, period, and phase shift of the function. y = 5cos(10x + π) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 5 Period = Phase Shift = Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02

152

44) State the amplitude, period, and phase shift of the function. y = 10sin(6 + π) A) Amplitude = 10; period =

; phase shift = -

B) Amplitude = -10; period = 3; phase shift = C) Amplitude = 10; period =

; phase shift = -

D) Amplitude = -10; period =

; phase shift =

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 45) State the amplitude, period, and phase shift of the function. y = 10cos(20 + π) Answer: Amplitude = 10 period = phase shift = Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 46) State the amplitude, period, and phase shift of the function. y = 4cos(9x - π) A) Amplitude = 4; period =

; phase shift =

B) Amplitude = 4; period = 9; phase shift = C) Amplitude = -4; period =

; phase shift = -

D) Amplitude = 4 period =

; phase shift =

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

153

47) State the amplitude, period, and phase shift of the function. y = 9cos(14x - 13) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 9 Period = Phase Shift = Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 48) State the amplitude, period, and phase shift of the function. y = -9sin(18x - 17) A) Amplitude = 9: period =

; phase shift =

B) Amplitude = 9: period =

; phase shift =

π

C) Amplitude = 9: period = 18; phase shift = D) Amplitude = 9: period =

; phase shift =

π

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

154

49) State the amplitude, period, and phase shift of the function. y = 3cos(17x - 18) Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 3 period = phase shift = Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 50) State the amplitude, period, and phase shift of the function. y = 7cos(9x - 10) π

A) Amplitude = 7; period =

; phase shift =

B) Amplitude = 7; period =

; phase shift = -

C) Amplitude = 7; period =

; phase shift =

D) Amplitude = -7; period = 9; phase shift = Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

155

51) State the amplitude, period, and phase shift of the function. y = 3sin

Amplitude = ________ Period = ________ Phase Shift = ________ Answer: Amplitude = 3 period = 16 phase shift = -6 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 52) State the amplitude, period, and phase shift of the function. y = 5cos A) Amplitude = 5; period = 10; phase shift = -2π π

B) Amplitude = 5; period = 5; phase shift =

C) Amplitude = -5; period = 10; phase shift = 2 D) Amplitude = 5; period = 10; phase shift = -2 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 53) Sketch the graph of the function y =

+

cos

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 156

over [-4π, 4π].

54) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

+

cos

B) y =

-

cos

C) y =

+

cos

D) y =

+

sin

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 55) Sketch the graph of the function

-

over [-4π, 4π].

cos

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

157

56) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

+

cos

B) y =

-

cos

C) y =

-

cos

D) y =

-

sin

Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 57) Sketch the graph of the function

+

over [-4π, 4π].

sin

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

158

58) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

-

cos

B) y =

+

cos

C) y =

+

sin

D) y =

+

cos

Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 59) Sketch the graph of the function y =

-

sin

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

159

over [-4π, 4π].

60) Match the graph of the cosine function to the equation over [-4π, 4π].

A) y =

-

B) y = C) y = D) y = -

cos -

-

cos cos

-

cos

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 61) Sketch the graph of the function y =

+

sin(2x - π)

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

160

62) Sketch the graph of the function y = 3 - 4sin(5x) over one period starting at

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

161

63) Match the graph of the sine function to the equation.

A)

-

sin(2x + π)

B)

+

sin(2x - π)

C)

-

cos(2x + π)

D)

+

cos(2x - π)

Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 64) Sketch the graph of the function y =

-

sin(2x - π)

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

162

65) Match the graph of the sine function to the equation.

A)

-

sin(2x - π)

B)

+

sin(2x + π)

C)

+

cos(2x - π)

D)

-

sin(2x + π)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 66) Sketch the graph of the function y =

+

sin(2x + π) over

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

163

.

67) Match the graph of the cosine function to the equation.

A)

+

cos(2x - π)

B)

-

sin(2x + π)

C)

+

cos(2x + π)

D)

+

cos(2x - π)

Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 68) Sketch the graph of the function y =

-

cos(2x + π)

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02

164

69) Match the graph of the sine function to the equation.

A) y =

-

sin(2x + π)

B) y =

+

sin(2x - π)

C) y =

-

cos(2x + π)

D) y =

-

sin(2x - π)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 70) The current, in amperes (amps), flowing through an alternating current (AC) circuit at time t is I = 220sin

t>0

What is the maximum current? What is the minimum current? What is the period? What is the phase shift?

Maximum current = ________ Amps Minimum current = ________ Amps Period = ________ seconds Phase shift = ________ seconds Answer: Maximum current = 220 Amps Minimum current = - 220 Amps Period =

seconds

Phase shift = 0.0100 seconds Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

165

71) The current, in amperes (amps), flowing through an alternating current (AC) circuit at time t is I = 220sin

t>0

What is the maximum current? What is the minimum current? What is the period? What is the phase shift?

A) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

π seconds; phase

shift = 100 seconds B) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

seconds; phase

shift = 0.0100 seconds C) Maximum current = 220 Amps; minimum current = - 220 Amps; period =

seconds; phase

shift = 100 seconds D) Maximum current = 220 Amps; no minimum current; period =

seconds; phase shift =

0.0100 seconds Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 72) If a roller coaster at an amusement park is built using the sine curve determined by where x is the distance from the beginning of the roller coaster in feet, then how high does the roller coaster go, and what distance is the roller coaster if it goes through four complete sine cycles?

Height is ________ ft Distance is ________ ft Answer: Height is 110 ft Distance is 5600 ft Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

166

73) If a roller coaster at an amusement park is built using the sine curve determined by where x is the distance from the beginning of the roller coaster in feet, then how high does the roller coaster go, and what distance is the roller coaster if it goes through five complete sine cycles?

A) Height is 85 ft Distance is 4000 ft B) Height is 4000 ft Distance is 85 ft C) Height is 1800 ft Distance is 2000 ft D) Height is 85 ft Distance is 4000π ft Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 74) The number of deer on an island varies over time because of the number of deer and amount of available food on the island. If the number of deer is determined by

where

t is in years, then what are the highest and lowest numbers of deer on the island, and how long is the cycle (how long between two different years when the number is the highest)?

Highest number of deer is ________ Lowest number of deer is ________ One cycle is ________ Answer: Highest number of deer is 3150 Lowest number of deer is 2250 One cycle is 4 years Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

167

75) The number of deer on an island varies over time because of the number of deer and amount of available food on the island. If the number of deer is determined by

where

t is in years, then what are the highest and lowest numbers of deer on the island, and how long is the cycle (how long between two different years when the number is the highest)?

A) Highest number of deer is 1500; lowest number of deer is 1000; one cycle is 8 years B) Highest number of deer is 750; lowest number of deer is 250; one cycle is 8 years C) Highest number of deer is 1500; lowest number of deer is 1000; one cycle is 4 years D) Highest number of deer is 1500; lowest number of deer is 250; one cycle is 4 years Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 168

Chapter 6 6.1

Analytic Trigonometry

Verifying Trigonometric Identities

1) Use the triangle to write cot θ, if A = 11, B = 60, and C = 61.

A) B) C) D) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01

169

2) Use the triangle to write tan θ, if A = 9, B = 40, and C = 41.

A) B) C) D) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 3) Use the triangle to write sin θ, if A = 3, B = 4, and C = 5.

A) B) C) D) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01

170

4) Use the triangle to write cos θ, if A = 24, B = 7, and C = 25.

A) B) C) D) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 5) Use the triangle to write csc θ, if A = 24, B = 7, and C = 25.

A) B) C) D) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01

171

6) Use the triangle to write sec θ, if A = 16, B = 30, and C = 34.

