Calculus i with precalculus 3rd edition larson solutions manual by dennis.gibson112

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Calculus

iii CONTENTS Chapter P Prerequisites............................................................................................ 1 Chapter 1 Functions and Their Graphs................................................................. 89 Chapter 2 Polynomial and Rational Functions...................................................173 Chapter 3 Limits and Their Properties................................................................277 Chapter 4 Differentiation.....................................................................................320 Chapter 5 Applications of Differentiation..........................................................407 Chapter 6 Integration...........................................................................................524 Chapter 7 Exponential and Logarithmic Functions...........................................606 Chapter 8 Exponential and Logarithmic Functions and Calculus.....................675 Chapter 9 Trigonometric Functions....................................................................725 Chapter 10 Analytic Trigonometry.......................................................................813 Chapter 11 Trigonometric Functions and Calculus.............................................885 Chapter 12 Topics in Analytic Geometry.............................................................944 Chapter 13 Additional Topics in Trigonometry.................................................1054 NOT FOR SALE INSTRUCTOR USE ONLY © Cengage Learning. All Rights Reserved. Calculus I with Precalculus 3rd Edition Larson Solutions Manual Visit TestBankDeal.com to get complete for all chapters

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Preface

The CompleteSolutionsManual for CalculusIwithPrecalculus:AOne-YearCourse, Third Edition, is a supplement to the text by Ron Larson and Bruce H. Edwards. Solutions to every exercise in the text are given with all essential algebraic steps included.

INSTRUCTOR USE ONLY

Prerequisites Section P.1 Solving Equations................................................................................... 2 Section P.2 Solving Inequalities.............................................................................. 17 Section P.3 Graphical Representation of Data........................................................ 36 Section P.4 Graphs of Equations............................................................................. 44 Section P.5 Linear Equations in Two Variables..................................................... 55 Review Exercises .......................................................................................................... 70 Chapter Test 83 Problem Solving ........................................................................................................... 85 INSTRUCTOR USE ONLY © Cengage Learning. All Rights Reserved.

CHAPTER P

Prerequisites Section P.1 Solving Equations

1. equation

2. 0 axb

3. extraneous

4. factoring; extracting square roots; completing the square; Quadratic Formula

5. 4144 xx is an identity by the Distributive Property. It is true for all real values at x

6. 635210 xx is conditional. There are real values of x for which the equation is not true.

7. 4124422422 xxxxxx

This is an identity by simplification. It is true for all real values of x

8. 2223264 xxxx is an identity by simplification. It is true for all real values of x

9. 14 3 11 x xx is conditional. There are real values of x for which the equation is not true.

10. 53 24 xx is conditional. There are real values of x for which the equation is not true (for example, 1 x ).

11. 1115 11111511 4 x x x 12. 719 719 719 7191919 12 x xxx x x x 13. 7225 772257 218 218 22 9 x x x x x

7223 722232 721 721 77 3 x x x x x 15. 85320 8353320 5520 555205 525 525 55 5 xx xxxx x x x x x 16. 73317 733331733 420 5 xx xxxx x x 17. 42576 276 26766 257 22572 55 55 1 yyy yy yyyy y y y y 18. 5 8 33511 39551 3945 39594559 85 xx xx xx xxxx x x 19. 32385 6985 5985 559855 98 xxx xxx xx xxxx No solution. NOT

14.

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ChapterP.1SolvingEquations 3 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 20. 9105225 9105410 910910 xxx xxx xx The solution is the set of all real numbers. 21. 34 4 83 34 24244 83 93296 2396 2323 96 23 xx xx xx x x 22. 3 3 5210 3 10103 5210 25303 630 5 xxx xxx xxx x x 23. 3 1 24 3 1 24 3 1 24 6 5 5240 452440 4542440 65240 630240 56 zz zz zz zz zz z z 24. 0.600.4010050 0.60400.4050 0.2010 50 xx xx x x 25. 822 824 84 84 xxx xxx xx Contradiction; no solution 26. 8232125 81663210 213210 1310 xxx xxx xx Contradiction; no solution 27. 100456 6 34 100456 1212126 34 4100435672 40016151872 31310 10 xx xx xx xx x x 28. 1732 100 1732 100 1732100 492100 4998 1 2 yy yy yy yyy yy yyy yy y y 29. 542 543 354254 1512108 520 4 x x xx xx x x 30. 156 43 156 7 9 7 97 9 7 xx xx x x x 31. 2 32 2 2 3222 2 36242 0 z zz z zz z 32. 12 0Multiply both sides by 5. 5 1520 350 35 5 3 xx xx xx x x x ChapterP.1Solvi n

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33. 4 20Multiply both sides by 4.

A check reveals that 4 x is an extraneous solution because it makes the denominator zero. There is no real solution. 34.

78 4Multiply both sides by 2121.

A check reveals that 3 x is an extraneous solution because it makes the denominator zero. There is no solution. 36. 35 62 Multiply both sides by 3. 33

A check reveals that 3 x is an extraneous solution because it makes the denominator zero. There is no solution. 37. 22

39. 2 238 xx

General form: 2 2830 xx

40. 2 2 2

This is a contradiction. So, the equation has no solution.

2012

13370 13314490 133421470

x xx xx

General form: 2 3421340 xx

4 ChapterPPrerequisites

4240 4280 3120 312 4 x

xx xx xx x x x

2121 72182142121 147168164 611 11 6 x

xx xxxxx xxxx x x 35. 2 341 33 341

33 343 3412 39 3 xxxx

xxxx xx xx x x

Multiply both sides by 3.

63235 6182315 418315 3

xxxx xxx xxx xx x

44569

0 xx xxxx xx x x 38.

441444

xxx xxxx

22 253

4969 20

2 2 22 2141

INSTRUCTOR

USE ONLY

form: 2 390100 xx 42. 2 22 2 2

251 251 4210 142110

50.

2 2 3 2

xxx xxx xx xx xx 53. 22 2

form: 2 4210 xx 43. 2 630 3210 xx xx 20 0 0

xx xx 44. 2 940 32320 x xx xab xabxab xabxab 0 0 xabxab xabxab 55. 2 49 7 x x 56. 2 32 3242 x x 57. 2 2

33 320or320 xx 381 27 33

45. 2 280 420 xx xx 40or20 4or2 xx xx x x x 58. 2 2

230xx

2 3520 3120 xx xx

2 12350 750 xx xx 70or50 7or5 xx xx x x x

2 1090 910 xx xx 909 101 xx xx 936 4 42

ChapterP.1SolvingEquations 5 ©

be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part.

General

1 2

0or

46.

47.

48.