A) B) C) D) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 7) Use the triangle to write csc θ, if A = 15, B = 8, and C = 17.

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01

172

8) Use the triangle to find the exact sin θ. Reduce the fraction if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 9) Use the triangle to find the exact cos θ. Rationalize the denominator and reduce the fraction if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 10) Use the triangle with C =

to find the exact tan θ. Reduce the fraction if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

173

11) Use the triangle to find the exact sec θ. Rationalize the denominator and reduce the fraction if necessary.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 12) Use the cofunction identity to fill in the blank: tan 6° = cot ________°.

A) 16° B) 174° C) 94° D) 84° Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 13) Use the cofunction identity to fill in the blank: csc E° = sec ________°.

A) (180 + E)° B) (180 - E)° C) (90 - E)° D) (90 + E)° Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 14) Use the cofunction identity to fill in the blank: sec 41° = csc ________°.

Answer: 49 Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 15) Use the cofunction identity to fill in the blank: sin F° = cos ________°.

Answer: (90 - F) Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01

174

16) Write cot(40° + A) in terms of its cofunction.

A) tan(85 + A)° B) cot(5 + A)° C) tan(50 - A)° D) csc(130 - A)° Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 17) Write cos(48° - B) in terms of its cofunction.

Answer: sin(42 + B)° Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 18) Write cot(A + B) in terms of its cofunction.

Answer: tan(90 - A - B)° Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 19) Write sin(x - y) in terms of its cofunction.

Answer: cos(90 - x + y)° Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 20) The Valley of the Kings near Luxor, Egypt is home to ancient pyramids that served as the final resting place for New Kingdom pharoahs. The pyramids have a square base and four triangular-shaped faces that meet at a point at the top of the pyramid. If θ is the angle between the base and the face of a pyramid, then the face becomes the hypotenuse of a right triangle. What is the length of the face of a pyramid if sin θ = 18.9/240.7, cos θ = 24/240.7, and the height is 132.3 feet? Round your answer to the nearest whole foot.

A) 153 feet B) 1685 feet C) 311 feet D) 196 feet Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 01

175

21) If θ is the angle between the base and the face of a pyramid, then the face becomes the hypotenuse of a right triangle. What is the length of the face of a pyramid if sin θ = 8/17, and the sum of the base and height is 69 feet?

A) 85 feet B) 68 feet C) 34 feet D) 51 feet Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 22) Pyramids in the Valley of the Kings near Luxor, Egypt have a square base and four triangular-shaped faces that meet at a point at the top of the pyramid. If θ is the angle between the base and the face of a pyramid, then the face becomes the hypotenuse of a right triangle. What is the length of the face of a pyramid if sin θ = 5.1/8.7, cos θ = 7/8.7, and the base is 35 feet? Round your answer to the nearest whole foot.

Answer: 44 feet Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 01 23) A rope is tied from the top of a tent to the ground, forming an angle θ with the ground. What is the length of the rope if sin θ = 25/43.8 cos θ = 36/43.8 and the sum of the base and height is 183 inches? Round your answer to the nearest inch.

Answer: 131 inches Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

176

24) Raja and Ariel are planning to hike to the top of a hill. If θ is the angle formed by the hill and the ground such that csc θ =

, find cos θ.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 25) Use fundamental identities to simplify sin (-x) csc (x).

A) sec2 x B) csc2 x C) 1 D) -1 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 26) Use fundamental identities to simplify cos (-x) csc (-x).

A) sec2 x B) csc2 x C) -cot x D) cot x Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 01 27) Use fundamental identities to simplify cos (-x) sec (-x) A) sin x x B) C) cos x x D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 28) Use fundamental identities to simplify

.

A) cos (x) B) sin (-x) C) cos (-x) D) sin (x) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 177

(x).

29) Use fundamental identities to simplify

.

A) -1 + csc x B) 1 + cot x C) 1 - cot x D) 1 - csc x Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 30) Use fundamental identities to simplify csc x (1 Answer: sin x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

x).

31) Use fundamental identities to simplify cos x ∙

.

Answer: 1 Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 32) Use fundamental identities to simplify

.

Answer: x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 33) Use fundamental identities to simplify

.

Answer: x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

178

34) Verify the trigonometric identity csc (x) - cos (-x) cot x = sin x algebraically.

Answer: csc x - cos (-x) cot x = sin x csc x - cos x ∙ -

= sin x = sin x

= sin x = sin x sin x = sin x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 35) Verify the trigonometric identity (sec (x) - tan x)(csc (x) +1) = cot x algebraically.

Answer: (sec (x) - tan x)(csc (x) +1) = cot x = cot x = cot x = cot x = cot x = cot x = cot x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

179

36) Verify the trigonometric identity Answer:

= sec x + tan x algebraically.

= sec x + tan x = sec x + tan x = sec x + tan x = sec x + tan x

+ +

= sec x + tan x = sec x + tan x

Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 37) Verify the trigonometric identity Answer:

+

+

= 1 algebraically.

=1

sin2 x + cos2 x = 1 sin2 x + cos2 x = 1 Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 38) Verify the trigonometric identity Answer:

- csc x - sec x algebraically.

- csc x - sec x

sec x + csc x - csc x = sec x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

180

39) Verify the trigonometric identity Answer:

-

-

= 2cot x algebraically.

= 2cot x

cot x + csc x -

= 2cot x

cot x + csc x +

= 2cot x

cot x + csc x + cot x - csc x = 2cot x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 40) Verify the trigonometric identity Answer: 1+

-1+

+

-

= csc x sec x algebraically.

= csc x sec x

= csc x sec x

= csc x sec x = csc x sec x = csc x sec x

Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 01 41) Verify the trigonometric identity

Answer:

= cos x algebraically.

= cos x = cos x = cos x

cos x = cos x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 181

42) Determine if = 5 is conditional or is an identity.

A) conditional B) identity Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 43) Determine if 4 A) conditional B) identity Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 44) Determine if

= sec x + csc x is conditional or is an identity.

= cos θ - sin θ is conditional or is an identity.

Answer: Identity Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01 45) Determine if sin θ csc θ θ= Answer: Identity Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 01

θ is conditional or is an identity.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 182

Chapter 6 6.2

Analytic Trigonometry

Sum and Difference Identities

1) Find the exact value of cos

.

A) B) C) D) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 2) Find the exact value of cot

.

A) B) C) D) 1 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 3) Find the exact value of cos

.

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 4) Find the exact value of cot

.

183

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 5) Find the exact value of cos(240°).

A) B) C) D) -1 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 6) Find the exact value of cot(240°).

Answer: Diff: 1 Var: 1 Chapter/Section: Ch 06, Sec 02 7) Write cos 12x cos 8x + sin 12x sin 8x as a single trigonometric function.

A) sin 4x B) cos 4x C) sin 20x D) cos 20x Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 8) Write cos 8]x cos 3x - sin 8x sin 3x as a single trigonometric function.

A) sin 5x B) cos 5x C) sin 11x D) cos 11x Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

184

9) Write cos 7x cos 5x + sin 7x sin 5x as a single trigonometric function.

Answer: cos 2x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 10) Write cos 6x cos 5x - sin 6x sin 5x as a single trigonometric function.

Answer: cos 11x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 11) Write sin 7x cos 2x + cos 7x sin 2x as a single trigonometric function.

A) sin 5x B) cos 5x C) sin 9x D) cos 9x Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 12) Write sin 6x cos 3x - cos 6x sin 3x as a single trigonometric function.

A) sin 3x B) cos 3x C) sin 9x D) cos 9x Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 13) Write sin 10x cos 2x + cos 10x sin 2x as a single trigonometric function.

Answer: sin 12x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 14) Write sin 8x cos 4x - cos 8x sin 4x as a single trigonometric function.

Answer: sin 4x Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 15) Choose the trigonometric function that is equivalent to -5 + .

A) -3 + 2sin(A + B) B) -7 - cos(A - B) C) -3 + 2cos(A - B) D) -3 + 2cos(A + B) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 185

+

16) Write -8 + + numerical constants.

Answer: -6 - 2cos(A - B) Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 17) Write

as a single trigonometric function and

as a single trigonometric function.

A) tan(9°) B) cot(9°) C) tan(83°) D) cot(83°) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 18) Write

as a single trigonometric function.

Answer: tan(63°) Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 19) Find the exact value of cos(α - β) if cos α = in II and the terminal side of β lies in IV. A) B) C) D) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02

186

and cos β =

if the terminal side of α lies

20) Find the exact value of cos(α + β) if cos α = -

and cos β =

if the terminal side of α lies in

quadrant III and the terminal side of β lies in quadrant I. Answer: Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 21) Find the exact value of sin(α - β) if sin α =

and cos β = -

if the terminal side of α lies in

quadrant I and the terminal side of β lies in quadrant III. A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 22) Find the exact value of sin(α + β) if sin α =

and cos β =

quadrant II and the terminal side of β lies in quadrant IV. Answer: Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

187

if the terminal side of α lies in

23) Find the exact value of tan(α - β) if sin α = -

and cos β =

if the terminal side of α lies

in quadrant IV and the terminal side of β lies in quadrant I. A) B) C) D) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 24) Find the exact value of tan (α + β) if sin α = -

and cos β = -

if the terminal side of α lies

in quadrant IV and the terminal side of β lies in quadrant III. Answer: Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 25) Find the exact value of sin (α + β) if sin α = -

and cos β =

in quadrant III and the terminal side of β lies in quadrant IV. A) B) C) D) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02

188

if the terminal side of α lies

26) Find the exact value of tan(α + β) if sin α =

and cos β =

if the terminal side of α lies in

quadrant II and the terminal side of β lies in quadrant IV. Answer: Diff: 3 Var: 1 Chapter/Section: Ch 06, Sec 02 x = cos x is conditional or an identity.

27) Determine if x+ A) conditional B) identity Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 28) Determine if

+

= 2tan θ is conditional or an identity.

A) conditional B) identity Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 29) Determine if 6 θ+6 θ = 6 is conditional or an identity.

Answer: identity Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02 30) Determine if 5cos θ + 5sin θ = 5 Answer: conditional Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

is conditional or an identity.

31) Functions. Consider a 22-foot ladder placed against a wall such that the distance from the top of the ladder to the floor is h feet and the angle between the floor and the ladder is θ?. a. Write the height, h, as a function of angle θ. b. If the ladder is pushed toward the wall, increasing the angle θ by 6°, write a new function for the height as the height as a function of θ + 6° and then express in terms of sines and cosines of θ + 6°.

Answer: a) h = 22sin(θ + 6°) b) h = 22sin θ cos 6° + 22cos θ sin 6° Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

189

32) Graph y = cos

sin x + sin

cos x by first rewriting as a sine or cosine of a difference or

sum.

Answer: sin

Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

190

33) Graph y = cos

cos x + sin

sin x by first rewriting as a sine or cosine of a difference or

sum.

Answer: cos

Diff: 2 Var: 1 Chapter/Section: Ch 06, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 191

Chapter 7 7.1

Vectors, the Complex Plane, and Polar Coordinates

Vectors

1) Find the magnitude of the vector AB. A = (11, 20) and B = (71, 31) Answer: 61 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 2) Find the magnitude of the vector AB. A = (3, 48) and B = (4, 52) Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 3) Find the magnitude of the vector AB. A = (29, 27) and B = (36, 28) Answer: 5 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 4) Find the magnitude and direction angle of the vector u. Give the angle in degrees rounded to one decimal place. u= Answer: 5; θ = 53.1 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 5) Find the magnitude and direction angle of the vector u. Give the angle in degrees rounded to one decimal place. u= Answer: ; θ = 18.4 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

192

6) Find the magnitude and direction angle of the vector u. Give the angle in degrees rounded to one decimal place. u= Answer: 2 ; θ = 26.6 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 7) Perform the indicated vector operation given u = 2u - 4v Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

8) Perform the indicated vector operation given u = 6(u - v) Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

9) Perform the indicated vector operation given u = -9u + 10v + 11w Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

10) Find a unit vector in the direction of the vector v. v= Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 11) Find a unit vector in the direction angle of the vector v. v= Answer: Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 01

193

.

.

.

12) Express the vector in terms of unit vectors i and j.

Answer: -4i + 12j Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 13) Perform the indicated vector operation.

(-9i - 27j ) + (2i - 15j) Answer: -7i - 42j Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 14) A force of 1110 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of 8.0°. What is the weight of the boat and its trailer? Round to the nearest pound.

Answer: 7976 pounds Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 15) A ship's caption sets a course due north at 19 mph. The water is moving at 6 mph due east.

What is the actual velocity of the ship, and in what direction is it traveling? Give the angle in degrees rounded to one decimal place.

Answer: 19.9 mph; 17.5° east due north Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 16) A plane has a heading of 30° and an airspeed of 305 mph. The wind is blowing at 80 mph from 120°. What are its actual heading and airspeed? Round to one decimal place.

Answer: 44.7°, 315.3 mph Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 17) A box weighing 205 pounds is held in place on an inclined plane that has an angle of 27°.

What force is required to hold it in place? Round to the nearest pound.

Answer: 93 pounds Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 18) A baseball player throws a ball with an initial velocity of 104 feet per second at an angle 26 degrees with the horizontal. What are the vertical and horizontal components of the velocity?

Round to one decimal place.

Answer: 45.6 ft/sec; 93.5 ft/sec Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

194

19) A force with a magnitude of 1426 pounds and another with a magnitude of 523 pounds are acting on an object. The two forces have an angle of 122 degrees between them. What is the direction of the resultant force? Round to one decimal place.

Answer: 21.1 degrees Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 20) A force with a magnitude of 422 pounds and another with a magnitude of 533 pounds are acting on an object. The two forces have an angle of 137 degrees between them. What is the magnitude of the resultant force? Round to the nearest pound.

Answer: 365 pounds Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 21) A force of 892 pounds is acting on an object at an angle of 59 degrees from the horizontal.

Another force of 709 pounds is acting at an angle 50 degrees from the horizontal. What is the angle of the resultant force with respect to the force 709 pounds? Round to one decimal place.

Answer: -38.4 degrees Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 22) A force of 1091 pounds is acting on an object at an angle of 76 degrees from the horizontal.

Another force of 510 pounds is acting at an angle 64 degrees from the horizontal. What is the magnitude of the resultant force? Round to the nearest pound.

Answer: 1593 pounds Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 23) Find the magnitude of the vector AB. A = (13, -12) and B = (25, -7) A) 57 B) 42 C) 17 D) 13 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

195

24) Find the magnitude of the vector AB. A = (25, 53) and B = (26, 57) A) B) 17 C) D) 5 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 25) Find the magnitude of the vector AB. A = (17, 49) and B = (23, 51) A) 40 B) 2 C) 11,600 D) 108 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 26) Find the magnitude and direction angle of the vector u. u= A) 4; θ = 77.3 B) 4; θ = 12.7 C) 1681; θ = 77.3 D) 1681; θ = 12.7 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 27) Find the magnitude and direction angle of the vector u. u= A) ; θ = 258.7 B) 26; θ = 191.3 C) ; θ = 191.3 D) 26; θ = 258.7 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

196

28) Find the magnitude and direction angle of the vector u. u= A) 3 ; θ = 26.6 B) 45.0; θ = 63.4 C) 3 ; θ = 24.1 D) 45.0; θ = 24.1 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 29) Perform the indicated vector operation given u = 9u - 6v A) B) C) D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

30) Perform the indicated vector operation given u = 2(u + v) A) B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

31) Perform the indicated vector operation given u = 3u + 7v + 6u A) B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

197

and v =

.