3 2

41. 2 2 1 2

1 5 31018 31090 30or120 3or xx xx

xx xx

General

30or210 xaxa xa xa xa 54. 2 2 0 0 0

21933 219330 23110 230 11011

xx xx xx xx xx 51. 2 2

412 4120 620

xx xx xx 60or20 6or2 xx xx

52. 2 2 1 8 160 81280 1680 xx xx xx 16016 808 xx

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NOT FOR SALE r equisites requisites

6 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 59. 2 1216 124 124 16or8 x x x xx 60. 2 1325 1325 135 1358,18 x x x x 61. 2 214 214 214 x x x 62. 2 530 530 530 x x x 63. 2 2118 2118 2132 132 2 x x x x 64. 2 2 23270 2327 2327 2333 2333 333 2 x x x x x x 65. 7322 73 xx xx 73or73 73or24 2 xxxx x x The only solution to the equation is 2. x 66. 5422 54 xx xx 9 2 54 54 or 54 or 54 29 xxxx xx x x The only solution to the equation is 9 2. x 67. 2 2 222 2 4320 432 42322 236 26 26 4or8 xx xx xx x x x xx 68. 2 2 222 2 620 62 6323 37 37 37 xx xx xx x x x 69. 2 2 222 2 12250 1225 126256 611 611 611 xx xx xx x x x 70. 2 2 22 2 8140 814 841416 42 42 42 xx xx xx x x x

ChapterP.1SolvingEquations 7 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 71. 2 2 2 2 222 2 840 480 480 48 4282 212 212 223 xx xx xx xx xx x x x 72. 2 2 2 2 2 2 414 39 42144 3399 18 2 39 2 3 2 3 2 3 91214 2 2 2 xx xx xx x x x x 73. 2 2 2 22 2 2 2580 258 5 4 2 555 4 244 589 416 589 44 589 44 589 4 xx xx xx xx x x x x 74. 2 2 2 2 2 2 99 4 99 11 244 100 1 24 1 2 1 2 9 111 222 44990 25 25 5, xx xx xx x x x x 75. 2 2 2 22 2 2 51570 7 30 5 7 3 5 373 3 252 317 220 317 220 317 2 25 317 2 25 385 210 1585 10 xx xx xx xx x x x x x x 76. 2 2 2 22 2 2 2 3950 5 30 3 5 3 3 353 3 232 359 234 37 212 37 212 37 2 23 37 2 23 321 26 921 6 xx xx xx xx x x x x x x x

INSTRUCTOR

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NOT FOR SALE r equisites requisites

8 ChapterPPrerequisites

Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 77. 2 210 xx 2 2 4 2 11421 22 131 ,1 42 bbac x a 78. 2 252030 xx 2 2 4 2 20204253 225 20400300 50 201031 , 5055 bbac x a 79. 2 2 220 220 xx xx 2 2 4 2 22412 21 223 13 2 bbac x a 80. 2 10220xx 2 2 4 2 10104122 21 1010088 2 1023 53 2 bbac x a 81. 2 14440xx 2 2 4 2 14144144 21 1425 75 2 bbac x a 82. 2 2 64 640 xx xx 2 2 4 2 66414 21 63616 2 6213 2 313 bbac x a 83. 2 2 1293 91230 xx xx 2 2 4 2 1212493 29 126727 1833 bbac x a 84. 2 2 4440 10 xx xx 2 2 4 2 11411 21 114 2 15 22 bbac x a 85. 2 924160 xx 2 2 4 2 24244916 29 240 18 4 3 bbac x a

NOT FOR SALE ChapterP.1Solvi n

ChapterP.1SolvingEquations 9 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 86. 2 164050 xx 2 2 4 2 40404165 216 401600320 32 40165 32 55 42 bbac x a 87. 2 2 28494 492840 xx xx 2 2 4 2 28284494 249 2802 987 bbac x a 88. 2 2 310 310 xx xx 2 2 4 2 33411 21 313313 222 bbac x a 89. 2 2 852 2850 tt tt 2 2 88425 48266 2 22242 bbac t a 90. 2 2580610 hh 2 2 4 2 808042561 225 8064006100 50 8103 550 83 55 bbac h a 91. 2 2 52 12250 yy yy 2 2 4 2 12124125 21 12211 611 2 bbac y a 92. 2 2 2 2 5 148 7 25 201968 49 25 281960 49 25137296040 xx xxx xx xx 2 2 4 2 137213724259604 225 1372921,984 50 6861966 25 bbac x a 93. 2 0.10.20.50 xx 2 2 4 2 0.20.240.10.5 20.1 1.449,3.449 xbbac a x x

INSTRUCTOR

USE ONLY

xx 2 2 4 2

20.005 0.1010.006341 0.01 2.137,18.063 bbac x a 95. 2 4225063470 xx 2 5065064422347 2422 1.687,0.488 x x 96. 2 3.220.0828.6510 xx 2 2 4 2 0.080.0843.2228.651 23.22 0.08369.031 2.995,2.971 6.44 bbac x a 97. 2 2 222 2 210Complete the square. 21 2111 12 12 12 xx xx xx x x x 98. 2 2 11330Factor. 1130 30 xx xx xx 0or30 3 xx x 99. 2 381Extract square roots. 39 x x 39or39 6or12 xx xx 100. 2 2 14490Extract square roots. 70 70 7 xx x x x 101. 2 2 22 2 2 11 4 11 4 1111 242 112 24 112 24 1 2 0Complete the square. 3 xx xx xx x x x 102. 2 2 3427Quadratic Formula 02311 xx xx 2 334211 22 397 4 397 44 x 103. 2 2 2 42428Factor. 440 410 110 10or10 11 xxx x x xx xx xx 104. 222 0Factor. 0 0 0 axb axbaxb b axbx a b axbx a 105. 42 22 2 2500 2250 2550 xx xx xxx 2 or50or50 20 or5or5 0 xxx xxx r equisites requisites INSTRUCTOR USE ONLY © Cengage Learning. All Rights Reserved.

2 0.0050.1010.1930

0.1010.10140.0050.193

ChapterP.1SolvingEquations 11 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 106. 3 2 5 2 5 2 201250 54250 525250 500 250 250 xx xx xxx xx xx xx 107. 4 2 2 810 9330 90 No real solution 303 303 x xxx x xx xx 108. 6 33 22 2 2 640 880 2242240 202 240 No real solution (by the Quadratic Formula) 202 240No real solution (by the Quadratic Formula) x xx xxxxxx xx xx xx xx 109. 3 33 2 2 2160 60 66360 606 6360 No real solution (by the Quadratic Formula) x x xxx xx xx 110. 432 22 2 2 2 4 3 924160 924160 340 00 340 xxx xxx xx xx xx 111. 32 2 2 330 330 310 3110 303 101 101 xxx xxx xx xxx xx xx xx 112. 32 2 2 2 2360 2320 230 202 30No real solution xxx xxx xx xx x 113. 43 43 3 3 2 2 1 10 110 110 1110 101 101 10No real solution (by the Quadratic Formula) xxx xxx xxx xx xxxx xx xx xx

NOT FOR

12 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 114. 433 43 3 3 2 2 21684 28160 2820 820 22420 202 240No real solution (by the Quadratic Formula) 202 xxxx xxx xxx xx xxxx xx xx xx 115. 42 22 430 310 33110 303 303 101 101 xx xx xxxx xx xx xx xx 116. 42 22 2 2 362970 36710 676710 7 670 6 7 670 6 10No real solution tt tt ttt tt tt t 117. 63 33 22 2 2 780 810 224110 202 240No real solution (by the Quadratic Formula) 101 10No real solution (by the Quadratic Formula) xx xx xxxxxx xx xx xx xx 118. 63 33 2 33322 33 320 210 222110 202 xx xx xxxxxx xx 2 33 2 2 220No real solution (by the Quadratic Formula) 101 10No real solution (by the Quadratic Formula) xx xx xx 119. 2100 210 2100 50 x x x x 120. 36 49 760 76 4936 x x x x 121. 1040 104 1016 26 x x x x 122. 530 53 59 4 x x x x

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SectionP.1SolvingEquations 13 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 123. 2530 253 259 24 2 x x x x x No solution. 124. 3220 322 324 21 1 2 x x x x x 125. 3 3 2180 218 21512 2513 513 2 x x x x x 126. 3 3 4320 432 438 45 5 4 x x x x x 127. 2 2 5264 5264 526816 13420 670 6or7 xx xx xxx xx xx xx 128. 525 525 10 xx xx x 129. 32 23 68 68 64 10 x x x x 130. 32 3 2 3 3 38 38 364 364 341 x x x x x 131. 23 32 35 35 355 355 x x x x 132. 43 2 234 2216 2216 xx xx 22 22 2 228or228 300140 650 114114 6or5 21 157 2 xxxx xxxx xx x xx x 133. 1232 12 12 12 2 5 31210 13210 1520 10101 520,extraneous xxx xxx xx xxx xx 134. 1343 2 1343 13 13 3 5 41610 221310 212310 21530 200 101 530 xxxx xxxx xxxx xxx xx xx xx

ectionP.1Solvi

NOT FOR SALE S

Sectionn P.1Solvi INSTRUCTOR USE ONLY

NOT FOR SALE r equisites requisites

140.

141. 2 3 xxx

Firstequation:

142. 2 6318xxx

Firstequation:

Secondequation:

14 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 135. 2 2 31 2 31 222 2 26 260 2320 3 230 2 202 x x xxxx x xx xx xx xx xx 136. 2 2 43 1 12 423112 483332 230 130 101 303 xx xxxx xxxx xx xx xx xx 137. 2 2 20 20 020 054 505 404 x x x xx xx xx xx xx 138. 2 2 3 41 3 41 43 430 4310 3 430 4 101 x x xxxx x xx xx xx xx xx 139. 215 2153 2152 x xx xx

11 13 13112 13112 13112 131121 x xx x xx

2 2 3 30 3 xxx x x Secondequation: 2 2 3 230 130 101 303 xxx xx xx xx

Only 3 x and 3 x are solutions to the original equation. 3 x and 1 x are extraneous

xx xx xx

2 2 6318 3180 360 303 606 xxx xx

xx xx

2 2 6318 0918 036 033 066 xxx xx xx

The solutions to the original equation are 3 x and 6. x

INSTRUCTOR

USE

143. 2 15xx

Firstequation:

Secondequation:

Only 3 x and 117 2 x are solutions to the original equation. 2 x and 117 2 x are extraneous.

144. 2 1010 xxx

Firstequation:

Secondequation:

The solutions to the original equation are 10 x and 1.1xx is extraneous.

145. The student should have subtracted 15x from both sides so that the equation is equal to zero. By factoring out an x, there are two solutions.

146. The zero-factor property states that if the product of two factors is zero, then one (or both) of the factors must be zero. To solve 2 4415, xx a student factors 4x from the left side of the equation and sets each factor equal to 15. The resulting incorrect solutions are 15 4 x and

14. x To attempt to solve a quadratic equation by factoring, the equation should be in general form first. If it factors, then the zero-factor property can be employed to solve the equation.

147. Equivalent equations are derived from the substitution principle and simplification techniques. They have the same solution(s).

238 x and 25 x are equivalent equations.

148. Remove symbols of grouping, combine like terms, reduce fractions.

Add(or subtract) the same quantity to (from) both sides of the equation.

Multiply (or divide) both sides of the equation by the same nonzero quantity. Interchange the two sides of the equation.

149. Female: 0.43210.44yx

For 16: y 160.43210.44 26.440.432

150. Male: 0.44912.15yx

For 19: y 190.44912.15

Yes, it is likely that both bones came from the same person because the estimated height of a male with a 19inch thigh bone is 69.4 inches.

SectionP.1SolvingEquations 15

copied or duplicated, or posted

a publicly accessible web site,

part.

scanned,

in whole or in

xx xx xx

2 2 15 60 320 303 202 xx xx

xx xx xx x

2 2 2 15 15 40 117 2

xx xx xx xx

2 2 1010 01110 0110 011 01010 xxx

2 2 1010 0910 0101 01010 011 xxx xx xx xx xx

0or6xx

xx xx xx 3 2 5 2

xx xx

2 2 4415 44150 23250

230 250

0.432 61.2inches

26.44

x x x x

31.150.449 69.4 x x x

S ectionP.1Solvi Sectionn P.1Solvi

ONLY

INSTRUCTOR USE

151. (a) 200 million when P

182.171.542 200 10.018 t t

20010.018182.171.542

2003.6182.171.542

2.05817.83

8.7 years

So, the total voting-age population reached 200 million during 1998.

(b) 182.171.542 241 10.018 t t

24110.018182.171.542

2414.338182.171.542

2.79658.83 21 years

The model predicts the total voting-age population will reach 241 million during 2011. This value is reasonable.

152. When 2.5: C 2.50.21

157. 12 and 12

One possible equation is:

Any non-zero multiple of this equation would also have these solutions.

158. 35,35,xx so:

159. 99

6.250.21

5.250.2 26.2526,250 passengers

x x x x

153. False—See Example 14 on page A58.

154. False. 0 x has only one solution to check, 0.

155. –3 and 6

One possible equation is: 2

xx xx xx

360 360 3180

Any non-zero multiple of this equation would also have these solutions.

So, 18 ab or .ab From the original equation you know that 9. b Some possibilities are: 9,9 10,8 or 10 11,7 or 11 12,6 or 12 13,5 or 13 14,4 or 14

156.

160. Isolate the absolute value by subtracting x from both sides of the equation. The expression inside the absolute value signs can be positive or negative, so two separate equations must be solved. Each solution must be checked because extraneous solutions may be included.

16 ChapterPPrerequisites

a publicly accessible

website, in whole or in part.

tt t t

2 4110 4110 15440 xx xx xx

2 2 2 2

12120 120 2120 210 xx xx x xx xx

12120

xx xx

35350 35350 640 xx

abab abab ab

99 ab ab 99OR99 1899

abab

baa baa baa

ba baa

baa

161. (a)

162. Sample answer:

(a) An identity is true for all real numbers, whereas a conditional equation is true for just some (or none) of the real numbers in the domain.

(b) Sample answer: 40 x

minus the product of 4, a, and c, all divided by the product of 2 and a

(d) No. For instance, 2 x is not equivalent to

and 2. x

Section P.2 Solving Inequalities

1. solution set

2. graph

3. negative

4. union

5. key; test intervals

6. zeros; undefined values

7. Interval: 0,9

(a) Inequality: 09 x

(b) The interval is bounded.

8. Interval: 7,4

(a) Inequality: 74 x

(b) The interval is bounded.

9. Interval: 1,5

(a) Inequality: 15 x

(b) The interval is bounded.

10. Interval: 2,10

(a) Inequality: 210 x

(b) The interval is bounded.

11. Interval: 11,

(a) Inequality: 11 x

(b) The interval is unbounded.

12. Interval: 5,

(a) Inequality: 5or5 xx

(b) The interval is unbounded.

has solutions

13. Interval: ,2

(a) Inequality: 2 x

(b) The interval is unbounded.

14. Interval: ,7

(a) Inequality: 7or7xx

(b) The interval is unbounded.

15. 3 x Matches (b).

16. 5 x Matches (h).

17. 34 x Matches (e).

18. 9 2 0 x Matches (d).

19. 333xx Matches (f).

20. 44or4xxx Matches (a).

21. 5 2 1 x Matches (g).

22. 5 2 1 x Matches (c).