.

.

32) Find a unit vector in the direction of the vector v. v= A) B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 33) Find a unit vector in the direction angle of the vector v. v= A) B) C) D) Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 01 34) Express the vector in terms of unit vectors i and j.

A) 13i - 9j B) -9i + 13j C) 16 D) -13i + 9j Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01

198

35) Perform the indicated vector operation.

(16i - 16j) + (8i + 6j) A) 24i - 10j B) 8i - 22j C) 8i - 10j D) 24i - 22j Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 36) A force of 538 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of 7.5°. What is the weight of the boat and its trailer?

A) 4087 pounds B) 543 pounds C) 4122 pounds D) no solution Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 37) A ship's caption sets a course due north at 21 mph. The water is moving at 4 mph due west.

What is the actual velocity of the ship, and in what direction is it traveling?

A) 21.4 mph; 10.8° west due north B) 457 mph; 79.2° west due north C) 25.0 mph; 11.0° west due north D) no solution Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 38) A plane has a heading of 48° and an airspeed of 540 mph. The wind is blowing at 60 mph from 138°. What are its actual heading and airspeed?

A) 54.3°, 543.3 mph B) 6.3°, 295,200.0ȝ mph C) 131.7°, 600.0 mph D) no solution Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

199

39) A box weighing 210 pounds is held in place on an inclined plane that has an angle of 32°.

What force is required to hold it in place?

A) 116 pounds B) 111 pounds C) 178 pounds D) no solution Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 40) A baseball player throws a ball with an initial velocity of 81 feet per second at an angle 61 degrees with the horizontal. What are the vertical and horizontal components of the velocity?

A) vertical component = 70.8 ft/sec; horizontal component = 39.3 ft/sec B) vertical component = 39.3 ft/sec; horizontal component = 70.8 ft/sec C) vertical component = -78.3 ft/sec; horizontal component = -20.9 ft/sec D) no solution Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 41) A force with a magnitude of 1497 pounds and another with a magnitude of 580 pounds are acting on an object. The two forces have an angle of 158 degrees between them. What is the direction of the resultant force with respect to the force 580 pounds?

A) 34.8 degrees B) 12.8 degrees C) 0.3 degrees D) no solution Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 42) A force with a magnitude of 532 pounds and another with a magnitude of 222 pounds are acting on an object. The two forces have an angle of 151 degrees between them. What is the magnitude of the resultant force?

A) 734 pounds B) 125,716 pounds C) 355 pounds D) 299 pounds Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

200

43) A force of 728 pounds is acting on an object at an angle of 17 degrees from the horizontal.

Another force of 344 pounds is acting at an angle 3 degrees from the horizontal. What is the angle of the resultant force? Round to one decimal place.

A) 9.5 degrees B) 11.5 degrees C) 2.1 degrees D) no solution Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 44) A force of 565 pounds is acting on an object at an angle of 32 degrees from the horizontal.

Another force of 689 pounds is acting at an angle -16 degrees from the horizontal. What is the magnitude of the resultant force? Round to the nearest pound.

A) 1147 pounds B) 1,314,911 pounds C) 522 pounds D) 532 pounds Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 45) Perform the indicated vector operation given u = u+v Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 46) Perform the indicated vector operation given u = -4u Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01

and v =

.

.

47) Express the vector in terms of unit vectors i and j.

Answer: 19.1i - 6.7j Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 201

Chapter 7 7.2

Vectors, the Complex Plane, and Polar Coordinates

The Dot Product

1) Find the dot product. ∙ Answer: -581 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 2) Find the dot product. ∙ Answer: 126.25 Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 3) Find the dot product. ∙ Answer: 545 Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 02 4) Find the dot product. ∙ Answer: 1023xy Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 5) Find the angle (round to the nearest degree) between the vectors. and Answer: 166° Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 6) Find the angle (round to the nearest degree) between the vectors. and Answer: 39° Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 202

7) Find the angle (round to the nearest degree) between the vectors. ∙ Answer: 126° Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 8) Determine if the vectors are orthogonal. and Answer: not orthogonal Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 9) Determine if the vectors are orthogonal. and Answer: not orthogonal Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 10) Determine if the vectors are orthogonal. and Answer: not orthogonal Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 02 11) Determine if the vectors are orthogonal. and Answer: not orthogonal Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 02 12) Determine if the vectors are orthogonal. and Answer: not orthogonal Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 02 13) How much work does it take to lift 203 pounds vertically 2 feet?

203

Answer: 406 ft lbs Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 14) How much work is done by a crane to lift a 2.6 ton car to a level of 18 feet?

Answer: 93,600 ft ton Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 15) To slide a crate across the floor, a force of 945 pounds at a 40° is needed. How much work is done if the crate is dragged 31 feet. Round to the nearest integer.

Answer: 22,441 ft lbs.

Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 16) A sliding door is closed by pulling a cord with a constant force of 46 pounds at a constant angle of 19°. The door is moved 1 feet to close it. How much work is done? Round to one decimal place.

Answer: 43.5 ft lbs.

Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 17) A car that weighs 20,000 lbs is parked on a hill in San Francisco with a slant of 35° from the horizontal. How much force will keep it from rolling down the hill? Round to the nearest integer.

Answer: 11,472 ft lbs.

Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 18) A car that weighs 8500 lbs. is parked on a hill in San Francisco with a slant of 36° from the horizontal. A tow truck has to remove the truck from its parking spot and move it 150 feet up the hill. How much work is required? Round to the nearest integer.

Answer: 1,031,497 ft lbs.

Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 19) Find the dot product. ∙ A) -442 B) 782 C) -1581 D) -20 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 204

20) Find the dot product. ∙ A) 66 B) 57 C) 117 D) -22 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 21) Find the dot product. ∙ A) -3155 B) -11,773 C) -607 D) 105 Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 07, Sec 02 22) Find the dot product. ∙ A) 1334xy B) -118xy C) 1254 + 352 D) 1254 + 1334xy + 352 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 23) Find the angle between the vectors. and A) 18° B) 72° C) 2052° D) 342° Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02

205

24) Find the angle between the vectors. and A) 75° B) 56° C) 34° D) 326° Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 25) Find the angle between the vectors. and A) 153° B) -63° C) -1547° D) 207° Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 26) Determine if the vectors are orthogonal. and A) orthogonal B) not orthogonal C) Unable to determine Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 27) Determine if the vectors are orthogonal. and A) not orthogonal B) orthogonal C) Unable to determine Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02

206

28) Determine if the vectors are orthogonal. and A) orthogonal B) not orthogonal C) Unable to determine Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 29) How much work does it take to lift 149 pounds vertically 1.5 feet?

A) 2235 ft lbs B) 22.4 ft lbs.

C) 223.5 ft lbs.

D) 99.3 ft lbs.

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 30) How much work is done by a crane to lift a 1.5 ton car to a level of 11 feet?

A) 33,000 ft ton B) 17 ft ton C) 3300 ft ton D) 330,000 ft ton Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 31) To slide a crate across the floor, a force of 94 pounds at a 19° is needed. How much work is done if the crate is dragged 63 feet?

A) 2 ft lbs.

B) 1928 ft lbs.

C) 2039 ft lbs.

D) 5599 ft lbs.

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 32) A sliding door is closed by pulling a cord with a constant force of 49 pounds at a constant angle of 40°. The door is moved 1 feet to close it. How much work is done?

A) 37.5 ft lbs.

B) 31.5 ft lbs.

C) 41.1 ft lbs.

D) 64.0 ft lbs.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 207

33) A car that weighs 6500 lbs is parked on a hill in San Francisco with a slant of 31° from the horizontal. How much force will keep it from rolling down the hill?

A) 3348 ft lbs.

B) 5572 ft lbs.

C) 3906 ft lbs.

D) 12,620 ft lbs.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 34) A car that weighs 4000 lbs. is parked on a hill in San Francisco with a slant of 33° from the horizontal. A tow truck has to remove the truck from its parking spot and move it 600 feet up the hill. How much work is required?

A) 1,307,134 ft lbs.

B) 2,012,809 ft lbs.

C) 1,558,578 ft lbs.

D) 8 ft lbs.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 208

Chapter 8 8.1

Systems of Linear Equations and Inequalities

Systems of Linear Equations in Two Variables

1) Solve the system of linear equations by substitution.

5x + 2y = -19 8x - 4y = -52 A) (5, -3) B) (-5, 3) C) (-5, -3) D) (5, 3) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 2) Solve the system of linear equations by substitution.

2x - 8y = 12 6x - 7y = -15 A) (6, -3) B) (-3, -6) C) (-6, -3) D) (6, 3) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 3) Solve the system of linear equations by substitution.

2z - 7w = 18 2z - 7w = 5 A) (2, 7) B) (18, 5) C) infinite number of solutions D) no solution Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01

209

4) Solve the system of linear equations by substitution.

-9p - 3q = -45 -18p - 6q = -90 A) (3, 6) B) (-1, 1) C) infinite number of solutions D) no solution Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 5) Solve the system of linear equations by elimination.

5d + 7f = 16 -5d - 3f = -24 A) (6, -2) B) (-2, 6) C) (-6, -2) D) (-2, -6) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 6) Solve the system of linear equations by elimination.

3x - 14y = 52 6x - 28y = -104 A) (-8, 2) B) (8, -2) C) infinite number of solutions D) no solution Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 7) Solve the system of linear equations by elimination.

-9x - 2y = 72 -18x + 6y = 54 A) (6, 9) B) (9, 6) C) (-9, -6) D) (-6, -9) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01

210

8) Solve the system of linear equations by elimination.

9t + 10q = -112 27t + 13q = -268 A) (8, -4) B) (-8, -4) C) (-4, -8) D) (-4, 8) E) None of the above.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 9) Solve the system of linear equations by graphing the following equations.

2x + 4y = -2 9x + 8y = 21 A) (5, -3) B) (-3, 5) C) (-5, -3) D) (5, 3) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 10) Solve the system of linear equations by graphing the following equations.

-10x + 5y = 110 -7x + 4y = 81 A) (8, -7) B) (-7, 8) C) (7, 8) D) (8, 7) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 11) Solve the system of linear equations by graphing the following equations.

-2x - 6y = 14 -5x + 7y = -31 A) (-3, 2) B) (2, -3) C) (-2, -5) D) (14, -31) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01

211

12) Solve the system of linear equations by graphing the following equations.

4x - 3y = 7 2x - 6y = 26 A) (-2, -5) B) (-5, -2) C) (5, -2) D) (-2, 5) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 13) Starbucks Coffee sells its House Blend for $9.52 per pound and its Sumatra coffee for $11.18 per pound. How many pounds of each type of coffee did a Starbucks outlet sell in one day if the total number of pounds sold was 60 and the day's receipts totaled $637.60? Let h represent the number of pounds of House Blend and s the number of pounds of Sumatra sold. Round your answer to the nearest pound.

A) h = 40 pounds, s = 20 pounds B) h = 20 pounds, s = 40 pounds C) h = 55 pounds, s = 5 pounds D) h = 5 pounds, s = 55 pounds Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01 14) A health food company mixes dried fruit with walnuts to make a trail mix blend. How many pounds of each ingredient must be mixed if dried fruit sells for $6.63 per pound, walnuts sell for $4.38 per pound, and the company produces 65 pounds per batch valued at $419.70? Let d represent the number of pounds of dried fruit and w the number of pounds of walnuts.

A) d = 15 pounds, w = 50 pounds B) d = 50 pounds, w = 15 pounds C) d = 5 pounds, w = 60 pounds D) d = 60 pounds, w = 5 pounds Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01

212

15) A catering company mixes cooked shredded beef with roasted Anaheim chilies to use as the filling in their house specialty burrito. How many pounds of both shredded beef that sells for$6.63 per pound and chilies that sell for $1.62 per pound must be mixed to produce 95 pounds of the mixture, witch sells for $454.50? Let b represent the number of pounds of beef and c represent the number of pounds of chilies.

A) b = 35 pounds, c = 60 pounds B) b = 60 pounds, c = 35 pounds C) b = 70 pounds, c = 25 pounds D) b = 25 pounds, c = 70 pounds Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01 16) Solve the system of linear equations by substitution.

7t - 2u = 39 2t + 6u = -48 Answer: (3, -9) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 17) Solve the system of linear equations by elimination.

-4j + 3k = 3 -3j - 3k = -45 Answer: (6, 9) Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01 18) A candy company mixes chocolate and peanuts to create one of their signature confections.

How many pounds of chocolate costing $11.82 per pound must be mixed with peanuts costing $4.37 per pound to create 50 pounds of mixture that costs $330.25? Let c represent the number of pounds of chocolate and p represent the number of pounds of peanuts.

Answer: 15 pounds chocolate, 35 pounds peanuts Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01 19) Solve the system of linear equations by substitution. x-

y = -30

x+

y = -1

Answer: (-36, 24) Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01

213

20) Solve the system of linear equations by elimination. x-

y = 13

x+

y = -44

Answer: (-96, -60) Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 01 21) Solve the system of linear equations by elimination.

10z - 2w = -46 10z - 2w = 5 A) (10, 2) B) (-46, 5) C) infinite number of solutions D) no solution Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 22) Solve the system of linear equations by elimination.

-4p - 8q = -64 -8p - 16q = -128 A) (6, 5) B) (3, -3) C) infinite number of solutions D) no solution Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 23) Solve the system of linear equations by elimination.

2.3t - 3.3u = -19.78 2t + 2.1u = 17.09 Answer: (1.3, 6.9) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01

214

24) Solve the system of linear equations by graphing the following equations.

-3x + 5y = -14 2x + 5y = -24

Answer: (-2, -4)

Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 215

Chapter 8 8.2

Systems of Linear Equations and Inequalities

Systems of Linear Equations in Three Variables

1) Solve the system of linear equations for a, b, and c.

6a - 4b + 7c = 65 2a + 7b - 2c = -33 6a - 5b + 8c = 73 A) (-4, -5, 3) B) ( 3, -5, 4) C) (4, -5, 3) D) (-5, 3, 4) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 2) Solve the system of linear equations for k, m, and n.

4k + 3m - 3n = 10 5k - 5m - 2n = 30 3k - 2m - 8n = 49 A) (1, -3, -5) B) (1, 3, -5) C) (-5, -3, 1) D) (-5, 3, 1) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 3) Solve the system of linear equations for s, t, and u.

6s - 7t + 4u = 19 7s + 6t + 4u = -21 7s - 8t + 2u = 19 A) (1, -3, -1) B) (-1, 1, -3) C) (-3, -1, 1) D) (-1, -3, 1) Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02

216

4) Solve the linear system of equations for k, m, and n.