2 b

2 4 x

2 x

because

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18 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible webs ite, in whole or in part. 23. 5120 x (a) ? 3 53120 30 Yes, 3 a solution. x xis (b) ? 3 53120 270 No, 3 a solution. x xisnot (c) ? 5 2 5 2 1 2 5 2 5120 0 Yes, a solution. x xis (d) ? 3 2 3 2 9 2 3 2 5120 0 No, a solution. x xisnot 24. 213 x (a) ? 0 2013 13 No, 0 a solution. x xisnot (b) ? 1 4 1 4 1 2 1 4 213 3 No, a solution. x xisnot (c) ? 4 2413 73 Yes, 4 a solution. x xis (d) ? 3 2 3 2 3 2 213 23 No, a solution. x xisnot 25. 2 02 4 x (a) ?? 4 42 02 4 1 02 2 Yes, 4 a solution. x xis (b) ?? 10 102 02 4 022 No, 10 a solution. x xisnot (c) ?? 0 02 02 4 1 02 2 No, 0 a solution. x xisnot (d) ?? 7 2 722 02 4 3 02 8 7 Yes, 2 a solution. x xis 26. 5211 x (a) ?? ? 1 2 1 2 1 2 5211 5111 521 Yes, a solution. x xis (b) ?? ?? 5 2 5 2 5 2 5211 5511 561 No, a solution. x xisnot (c) ?? ?? 4 3 4 3 8 3 5 3 4 3 5211 511 51 No, a solution. x xisnot (d) ?? 0 52011 511 Yes, 0 a solution. x xis 27. 103 x (a) ? 13 13103 33 Yes, 13 a solution. x xis (b) ? 1 1103 113 Yes, 1 a solution. x xis (c) ? 14 14103 43 Yes, 14 a solution. x xis (d) ? 9 9103 1 x 3 No, 9 a solution. xisnot

r equisites requisites

SectionP.2SolvingInequalities 19 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 28. 2315 x (a) ? 6 26315 1515 No, 6 a solution. x xisnot (b) ? 0 20315 315 Yes, 0 a solution. x xis (c) ? 12 212315 2115 No, 12 a solution. x xisnot (d) ? 7 27315 1115 Yes, 7 a solution. x xis 29. 11 44 412 412 3 x x x 30. 1040 4 x x 31. 11 22 3 2 23 23 x x x 32. 155 62 615 or x xx 33. 57 12 x x 34. 712 5 x x 35. 2734 24 2 xx x x 36. 1 2 312 21 xx x x 37. 2 7 2115 72 xx x x 38. 6428 26 3 xx x x 39. 4233 4293 5 xx xx x 40. 1 2 4123 4423 21 xx xx x x 41. 3 4 1 4 67 1 4 xx x x 42. 2 7 32 212714 535 7 xx xx x x 43. 5 1 22 5 1 22 813 43 2 xx xx x 44. 3 4 1 6 91162 364486 122 xx xx x x 45. 3.6113.4 3.614.4 4 x x x 46. 15.61.35.2 1.320.8 16 x x x 47. 1239 226 13 x x x 48. 83513 83513 3318 61 x x x x 12345 x 65432 x 10123 x 2 2 3 43 2 2 5 1 x 1011121314 x 34567 x 01234 x 101 1 2 2 x 1 −2 012 x 2 7 5 x 4321 2 2 1 1 01 x 4 3567 x 34 256 x 12 034 x 6 5789 x 0123 x 1 1 6 1415161718 x 65432 x 10123 x 65401 x 321

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20 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 49. 813213 813613 87313 1536 52 x x x x x 50. 1 3 023120 023320 01320 1321 7 x x x x x 51. 23 44 3 122312 9215 915 22 x x x x 52. 3 05 2 0310 37 x x x 53. 3 1 44 3 1 44 3 1 44 1 x x x 54. 121 3 363 93 39 x x x x 55. 3.20.414.4 4.20.45.4 10.513.5 x x x 56. 1.56 4.510.5 2 91.5621 31.515 210 x x x x There is no solution. 57. 5 55 x x 58. 8 8or8 x xx 59. 1 2 1or1 22 22 x xx xx 60. 3 5 3or3 55 1515 x xx xx 61. 51 x No solution. The absolute value of a number cannot be less than a negative number. 62. No solution. The absolute value of a number cannot be less than a negative number. 63. 206 6206 1426 x x x 64. 80 80or80 880 8 8 x xx xx x x All real numbers x. 65. 3 2 349 349or349 41246 3 x xx xx xx 66. 125 x 5125 624 32 23 x x x x 012345 x 21 x 760 54321 1 3 6420246 22 915 8 x 42 3 0246 7 8 x 0 4 3 1 4 1 1 x 1357 x 911 1112 101314 x 10.513.5 x 88 404 3210123 x −20−10 010 x 20 1520 102530 x 1426 30123 21 x 3 2 −2−1 1 0234 x 210123 x x 60246 42 55

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SectionP.2SolvingInequalities 21 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 67. 3 4 2 33 4or4 22 3838 511 x xx xx xx 68. 2 11 3 2 111 3 2 20 3 30 03 x x x x x 69. 9221 921 1921 1028 54 45 x x x x x x 70. 14317 1414 x x 1414or1414 280 xx xx 71. 9 2 99 22 29 11 22 2109 10 10or10 x x xx xx 72. 7 1 55 7 1 55 3459 453 3453 751 x x x x x x 73. 612 2 x x 74. 315 36 2 x x x 75. 521 24 2 x x x 76. 7 2 2061 216 x x x 77. 438 4128 520 4 xx xx x x 78. 317 337 24 2 xx xx x x 79. 814 14814 622 x x x 80. 2913 2913or2913 22224 112 x xx xx xx 1050 1551015 x 11 101234 x 45 36 x 35282114707 x 12 2911 8 22 164 x 2 7 55 1 1 0 x 10 10 10 10 10 10 10 10 10 10 1010 10 10 10 10 10 10 1010 10 10 10 10 10 10 1024 15 10 9 10

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88. 4 615 x 5 2

6150 615 x x x 5 2 ,

89. 108 x

All real numbers within 8 units of 10.

90. 84 x

All real numbers more than 4 units from 8.

91. The midpoint of the interval 3,3 is 0. The interval represents all real numbers x no more than 3 units from 0. 03 3 x x

92. The graph shows all real numbers more than 3 units from 0. 03 3 x x

93. The graph shows all real numbers at least 3 units from 7. 73 x

94. The graph shows all real numbers no more than 4 units from 1. 14 x

95. All real numbers within 10 units of 12. 1210 x

96. All real numbers at least 5 units from 8. 85 x

97. All real numbers more than 4 units from 3. 34

x x

98. All real numbers no more than 7 units from 6. 67 x

22 ChapterPPrerequisites

Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 81. 13 2 1313 22 27 1 22 2713 7 7or7 x x xx xx 82. 1 2 13 16 616 75 x x x x 83. 50 5 x x 5, 84. 10 x 100 10 x x 10, 85. 30 3 x x 3, 86. 3 x 30 3 x x ,3 87. 7 2 720 27 x x x 7 2 ,

15 10 1 10 10 10 10 10

INSTRUCTOR USE ONLY

SectionP.2SolvingInequalities 23 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 99. 2 30 x (a) 3 x (b) 0 x (c) 3 2 x (d) 5 x ? 2 330 60 ? 2 030 30 ? 2 3 2 3 4 30 0 ? 2 530 220 No, 3 xisnot Yes, 0 xis Yes, 3 2 xis No, 5 xisnot a solution. a solution. a solution. a solution. 100. 2 120 xx (a) 5 x (b) 0 x (c) 4 x (d) 3 x ? 2 55120 80 Yes, 5 a solution. xis ? 2 00120 120 No, 0 a solution. xisnot ? 2 ? 44120 164120 80 Yes, 4 a solution. xis ? 2 ? 33120 93120 00 Yes, 3 a solution. xis 101. 2 3 4 x x (a) ? 5 52 3 54 73 Yes, 5 a solution. x xis (b) ? 4 42 3 44 6 is undefined. 0 No, 4 a solution. x xisnot (c) ? 9 2 9 2 2 3 9 4 2 5 3 17 9 No, 2 a solution. x xisnot (d) ? 9 2 9 2 2 3 9 4 2 133 9 Yes, 2 a solution. x xis 102. 2 2 3 1 4 x x (a) 2 ? 2 2 32 1 24 12 1 8 No, 2 a solution. x xisnot (b) 2 ? 2 1 31 1 14 3 1 5 Yes, 1 a solution. x xis (c) 2 ? 2 0 30 1 04 01 Yes, 0 a solution. x xis (d) 2 ? 2 3 33 1 34 27 1 13 No, 3 a solution. x xisnot 103. 2 2 3 32321 320 101 xxxx xx xx The key numbers are 2 3 and 1. 104. 32 2 2 25 9 9250 9250 00 9250 xx xx xx xx The key numbers are 0 and 25 9