-6k - 3m + 4n = -21 -4k + 5m - 2n = -21 -3k - 8m - 8n = -47 A) (1, 5, 3) B) (3, 1, 5) C) (5, 1, 3) D) (5, 3, 1) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 5) Ocean Beach Financial Planning offers three types of investments: low-risk, medium-risk, and high-risk. A customer decides to invest $6600 and is given three options for investing in the three funds. Determine the interest rate percentage for the low-risk, l, medium-risk, m, and high-risk, h, investments based on the interest earned for each option in the first year. $300l + $750m + $5550h = $429.00 $500l + $1150m + $4950h = $409.00 $350l + $1200m + $5050h = $417.00 A) (2%, 6%, 8%) B) (0%, 4%, 6%) C) (1%, 5%, 7%) D) (7%, 5%, 1%) Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 08, Sec 02 6) Solve the system of linear equations for v, w, and x.

-4v - 5w + 8x = 14 8v - 8w - 2x = 122 7v + 4w + 6x = 64 Answer: (10, -6, 3) Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02

217

7) An object is thrown upward, and the following table depicts the height of the ball t seconds after the projectile is released. t seconds 1 2 3

Height (Feet) 62 87 80

Find the initial height (h0), initial velocity (v0), and acceleration (a) due to gravity.

Answer: a = -32 ft/ , = 73 ft/sec, = 5 ft Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 8) Solve the system of equations.

18x - 9y = -3 9x - 3z = -3 Answer: x =

a-

,y=

a-

,z=a

Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 9) Solve the system of linear equations for a, b, and c.

A) (-3, -3, 5) B) (5, -3, 3) C) (3, -3, 5) D) (-3, 5, 3) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02

218

10) Solve the system of linear equations for x, y, and z.

A) (-3, -1, 2) B) (-3, 1, 2) C) (2, -1, -3) D) (2, 1, -3) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 11) Solve the system of linear equations for x, y, and z.

A) (-3, 2, -2) B) (-3, -2, -2) C) (-2, 2, -3) D) (-2, -2, -3) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

219

Precalculus, 4e (Young) Chapter 9 Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations 9.1

Conic Basics

1) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

- 2x + + 8y + 4 = 7 Select the choice that best describes the graph of the equation.

A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 2) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

16 + 4 = 81 A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 3) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-y=6 A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01

220

4) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

81 - 49 = 4 A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 5) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. + 6x + - 10y + 11 = 18 A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 6) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

15 - 3x + 4 - 16y + 4 = 17 A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 7) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-1 - 18x - y = 12 A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01

221

8) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

18 - 14x- 16 + 14y + 8 = -7 Select the choice that best describes the graph of the equation.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 9) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points exactly four units from the point (-14, -17).

A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 10) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (8, 2) and the line y = -4.

A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 11) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (3, 14) plus the distance from the point is exactly 7 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01

222

12) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose difference of the distances to the points 18 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01

and

is exactly

13) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points exactly 3 units from the point (14, -20).

A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 14) Identify the conic section as a parabola, circle, ellipse, or hyperbola: The set of all points equidistant from the point (-11, -4) and the line A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 15) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (-5, 9) plus the distance from the point exactly 8 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01

223

is

16) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose difference of the distances to the points (-11, 7) and (4, 7) is exactly 1 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 17) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (-2, 15) plus the distance from the point is exactly 16.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 18) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (20, -12) and the line A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 19) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

45 - 41 = 30 Answer: hyperbola Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 20) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (4, -15) and from the line x = -4.

Answer: parabola Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01

224

21) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (4, 9) plus the distance from the point exactly 39 units.

Answer: ellipse Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 22) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

- 4x + + 6y + 4 = 7 Answer: circle Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 23) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

16 + 25 = 81 Answer: ellipse Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 24) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-y=6 Answer: parabola Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 25) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

100 - 4 = 49 Answer: hyperbola Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 26) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. + 4x + - 6y + 20 = 3 Answer: circle Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01

225

is

27) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

3 - 7x + 17 - 7y + 16 = 7 Answer: ellipse Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 28) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-4 - 18x - y = 15 Answer: parabola Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 29) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

17 - 16x - 4 + 13y + 16 = 8 Answer: hyperbola Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 226

Chapter 9 Equations 9.2

Conics, Systems of Nonlinear Equations and Inequalities, and Parametric

The Parabola

1) Find an equation for the parabola with vertex (4, 5) and focus (4, 11).

A) = 24( y - 5) B) = 24( y - 4) C) = 6( y - 5) D) = 24( y + 5) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 2) Find an equation for the parabola with vertex (1, 8) and focus (3, 8).

A) = -2(x - 1) B) = -8(x + 1) C) = -8(x - 1) D) = -8( y - 1) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 3) Find an equation for the parabola with vertex (2, 8) and focus (4, 8).

A) - 16x - 8y + 48 = 0 B) - 16y - 8x + 48 = 0 C) - 16y + 8x + 48 = 0 D) - 16x + 8y + 48 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 4) Find an equation for the parabola with vertex (-2, 10) and focus (-5, 10).

A) - 20y + 12x + 124 = 0 B) - 20x + 12y + 124 = 0 C) - 20x - 12y + 124 = 0 D) - 20y - 12x + 124 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

227

5) Find an equation for the parabola with vertex (8, 3) and focus (8, 10).

A) - 16y - 28x + 148 = 0 B) - 16x + 28y + 148 = 0 C) - 16x - 28y + 148 = 0 D) - 16y + 28x + 148 = 0 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 6) Find an equation for the parabola with vertex (7, 1) and focus (7, -5).

A) - 14x + 24y + 25 = 0 B) - 14x - 24y + 25 = 0 C) - 14y - 24x + 25 = 0 D) + 14y + 24x + 25 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 7) Find an equation for the parabola with focus (14, 3) and directrix x = 4.

A) - 6x + 20y + 189 = 0 B) - 6x - 20y + 189 = 0 C) - 6y - 20x + 189 = 0 D) - 6y + 20x + 189 = 0 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 8) Find an equation for the parabola with focus (9, 7) and directrix x = 11.

A) - 14y - 4x + 9 = 0 B)

- 14y + 4x + 9 = 0

C) - 14x - 4y + 9 = 0 D) - 14x + 4y + 9 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

228

9) Find an equation for the parabola with focus (1, 11) and directrix y = 7.

A) - 2y - 8x + 73 = 0 B) - 2x - 8y + 73 = 0 C) - 2x + 8y + 73 = 0 D) - 2y + 8x + 73 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 10) Find an equation for the parabola with focus (8, -2) and directrix y = 4.

A) - 16x + 12y + 52 = 0 B) - 16x - 12y + 52 = 0 C) - 16x + 12y + 52 = 0 D) - 16x - 12y + 52 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 11) Find an equation of the form A + Bx + Cy + D = 0 or A with vertex (-1, 6) and focus (5, 6).

Answer: - 12y - 24x - 12 = 0 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

+ By + Cx + D = 0 for the parabola

12) Find an equation of the form A + Bx + Cy + D = 0 or A with focus (10, -8) and directrix y = 8.

Answer: - 20x + 32y + 100 = 0 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

+ By + Cx + D = 0 for the parabola

229

13) Graph the equation.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 14) Write an equation for the parabola.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02

230

15) Match the parabola to the equation.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

231

16) Match the equation to the parabola.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 232

17) Graph the parabola and label the coordinates of the vertex.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 18) Graph the parabola and label the coordinates of the vertex.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

233

19) Match the parabola to an equation in standard form.

A) B) C) D) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 20) Match the parabola to an equation in general form.

A) B) C) D) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02

234

21) Match the equation to the parabola.

A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 235

22) Match the equation to the parabola.

A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 236

23) Write an equation for the parabola in standard form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 24) Write an equation for the parabola in standard form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02

237

25) Write an equation for the parabola in general form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 26) A satellite dish measures 72 feet across its opening and 9 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?

A) The focus will be at (0, 9) so the receiver should be placed 36 feet from the vertex.

B) The focus will be at (0, 36) so the receiver should be placed 9 feet from the vertex.

C) The focus will be at (36, 0) so the receiver should be placed 9 feet from the vertex.

D) The focus will be at (0, 36) so the receiver should be placed 72 feet from the vertex.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 27) A bridge with a parabolic shape has an opening 98 feet wide at the base of the bridge (where the bridge meets the water), and the height in the center of the bridge is 40 feet. A sailboat whose mast reaches 50 feet above the water is traveling under the bridge 23 feet from the center of the bridge. Will it clear the bridge without scraping its mast? Justify your answer.

A) No. The opening height is 50 feet, and the mast is 31.2 feet.

B) Yes. The opening height is 50 feet, and the mast is 31.2 feet.

C) No. The opening height is 31.2 feet, and the mast is 50 feet.

D) No. The opening height is 32 feet, and the mast is 50 feet.

Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 28) Find the vertex of the parabola with equation Answer: (8, 9) Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 02

= 20( y - 9).

29) Find the vertex of the parabola with equation Answer: (4, 1) Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 02

= -24(x - 4).

238

30) Find the vertex of the parabola with equation Answer: (1, 7) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 14y - 24x + 25 = 0.

31) Find the vertex of the parabola with equation Answer: (-5, 1) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 2y + 8x + 41 = 0.

32) Find the focus of the parabola with equation Answer: (3, 14) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= 24( y - 8).

33) Find the focus of the parabola with equation Answer: (5, 4) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= -12(x - 2).

34) Find the focus of the parabola with equation Answer: (16, 8) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 16y - 4x + 4 = 0.

35) Find the focus of the parabola with equation Answer: (-13, 7) Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 14y + 32x + 209 = 0.

36) Find the equation of the directrix of the parabola with equation Answer: x = 2 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= 12( y - 5).

37) Find the equation of the directrix of the parabola with equation Answer: y = 1 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= -8(x - 3).

38) Find the equation of the directrix of the parabola with equation Answer: y = -1 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 12y - 12x + 12 = 0.

239

39) Find the equation of the directrix of the parabola with equation Answer: x = -2 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 6x - 32y + 201 = 0.

40) Find the length of the latus rectum of the parabola with equation Answer: 20 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= 20( y - 4).

41) Find the length of the latus rectum of the parabola with equation Answer: 8 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

= -8(x - 7).

42) Find the length of the latus rectum of the parabola with equation Answer: 4 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 18y - 4x + 77 = 0.

43) Find the length of the latus rectum of the parabola with equation Answer: 8 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02

- 16x - 8y + 120 = 0.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 240

Chapter 10 10.1

Sequences and Series

Sequences and Series

1) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

=

B)

= 7,

=

,

=

,

=

C)

= 1,

=

,

=

,

=

D)

=

,

,

=

=

,

,

=

=

,

=

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01 2) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

=

B)

=

,

=

,

=

,

=

C)

=

,

=

,

=

,

=

D)

= 1,

=

,

,

=

=

,

,

=

=

Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01

241

3) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

= -22,

B)

= -11,

= -11,

C)

= -22,

=-

D)

= 1,

= -22,

= -11,

= -11

= -11, ,

==-

= -11 ,

,

==-

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01 4) Find the term A)

=

B)

= 243

C)

= 15

D)

=

of the sequence

=

.

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01 5) Find the term A)

=

B)

=6

C)

= 19

D)

=

of the sequence

=

.

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01

242

6) Find the term A)

=9

B)

=9

C)

= 1/ 9

D)

= 1/9

of the sequence

=

.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 7) Find the term A)

=-

B)

= -51

C)

=-

D)

= 10

of the sequence

=

.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 8) Write an expression for the term of the sequence 1, 6, 11, 16, 21, ...

A) = 5n - 4, for n = 1, 2, 3, ...

B)

= 4n + 5, for n = 1, 2, 3, ...

C)

= 4n - 5, for n = 1, 2, 3, ...

D)

= n + 4, for n = 1, 2, 3, ...

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01

243

9) Write an expression for the A)

=

, for n = 1, 2, 3, ...

B)

=

, for n = 1, 2, 3, ...

C)

= n + 2, for n = 1, 2, 3, ...

D)

= 3n + 2, for n = 1, 2, 3, ...

term of the sequence

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 10) Simplify the ratio of factorials

.

A) 10 B) 2 C) 24 D) 30 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 11) Simplify the ratio of factorials

.

A) 1190 B) 2 C) 68 D) 1155 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 12) Simplify the ratio of factorials

.

A) 188 B) 4 C) 79,727,040 D) 8832 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01

244

,

,

,

,

, ...

13) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

A)

= 1,

= 2,

= 12,

= 22

B)

= 2,

= 12,

= 22,

= 32

C)

= 0,

= 2,

= 12,

= 22

D)

= 12,

= 22,

= 32,

= 42

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 14) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

A)

= 2,

= 3,

= 12,

= 18

B)

= 1,

= 2,

= 3,

= 36

C)

= 36,

= 648,

D)

= 2,

= 3,

= 139,968, = 36,

= 544,195,584

= 648

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 15) Evaluate the finite series.

A) 26 B) 15 C) 14 D) 18 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01

245

16) Evaluate the finite series.

A) 40 B) 120 C) 118 D) 324 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 17) Evaluate the finite series.

A) 15,625 B) 3413 C) 55 D) 701 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 18) Write the first four terms of the sequence. Assume that n starts at 1. = Answer:

= 256,

= -16,384,

= 331,776,

Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 19) Find the term Answer:

of the sequence

=

.

=

Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 01 20) Simplify the ratio of factorials.

Answer: 22,650 Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 246

= -4,194,304

21) Evaluate the finite series.

Answer: 16 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 22) Dylan sells his car freshman year and puts $3100 in an account that earns 6.2% interest compounded monthly. The balance in the account after n months is = 3100 Calculate

n = 1, 2, 3,... .

What does

represent?

A) $3132.12,

represents the balance in 24 months or 2 years.

B) $3508.13,

represents the balance in 24 years.

C) $3508.13,

represents the balance in 24 months or 2 years.

D) $74,784.40ȝ,

represents the balance in 24 months or 2 years.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01 23) Simplify the ratio of factorials

.

Answer: 25 + 145n + 210 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 24) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

Answer:

= 2,

= 24,

= 96,

= 96

Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 01

247

25) Evaluate the finite series.

Answer: 27 +81 + 243 + 729 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 26) Evaluate the infinite series if possible.

Answer: 112.5 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01 27) Apply sigma notation to write the sum.

1+

+

+

+

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 01

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248

Precalculus, 4e (Young) Chapter 10 Sequences and Series 10.2

Arithmetic Sequences and Series

1) Find the common difference d of the arithmetic series 5, 7, 9, 11, 13, ...

A) d = -2 B) d = 2 C) d = 8 D) d = 7 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 02 2) Find the common difference d of the arithmetic series 74, 70, 66, 62, 58, ...

A) d = -16 B) d = 16 C) d = 4 D) d = -4 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 02 3) Find the first four terms of the sequence

= -3n + 9, for n = 1, 2, 3, ... If the sequence is

arithmetic, find the common difference d.

A) = 12, = 15, = 18, = 21; not arithmetic B)

= 6,

= 3,

C)

= 12,

= 15,

D)

= 6,

= 3,

= 0, a4 = -3; not arithmetic = 18, a4 = 21; d = 3 = 0, a4 = -3; d = -3

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 02 4) Find the first four terms of the sequence

= 8(n - 7), for n = 1, 2, 3, ... If the sequence is

arithmetic, find the common difference d.