NOT FOR SALE S ectionP.2Solvin Sectiong P.2Solving

x x

16 160

24 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible webs ite, in whole or in part. 105. 115 1 1 55 4 5 404 505 x xx x x xx xx The key numbers are 4 and 5. 106. 2 122 2 2121 24 21 41 21 410 404 101 210 202 101 xxxx xxxx xxx xx xx xx xx xx xx xx xx xx The key numbers are 2,1,1,and 4. 107. 2 2 9 90 330 x x xx Key numbers: 3 x Test intervals: ,3,3,3,3, Test: Is 330?xx Interval x-Value Value of 2 9 x Conclusion ,3 –4 7 Positive 3,3 0 –9 Negative 3, 4 7 Positive Solution set: 3,3

440

numbers:

Test intervals:

Test: Is

Interval x-Value Value of 2 16 x Conclusion ,4 –5 9 Positive 4,4 0 16 Negative 4, 5 9 Positive Solution set: 4,4 109. 2 2 2 225 4425 4210 730 x xx xx xx Key numbers: 7,3xx Test intervals:

Test: Is 730?xx Interval x-Value Value of Conclusion 73xx ,7 –8 11111 Positive 7,3 0 7321 Negative 3, 4 11111 Positive Solution set: 7,3 110. 2 2 31 680 240 x xx xx Key numbers: 2,4xx Test intervals: ,2240 2,4240 4,240 xx xx xx Solution set: ,24, x 321 410234 −6−4−2 0246 x 642 82046 x 73 3 1245 x NOT

Key

4 x

,4,4,4,4,

440?xx

,7,7,3,3,

FOR SALE

SectionP.2SolvingInequalities 25 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 111. 2 2 449 450 510 xx xx xx Key numbers: 5,1xx Test intervals: ,5,5,1,1, Test: Is 510?xx Interval x-Value Value of Conclusion 51xx ,5 6 177 Positive 5,1 0 515 Negative 1, 2 717 Positive Solution set: ,51, 112. 2 2 6916 670 170 xx xx xx Key numbers: 1,7xx Test intervals: ,1170 1,7170 7,170 xx xx xx Solution set: 1,7 113. 2 2 6 60 320 xx xx xx Key numbers: 3,2xx Test intervals: ,3,3,2,2, Test: Is 320?xx Interval x-Value Value of Conclusion 32xx ,3 4 166 Positive 3,2 0 326 Negative 2, 3 616 Positive Solution set: 3,2 114. 2 2 23 230 310 xx xx xx Key numbers: 3,1xx Test intervals: ,3310 3,1310 1,310 xx xx xx Solution set: ,31, 115. 2 230 310 xx xx Key numbers: 3,1xx Test intervals: ,3,3,1,1, Test: Is 310?xx Interval x-Value Value of Conclusion 31xx ,3 4 155 Positive 3,1 0 313 Negative 1, 2 515 Positive Solution set: 3,1 116. 2 2 28 280 420 xx xx xx Key numbers: 2,4xx Test intervals: ,2,2,4,4, Test: Is 420?xx Interval x-Value Value of Conclusion 42xx ,2 –3 717 Positive 2,4 0 428 Negative 4, 5 177 Positive Solution set: ,24, x 65402 31 21 2 1 2 046 7 8 x 321012 x 4321012 x 21 301 x 2101234 35 x

NOT FOR

117. 2 2

31120 311200 3450

xx xx xx

Key numbers: 4 3 5, xx

Test intervals: 44 53 ,,,5,5, Test: Is 3450? xx

119. 2 3180 360 xx xx

Key numbers: 3,6xx Test intervals: ,3,3,6,6, Test: Is 360?xx

26 ChapterPPrerequisites

Cengage

Learning.

Interval x-Value Value of Conclusion 345 xx 4 3 , –3 5840 Positive 4 3 ,5 0 4–520 Negative 5, 6 22122 Positive Solution set: 4 3 ,5, 118. 2 2 26150 26150 xx xx 2 664215 22 6156 4 6239 4 339 22 x

339339 , 2222 xx

2 2 2

22 339339

xx xx xx

Key numbers:

Test intervals:

339 ,26150

,26150 2222 339 ,26150 22

Solution set: 339339 ,, 2222

Interval x-Value Value of Conclusion 36xx ,3 –4 11010 Positive 3,6 0 3–618 Negative 6, 7 10110 Positive Solution set: ,36,

2 2 2 2480 2420 240 220 xxx xxx xx xx Key numbers: 2,2xx Test intervals: 32 32 32 ,22480 2,22480 2,2480 xxx xxx xxx Solution set: ,2 1 21023456 x 4 3 202 x 11345 3 22 393 22 39 + x 2 420468 3 1 0234 x

120. 32

NOT FOR SALE r equisites

SectionP.2SolvingInequalities 27 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 121. 32 32 2 2 33 330 330 310 3110 xxx xxx xxx xx xxx Key numbers: 1,1,3xxx Test intervals: ,1,1,1,1,3,3, Test: Is 3110?xxx Interval x-Value Value of 311xxx Conclusion ,1 –2 51315 Negative 1,1 0 3113 Positive 1,3 2 1313 Negative 3, 4 15315 Positive Solution set: 1,13, 122. 32 32 2 2 2138466 2138520 21342130 21340 213220 xxx xxx xxx xx xxx Key numbers: 13 2 ,2,2xxx Test intervals: 32 32 32 32 13 2 13 2 ,2138520 ,22138520 2,22138520 2,2138520 xxx xxx xxx xxx Solution set: 13 2 ,2,2, 123. 2 2 4410 210 xx x Key number: 1 2 x Test intervals: 11 22 ,,, Test: Is 2 210? x Interval x-Value Value of 2 21 x Conclusion 1 2 , 0 2 11 Positive 1 2 , 1 2 11 Positive Solution set: 1 2 x 124. 2 380xx The key numbers are imaginary: 323 22 i So the set of real numbers is the solution set. x 1 2102345 1012 x 2 1 2 30123 21 x 4 x 860422 13 2

NOT FOR SALE S ectionP.2Solvin Sectiong P.2Solving

NOT FOR SALE r equisites requisites

28 ChapterPPrerequisites

be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2230 xx xx Key numbers: 3 2 0, xx Test intervals: 2 2 2 3 2 3 2 ,02230 0,22230 ,2230 xx xx xx Solution set: 3 2 ,00, 126. 32 2 4120 430 xx xx Key numbers: 0,3xx Test intervals: 2 2 2 ,0430 0,3430 3,430 xx xx xx Solution set: 3, 127. 3 40 220 xx xxx Key numbers: 0,2xx Test intervals: ,2220 2,0220 0,2220 2,220 xxx xxx xxx xxx Solution set: 2,02, 128. 34 3 20 20 xx xx Key numbers: 0,2xx Test intervals: 3 3 3 ,020 0,220 2,20 xx xx xx Solution set: ,02, 129. 23 120xx Key numbers: 1,2xx Test intervals: 23 23 23 ,2120 2,1120 1,120 xx xx xx Solution set: 2,

4 30 xx Key numbers: 0,3xx Test intervals: 4 4 4 ,030 0,330 3,30 xx xx xx Solution set: ,3 131. 41 0 x x Key numbers: 1 0, 4 xx Test intervals: 11 44 ,0,0,,, Test: Is 41 0? x x Interval x-Value Value of 41 x x Conclusion ,0 –1 5 5 1 Positive 1 0, 4 1 8 1 2 4 1 8 Negative 1 , 4 1 3 3 1 Positive Solution set: 1 ,0, 4 1 2012 x 1 4

125. 32

460

130.

INSTRUCTOR

USE ONLY

SectionP.2SolvingInequalities 29 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 132. 2 1 0 11 0 x x xx x Key numbers: 1,0,1xxx Test intervals: ,1,1,0,0,1,1, Interval x-Value Value of Conclusion 11xx x ,1 –2 31 3 22 Negative 1,0 1 2 31 3 22 1 2 2 Positive 0,1 1 2 13 3 22 1 2 2 Negative 1, 2 13 3 22 Positive Solution set: ,10,1 133. 35 0 5 x x Key numbers: 5 ,5 3 xx Test intervals: 55 ,,,5,5, 33 Test: Is 35 0? 5 x x Interval x-Value Value of 35 5 x x Conclusion 5 , 3 0 5 1 5 Positive 5 ,5 3 2 651 253 Negative 5, 6 185 13 65 Positive Solution set: 5 ,5, 3 134. 57 4 12 57412 0 12 x x xx x 1 0 12 x x Key numbers: 1 ,1 2 xx Test intervals: 11 ,,,1,1, 22 Test: Is 1 0? 12 x x Interval x-Value Value of 1 12 x x Conclusion 1 , 2 –1 2 2 1 Negative 1 ,1 2 0 1 1 1 Positive 1, 2 11 55 Negative Solution set: 1 ,1, 2 135. 6 20 1 621 0 1 4 0 1 x x xx x x x Key numbers: 1,4xx Test intervals: 4 ,10 1 4 1,40 1 4 4,0 1 x x x x x x Solution set: ,14, 1 202 1 x 1 02456 3 x 5 3 21012 1 2 x 21012345 x

ectionP.2Solvin

NOT FOR SALE S

Sectiong P.2Solving

NOT FOR SALE r equisites requisites

30 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 136. 12 30 2 1232 0 2 62 0 2 x x xx x x x Key numbers: 2,3xx Test intervals: 62 ,20 2 62 2,30 2 62 3,0 2 x x x x x x Solution interval: 2,3 137. 21 53 21 0 53 2315 0 53 11 0 53 xx xx xx xx x xx Key numbers: 5,3,11xxx Test intervals: 11 ,50 53 11 5,30 53 11 3,110 53 11 11,0 53 x xx x xx x xx x xx Solution set: 5,311, 138. 53 62 5236 0 62 228 0 62 xx xx xx x xx Key numbers: 14,2,6xxx Test intervals: 228 ,140 62 228 14,20 62 228 2,60 62 228 6,0 62 x xx x xx x xx x xx Solution intervals: 14,26, 139. 19 343 19 0 343 4393 0 343 305 0 343 xx xx xx xx x xx Key numbers: 3 3,,6 4 xxx Test intervals: 3305 ,0 4343 3305 ,30 4343 305 3,60 343 305 6,0 343 x xx x xx x xx x xx Solution set: 3 ,36, 4 210123 x x 63 9306912 511 15 15 14 5 2 1005 6 10 x 4202 3 3 4 4 68 x

SectionP.2SolvingInequalities 31 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 140. 11 3 131 0 3 3 0 3 xx xx xx xx Key numbers: 3,0xx Test intervals: 3 ,30 3 3 3,00 3 3 0,0 3 xx xx xx Solution intervals: ,30, 141. 2 2 2 0 9 2 0 33 xx x xx xx Key numbers: 0,2,3xxx Test intervals: ,0 2 ,30 33 2 3,20 33 2 20 33 2 0,30 33 2 3,0 33 xx xx xx xx xx xx xx xx xx xx Solution set: 3,20,3 142. 2 6 0 32 0 xx x xx x Key numbers: 3,0,2xxx Test intervals: 32 ,30 32 3,00 32 0,20 32 2,0 xx x xx x xx x xx x Solution set: 3,02, 143. 2 32 1 11 3121111 0 11 32 0 11 x xx xxxxx xx xx xx Key numbers: 1,1xx Test intervals: 2 2 2 32 ,10 11 32 1,10 11 32 1,0 11 xx xx xx xx xx xx Solution set: ,11, 423101 x 3210123 x 3210123 x 432101234 x

NOT FOR SALE S ectionP.2Solvin Sectiong P.2Solving INSTRUCTOR USE ONLY

NOT FOR SALE r equisites

147. 2 9200 450 xx xx

32 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 144. 2 3 3 14 341341 0 14 412 0 14 62 0 14 xx xx xxxxxx xx xx xx xx xx Key numbers: 4,2,1,6xxxx Test: intervals 62 ,40 14 62 4,20 14 62 2,10 14 62 1,60 14 62 6,0 14 xx xx xx xx xx xx xx xx xx xx Solution set: ,42,16, 145. 2 40 220 x xx Key numbers: 2 x Test intervals: 2 2 2 ,240 2,240 2,40 x x x Domain: 2,2 146. 2 40 220 x xx Key numbers: 2,2xx Test intervals: ,2220 2,2220 2,220 xx xx xx Domain: ,22,

numbers:

Test intervals: ,4,4,5,5, Interval x-Value Value of Conclusion 45xx ,4 0 4520 Positive 4,5 9 2 111 224 Negative 5, 6 212 Positive Domain: ,45,

92920 x xx Key numbers: 9 2 x Test intervals: 9999 ,,,,, 2222 Interval x-Value Value of Conclusion 9292xx 9 , 2 –5 19119 Negative 99 , 22 0 9981 Positive 9 , 2 5 11919 Negative Domain: 99 , 22 149. 2 0 235 0 57 x xx x xx Key numbers: 0,5,7xxx Test intervals: ,50 57 5,00 57 0,70 57 7,0 57 x xx x xx x xx x xx Domain: 5,07, 026 4 x 42 1

Key

4,5xx

148.

8140

NOT FOR SALE S ectionP.2Solvin Sectiong P.2Solving

Key numbers: 2.39,2.26

Test intervals: ,2.26,2.26,2.39,2.39,

set: 1.19,1.30

xa xaxa xaxa

157. 2 2or2 2or2

Matches graph (b)

158. 4 44 44

xb xb bxb

Matches graph (b)

159. must be greater than or equal to zero. axbcc caxbc bcaxbc

Let 1, a then 0 bc and 10. bc

This is true when 5. bc

One set of values is: 1,5,5.abc

(Note: This solution is not unique. The following are also solutions. 2,10 3,15.) abc abc

In general, ,5, 0 akbckk or ,5,5,0akbkckk

SectionP.2SolvingInequalities 33 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 150. 2 0 9 0 33 x x x xx Key numbers: 3,0,3xxx Test intervals: ,30 33 3,00 33 0,30 33 3,0 33 x xx x xx x xx x xx Domain: 3,03, 151. 2 2 2 0.45.2610.2 0.44.940 0.412.350 x x x Key numbers: 3.51 x Test intervals: ,3.51,3.51,3.51,3.51, Solution set: 3.51,3.51 152. 2 2 1.33.782.12 1.31.660 x x Key numbers: 1.13 x Test intervals: ,1.13,1.13,1.13,1.13, Solution set: 1.13,1.13 153. 2 0.512.51.60 xx Key numbers: 0.13,25.13xx Test intervals: ,0.13,0.13,25.13,25.13, Solution set: 0.13,25.13 154.