A) = -48, = -40, = -32, = -24; not arithmetic B)

= -48,

= -40,

= -32,

C)

= 48,

= 40,

= 32,

D)

= -48,

= -40,

= -32,

= -24; d = 8 = 24; not arithmetic = -24; d = -8

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 02 249

5) Find the first four terms of the sequence

=

the common difference d.

A) = -2, = 4, = -6,

= 8; not arithmetic

B)

= -2,

= 4,

= -6,

= 8; d = 2

C)

= -2,

= 4,

= -6,

= 8; d = -2

D)

= 2,

= -4,

= 6,

= -8; not arithmetic

(2n). If the sequence is arithmetic, find

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 02 6) Find the general, or A)

= -4n - 6

B)

= 4n - 6

C)

= -6n - 4

D)

= -2n - 6

, term of the sequence given

= -2 and d = -6.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 02 7) Find the general, or A)

= kn + (7 + k)

B)

= kn + (7 - k)

C)

= 7n + (7 - k)

D)

= kn - (7 - k)

, term of the sequence given

Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02

250

= 7 and d = k.

8) Find the general, or A)

=

B)

= -10n -

C)

=

n+

D)

=

n-

, term of the sequence given

n-

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 10, Sec 02 9) Find the term of the sequence 8, 13, 18, 23, 28, ...

A) 45 B) 43 C) 38 D) 33 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 10) Find the term of the sequence -6, 0, 6, 12, ...

A) 1164 B) 1170 C) 1176 D) -1200 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 11) Find the sum: A) 330 B) 226 C) 225 D) 275 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02

251

= -10 and

12) Find the sum: A) 247 B) 299 C) 210 D) 287 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 13) A minor league baseball stadium has 160 seats in the front row, and each subsequent row has 15 more seats than the previous row. How many seats are in the stadium if there are 50 rows?

A) 223,125 seats B) 26,375 seats C) 910 seats D) 26,535 seats Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 14) Find the common difference d of the arithmetic sequence 136, 120, 104, 88, 72, ...

Answer: -16 Diff: 1 Var: 1 Chapter/Section: Ch 10, Sec 02 15) Find term number 23 of the sequence 13, 26, 39, 52, 65, ...

Answer: 299 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 16) An outdoor amphitheater has 90 seats in the front row and each subsequent row has 2 more seats than the previous row. How many seats are in in the amphitheater if there are 38 rows?

Answer: 4826 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 17) Find the sum.

-4 - 3 - 2 - ... + 31 A) 486 B) 472.5 C) 972 D) -486 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 252

18) Find the sum of the first 65 terms of the series 7 + 14 + 21 + 28 + ...

Answer: 1137.5 Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02 19) For the arithmetic series with 13th term 66 and 34th term 192, find

and d and construct the

sequence by stating the general, or nth, term.

Answer: = -6; d = 6; = -6 + 6(n - 1) Diff: 3 Var: 1 Chapter/Section: Ch 10, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 253

Chapter 11 11.1

Limits: A Preview to Calculus

Introduction to Limits: Estimating Limits Numerically and Graphically

1) Complete a table of values to four decimal places and use the result to estimate the limit.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 2) Complete a table of values to four decimal places and use the result to estimate the limit.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 3) Complete a table of values to four decimal places and use the result to estimate the limit.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 4) Complete a table of values to four decimal places and use the result to estimate the limit.

Answer: 0 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01

254

5) Complete a table of values to four decimal places and use the result to estimate the limit.

Answer: Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 01 6) Complete a table of values to four decimal places and use the result to estimate the limit. ln x Answer: 0 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 7) Use the graph to estimate the limit, if it exists.

Answer: 0 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 8) Use the graph to estimate the limit, if it exists. f (x), where f (x) =

Answer: 0 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 255

9) For the graph of the function f shown, state the value of the given quantity. f (x)

Answer: does not exist Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 10) For the graph of the function f shown, state the value of the given quantity. f (-1)

Answer: 1 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 11) Complete a table of values to four decimal places and use the result to estimate the limit.

A) 18 B) -18 C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 256

12) Complete a table of values to four decimal places and use the result to estimate the limit.

A) -2 B) C) D) 2 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 13) Complete a table of values to four decimal places and use the result to estimate the limit.

A) B) 12 C) D) -12 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01 14) Complete a table of values to four decimal places and use the result to estimate the limit.

A) does not exist B) 0 C) 1 D) -1 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01

257

15) Complete a table of values to four decimal places and use the result to estimate the limit.

A) 0 B) C) D) does not exist Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 01 16) Complete a table of values to four decimal places and use the result to estimate the limit. ln x A) does not exist B) 0 C) ∞ D) -∞ Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01

258

17) For the graph of the function f shown, state the value of the given quantity. f (x)

Answer: 3 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 01

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

Precalculus, 4e (Young) 259

Chapter 11 11.2

Limits: A Preview to Calculus

Techniques for Finding Limits

1) Given the graphs of the functions f and g, find the limit, if it exists.

[5 f (x)+ 7g(x)]

Answer: 90 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 2) Given the graphs of the functions f and g, find the limit, if it exists.

Answer: 144 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02

260

3) Given the graphs of the functions f and g, find the limit, if it exists.

Answer: -1/5 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 4) Find the limit by using limit laws and special limits.

Answer: -12 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 5) Find the limit by using limit laws and special limits.

Answer: 8 Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 6) Find the limit, if it exists.

Answer: 9 Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 261

7) Find the limit, if it exists.

Answer: -18 Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 8) Find the limit, if it exists.

Answer: Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 9) Find the limit, if it exists.

Answer: Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 10) Find

.

f (x) = 6 + 11x - 24 Answer: f (x) = 12x + 11 Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

262

11) Find

.

f (x) = Answer: Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 12) Find

.

f (x) = Answer: Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 13) Evaluate the one-sided limit in order to find the limit, if it exists.

Answer: Does not exist Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 14) A person standing near the edge of a cliff 286 feet high throws a rock upward with an initial speed of 118 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time: h(t) = -16 + 118t + 286. Find the velocity of the rock when Answer: -170 feet per second Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 15) Evaluate the one-sided limits in order to find the limit, if it exists. f (x), where f (x) = Answer: does not exist Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

263

16) Find the limit by using limit laws and special limits.

A) 125 B) 3 C) -125 D) -3 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 17) Find the limit by using limit laws and special limits.

A) Does not exist B) C) 3 D) 9 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 18) Find the limit, if it exists.

A) -5 B) 5 C) 4 D) -4 Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

264

19) Find the limit, if it exists.

A) -500 B) 0 C) 125 D) 500 Answer: D Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 20) Find the limit, if it exists.

A) 10 B) C) Does not exist D) Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 21) Find the limit, if it exists.

A) -144 B) 144 C) D) Answer: D Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

265

22) Find

.

f (x) = 10 - 7x - 7 A) f (x) = -20x + 7 B) f (x) = 20x + 7 C) f (x) = -20x - 7 D) f (x) = 20x - 7 Answer: D Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 23) Find

.

f (x) = A) B) C) D) Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

266

24) Find

.

f (x) = A) B) C) D) Answer: D Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02 25) Evaluate the one-sided limit in order to find the limit, if it exists.

A) 0 B) Does not exist C) 1 D) -1 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02 26) A person standing near the edge of a cliff 51 feet high throws a rock upward with an initial speed of 49 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time: h(t) = -16 + 49t + 51. Find the velocity of the rock when seconds.

A) -23.5 inches per second B) 54 feet per second C) -47 feet per second D) -23.5 feet per second Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 11, Sec 02

267

27) Evaluate the one-sided limits in order to find the limit, if it exists. f (x), where f (x) = A) 3 B) does not exist C) 4 D) -3 Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 11, Sec 02

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

268