1.24.82.20

Test intervals: ,4.42,4.42,0.42,0.42,

155. 1 3.4 2.35.2 1 3.40 2.35.2 13.42.35.2 0 2.35.2 7.8218.68 0 2.35.2 x x x x x x

2 2 1.24.83.15.3

xx xx Key numbers: 4.42,0.42xx

Solution set: 4.42,0.42

156. 2 5.8 3.13.7 25.83.13.7 0 3.13.7

x x x x x

intervals: 23.4617.98 ,1.190 3.13.7 23.4617.98 1.19,1.300 3.13.7 23.4617.98 1.30,0 3.13.7 x x x x x x Solution

Solution set: 2.26,2.39

23.4617.98

3.13.7

Key numbers: 1.19,1.30xx Test

160. xaxb

(a) The polynomial is zero when xa or .xb

166. Let number x of dozens of doughnuts sold per day.

Revenue: 4.50 Rx

Cost: 2.75220Cx

(b) : : :

xa xb xaxb

161. 9.000.7513.50

0.754.50 6

x x x

You must produce at least 6 units each hour in order to yield a greater hourly wage at the second job.

162. Let gross x sales per month

10000.043000

x x x

0.042000 $50,000

You must earn at least $50,000 each month in order to earn a greater monthly wage at the second job.

r r r r r

163. 1000121062.50 121.0625 20.0625 0.03125 3.125%

164. 82575012

82575012

8257501500 751500 0.05

r r r r r

The rate must be more than 5%.

165. 1.5268.0Et

(a) 701.5268.080

2.01.5212.0 1.327.89

t t t

The annual egg production was between 70 and 80 billion eggs between 1991 and 1997.

(b) 1.5268.0100 1.5232.0 21.05

t t t

The annual egg production will exceed 100 billion eggs sometime during 2011.

Profit: 4.502.75220 1.75220

601.75220270

2801.75490 160280

PRC xx x x x x

The daily sales vary between 160 and 280 dozen doughnuts per day.

h h h

167. 68.5 1 2.7 68.5 11 2.7 2.768.52.7

65.8 inches71.2 inches h

168. 5030 305030 2080

h h h

The minimum relative humidity is 20 and the maximum is 80.

169. 2210050 LWWL 2

LW LL LL

500 50500 505000

By the Quadratic Formula you have:

Key numbers: 2555 L

Test: Is 2 505000?LL

Solution set: 25552555

13.8 meters36.2 meters L L

170. 22440220 LWWL

LW LL LL

8000 2208000 22080000

By the Quadratic Formula we have:

Key numbers: 1101041 L

Test: Is 2 22080000?LL

Solution set: 11010411101041 45.97 feet174.03 feet L L

34 ChapterPPrerequisites

to a publicly accessible website, in whole

in part.

posted

66676869 65707172 h 65712 8 a x b ++ + ++

NOT FOR SALE

ectionP.2Solvin

171. 2 2 2 2

100011100 11.1 121.10 20.10

r r rr rr

By the Quadratic Formula we have: Critical Numbers: 11.1 r

Since r cannot be negative, 11.10.0488 4.88%. r

Thus, 4.88%. r

500.000212150,000 0.000238150,000

2 2 P xx xx

Key numbers: 90,000 x and 100,000 x

Test intervals: 0,90,000,90,000,100,000,100,000,

The solution set is 90,000,100,000 or 90,000100,000. x The price per unit is 500.0002. R px x

For 90,000,$32.xp For 100,000, x $30. p So, for 90,000100,000, x $30$32. p

173. 22 00 1616160 stvtstt

174. 22 00 1616128 stvtstt

(a) 2 161280 1680 1600 808

tt tt tt tt

It will be back on the ground in 8 seconds.

(b) 2 2 2 2

16128128 161281280 16880 880

tt tt tt tt

Key numbers: 422,422tt

(a) 2 161600 16100 0,10

tt tt tt

It will be back on the ground in 10 seconds.

(b) 2 2 2 2

16160384 161603840 1610240 10240 460 tt tt

Key numbers: 4,6tt

Test intervals: ,4,4,6,6,

175. 1 11 11 1 1 111 2 22 22 2 2 RR RRRR RRR R R R Because 1, R 1 1 1 1 1 1 2 1 2 2 10 2 2 0. 2 R R R R R R Because 1 0, R the only key

is 1 2. R The inequality is

when 1 2 ohms. R

172. 500.0002 Rxx and 12150,000Cx 2 2 PRC xxx xx

1,650,000 0.000238150,0001,650,000 0.0002381,800,0000

tt tt

Solution set: 4 seconds6 seconds t

Test intervals: ,422,422,422, 422, Solution set: 0 seconds 422 seconds t and 422 seconds8 seconds t

number

satisfied

NOT FOR SALE

Sectiong P.2Solving

177. False. If c is negative, then .acbc

178. False. If 108, x then 10 x and 8. x

179. True

The y-values are greater than zero for all values of x

180. When each side of an inequality is multiplied or divided by a negative number the direction of the inequality symbol must be reversed.

Section P.3 Graphical Representation of Data

1. (a) v horizontal real number line

(b) vi vertical real number line

(d) iv four regions of the coordinate plane

(e) iii directed distance from the y-axis

(f) ii directed distance from the x-axis

(b) 2 2 2 2000168.5472.1 2472.1168.5 14.67 3.83 d d d d The minimum depth is 3.83 inches.

176. (a)

2. Cartesian 3. Distance Formula 4. Midpoint Formula 5. :2,6,:6,2,:4,4,:3,2 ABCD 6. 35 22 :,4;:0,2;:3,,:6,0 ABCD 7. 8. 9. 10. 11. 3,4 12. 4,8 13. 5,5 14. 12,0 15. 0 x and 0 y in Quadrant IV. 16. 0 x and 0 y in Quadrant III. 17. 4 x and 0 y in Quadrant II. 18. 2 x and 3 y in Quadrant I. 19. 5 y in Quadrant III or IV. d 4 6 8 10 12 Load 2223.9 5593.9 10,312 16,37823,792 Depthofthebeam Maximum safe load d 4681012 5,000 10,000 15,000 20,000 25,000 L 42 6246 2 4 6 2 4 6 y x 21 3123 1 2 2 1 3 4 y x y x 42 62468 4 2 6 2 4 6 8 21 323 1 2 2 1 3 4 y x NOT FOR SALE r equisites requisites INSTRUCTOR USE ONLY 1 in III or IV. IV. S © Cengage Learning. All Rights Reserved.

20. 4 x in Quadrant I or IV.

21. , xy is in the second Quadrant means that , xy is in Quadrant III.

22. If , xy is in Quadrant IV, then , xy must be in Quadrant III.

23. ,,0xyxy means x and y have the same signs. This occurs in Quadrant I or III.

24. If 0, xy then x and y have opposite signs. This happens in Quadrant II or IV. 25.

26. 27. 538 d 28. 1877 d 29.

d 30. 461010 d 31. 22 2121 2 2 22 3266 512 25144 13units dxxyy 32. 22 2121 22 22 08205 815 64225 289 17units dxxyy 33. 22 2121 22 22 5114 65 3625 61units dxxyy 34. 22 2121 22 22 3123 25 425 29units dxxyy 35. 22 2121 22 22 14 21 23 37 23 949 49 277 36 277 units 6 dxxyy Month, x Temperature, y 1 –39 2 –39 3 –29 4 –5 5 17 6 27 7 35 8 32 9 22 10 8 11 –23 12 –34 y x 1234567 4000 4500 5000 5500 6000 7000 6500 7500 Year(0 ↔2000) Number of stores Temperature ( i n ° F) Month(1 ↔ January) x 40 10 30 20 10 20 30 2681012 40 0 y NOT FOR SALE S ectionP.3GraphicalRepresent Sectiona P.3GraphicalRepresent INSTRUCTOR USE ONLY © Cengage Learning. All Rights Reserved.

235

41. (a) The distance between 1,1 and 9,1 is 10. The distance between 9,1 and 9,4 is 3. The distance between 1,1 and 9,4 is

38 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 36. 22 2121 2 2 22 25 13 34 17 34 149 916 457 144 457 units 12 dxxyy 37. 22 2121 2 2 22 12.54.24.83.1 8.31.7 68.892.89 71.78 8.47units dxxyy 38. 22 2121 2 2 22 3.99.58.22.6 13.410.8 179.56116.64 296.2 17.21units dxxyy

The

22 4052169255.

40. (a)

22 22 Distance13150 12516913 13,5,13,0 Distance5055 1,0,13,0 Distance1131212 (b) 222 5122514416913

39. (a) The distance between 0,2 and 4,2 is 4. The distance between 4,2 and 4,5 is 3.

distance between 0,2 and 4,5 is

(b) 222 43169255

1,0,13,5

2 2 91411009109.

103109109

2 2 22 Distance1552 47164965 1,5,1,2 Distance525277 1,2,5,2 Distance1544 (b) 2 22 4716496565 43. 22 1 22 2 22 3 4201415 4105252550 211593645 d d d 222 54550 44. 2 2 1 22 2 2 2 3 315316420 531541620 511336440 d d d 222 202040 45. 22 1 22 2 22 3 12 133242529 322425429 123494958 d d d dd 46. 22 1 22 2 2 2 3 12 429343640 247936440 2237161632 d d d dd

(b)

42. (a) 1,5,5,2

NOT FOR SALE r equisites

SectionP.3GraphicalRepresentationofData 39 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part. 47. (a) (b) 22 9171643610 d (c) 9171 ,5,4 22 48. (a) (b) 22 161202514413 d (c) 161207 ,,6 222 49. (a) (b) 4451022 6422517 d (c) 445105 ,0, 222 50. (a) (b) 724822 8114415 d (c) 72485 ,,2 222 51. (a) (b) 514222 364210 d (c) 1524 ,2,3 22 52. (a) (b) 21010222 646482 d (c) 210102 ,6,6 22 53. (a) (b) 15422 1 223 182 9 93 d (c) 5212431 7 ,1, 226 x (1,1) (9,7) 12 10 8 6 4 2 2 246810 y x (6,0) 12(1,12) 10 8 6 4 2 2 246810 y x (4,10) (4,5) 8464268 6 4 2 6 8 10 y (7,4) (2,8) 8 6 2 1086 2 4 22 x y x (5,4) (1,2) 1 12345 3 1 4 5 y x 2 4 6 8 10 246810 (2,10) (10,2) y x ()() ,1 2 5 31 4 2 2 2 3 1 2 5 2 1 2 1 2 3 2 5 2 , y 21 NOT FOR SALE S ectionP.3GraphicalRepresent Sectiona P.3GraphicalRepresent INSTRUCTOR

USE ONLY

57.

The plane flies about 192 kilometers.

42185012 2438 2020 2505 45

58. 22 22

The pass is about 45 yards.

xxyy

59. midpoint,1212 22

2003200741744656 , 22

2005,4415

In 2005, the sales for Big Lots were about $4415 million.

xxyy

60. midpoint,1212 22

2003200728004243 , 22

2005,3521.50

In 2005, the sales for the Dollar Tree were about $3521.50 million.

40 ChapterPPrerequisites © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 54. (a) (b) 111122 3632 112 36366 d (c) 1111 15 3632 , , 22 412 55. (a) (b) 6.23.75.41.822 98.0112.96110.97 d (c) 6.23.75.41.8 ,1.25,3.6 22 56. (a) (b) 22 16.85.612.34.9

16.85.612.34.9 ,5.6,8.6 22

501.7654.76556.52

(c)

36,900

22 120150

3041 192.09 d

61. 22,450,1 22,354,2 12,151,4 62. 36,633,3 56,331,0 36,033,3 16,335,0 63. 74,283,6 24,282,10 24,482,4 74,483,4 64. 510,865,2 310,667,0 710,663,0 510,265,4 1 1 3 32 1 1 1 1 6 6 6 66 3 6 3 2 2 ,6 , () () x y x 2 2 4 6 8 22 446 (62,54) (37,18) y 5 5 10 15 20 15105 205 (16.8,12.3) (5.6,4.9) x y

equisites

INSTRUCTOR

Rights Reserved.

requisites

USE ONLY

Learning. All

65. To reflect the vertices in the y-axis, negate each xcoordinate.

each x-coordinate.

SectionP.3GraphicalRepresentationofData 41

Cengage Learning. All Rights

May not be scanned, copied or duplicated, or posted to a publicly accessible web site, in whole or in part.

Reserved.

OriginalPointReflectedPoint 1,5 1,5 5,4 5,4 2,2 2,2 66. Negate

OriginalPointReflectedPoint 4,5 4,5 2,3 2,3 5,1 5,1

OriginalPointReflectedPoint 0,3 0,3 3,2 3,2 6,3 6,3 3,8 3,8 68.

OriginalPointReflectedPoint 7,1 7,1 5,4 5,4 1,4 1,4 3,1 3,1 69. 2 222 1 2222 2 22 22 3 2213422025 1251364535 21351865 d d d Since 222 123 204565,ddd the triangle is a right triangle. 70. 2 222 1 2 222 2 2 222 3 2451242025 10441634535 102458165 d d d Since 222 123 204565,ddd the triangle is a right triangle. 71. On the x-axis, 0 y On the y-axis, 0 x x (4,1) (10,4) (2,5) 2 2 4 6 8 10 2 26810 y d1 d2 d3 x (2,1) (1,5) (2,3) 62 4 6 6 4 246 y d1 d2 d3 NOT

SALE S ectionP.3GraphicalRepresent Sectiona P.3GraphicalRepresent INSTRUCTOR

each x-coordinate.

67. Negate

Negate each x-coordinate.

FOR

USE ONLY

72.

(a) The point is reflected through the y-axis.

(b) The point is reflected through the x-axis.

73. The highest price of milk is approximately $3.87. This occurred in 2007.

74. Price of milk in 1996$2.73

Highest price of milk$3.87 in 2007 3.872.73

Percent change41.8% 2.73

75. (a) Cost during Super Bowl XXXVIII 2004$2,302,000

Cost during Super Bowl XXXIV 2000$2,100,000

Increase$2,302,000$2,100,000$202,000 $202,000

Percent increase0.096 or 9.6% $2,100,000

(b) Cost during Super Bowl XLII 2008$2,700,000

Cost during Super Bowl XXXIV 2000$2,100,000

Increase$2,700,000$2,100,000$600,000 $600,000

Percent increase0.286 or 28.6% $2,100,000

76. (a) Cost during 2002 awards$1,290,000

Cost during 1996 awards$795,000

Increase$1,290,000$795,000$495,000 $495,000

Percent increase0.623 or 62.3% $795,000

(b) Cost during 2007 awards$1,700,000

Cost during 1996 awards$795,000

Increase$1,700,000$795,000$905,000 $905,000

Percent increase1.138 or 113.8% $795,000

77. The number of performers elected each year seems to be nearly steady except for the middle years. Five performers will be elected in 2010.

78. (a) The minimum wage had the greatest increase in the 2000s.

(b) Minimum wage in 1990:$3.80

Minimum wage in 1995:$4.25 $4.25$3.80

Percent increase:10011.8% $3.80

Minimum wage in 1995:$4.25

Minimum wage in 2009:$7.25 $7.25$4.25

Percent increase:10070.6% $4.25

The minimum wage will be approximately $12.37 in the year 2013.

(d) Answers will vary. Sampleanswer: No, the prediction is too high because it is likely that the percent increase over a 4-year period (2009–2013) will be less than the percent increase over a 14-year period (1995–2009).

42 ChapterPPrerequisites