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Daytona State

Miami-Da de Colleg e

Julie Miller

Daytona State College

Donna Gerken

PRECALCULUS

Printed in the United States of America. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

This book is printed on acid-free paper.

1 2 3 4 5 6 7 8 9 0 DOW/DOW 1 0 9 8 7 6

ISBN 978–0–07–803560–9

MHID 0–07–803560–0

ISBN 978–0–07–753818–7 (Annotated Instructor’s Edition)

MHID 0–07–753818–8

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All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

Names: Miller, Julie, 1962- | Gerken, Donna.

Title: Precalculus/Julie Miller, Donna Gerken.

Description: First edition. | New York, NY: McGraw-Hill Education, [2017] | Includes index.

Identifiers: LCCN 2015040407 | ISBN 9780078035609 (alk. paper) | ISBN 0078035600 (alk. paper) | ISBN 9780077538187 (alk. paper) | ISBN 0077538188 (alk. paper)

Subjects: LCSH: Precalculus—Textbooks. | Functions—Textbooks.

Classification: LCC QA303.2 .M534 2017 | DDC 510—dc23 LC record available at http://lccn.loc.gov/2015040407

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

About the Authors

Julie Miller

is from Daytona State College where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at DSC, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored textbooks in developmental mathematics, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

“My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I remember doing simple calculations with him and using graph paper to plot data points for his experiments. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me, and I’d like to see math come alive for my students.”

is a professor at Miami Dade College where she has taught developmental courses, honors classes, and upper-level mathematics classes for decades. Throughout her career she has been actively involved with many projects at Miami Dade including those on computer learning, curriculum design, and the use of technology in the classroom. Donna’s bachelor of science in mathematics and master of science in mathematics are both from the University of Miami.

Letter from the Authors

Precalculus is a foundation course essential to success in Calculus and all subsequent courses in science, technology, engineering, and mathematics. To support student success in this course, we accommodate a variety of learning styles by bringing together a seamless integration of print and digital content. The clear, concise writing style and pedagogical features of our textbook continue throughout the online content in ConnectMath, throughout our instructional videos, and throughout the adaptive reading and learning experience of SmartBook. Furthermore, to enhance preparation for Calculus, we have dedicated exercise sets that specifically target skills needed in Calculus.

The main objectives of this Precalculus textbook and its print and digital content are threefold:

• To provide students with a clear and logical presentation of fundamental concepts that will prepare them for continued study in mathematics.

• To help students develop logical thinking and problem-solving skills that will benefit them in all aspects of life.

• To motivate students by demonstrating the significance of mathematics in their lives through practical applications.

Julie Miller

donna gerken

julie.miller.math@gmail.com

donna.gerken.math@gmail.com

Dedications o our students: Enjoy your journey with mathematics and the doors it opens to science, business, and the natural world around you. —Julie Miller or Eddie and Aurora—true friendship needs no words, but it does require the ability to appear interested while someone talks about trigonometry applications during every shared holiday dinner. Donna Gerken

Donna Gerken

Applications Index xxi

CHAPTER R Review of Prerequisites 1

Section R.1 Sets and the Real Number Line 2

Section R.2 Exponents and Radicals 16

Section R.3 Polynomials and Factoring 29

Problem Recognition Exercises: Simplifying Algebraic Expressions 42

Section R.4 Rational Expressions and More Operations on Radicals 43

Section R.5 Equations with Real Solutions 54

Section R.6 Complex Numbers and More Quadratic Equations 71

Section R.7 Applications of Equations 82

Section R.8 Linear, Compound, and Absolute Value Inequalities 95

Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 106

Algebra for Calculus 106

Equations and Inequalities for Calculus 107

Key Concepts 108

Review Exercises 112

Test 115

CHAPTER 1 Functions and Relations 119

Section 1.1 The Rectangular Coordinate System and Graphing Utilities 120

Section 1.2 Circles 131

Section 1.3 Functions and Relations 137

Section 1.4 Linear Equations in Two Variables and Linear Functions 151

Section 1.5 Applications of Linear Equations and Modeling 167

Problem Recognition Exercises: Comparing Graphs of Equations 182

Section 1.6 Transformations of Graphs 183

Section 1.7 Analyzing Graphs of Functions and Piecewise-Deﬁned Functions 197

Section 1.8 Algebra of Functions and Function Composition 216

Key Concepts 229

Review Exercises 231

Test 236

Cumulative Review Exercises 237

CHAPTER 2 Polynomial and Rational Functions 239

Section 2.1 Quadratic Functions and Applications 240

Section 2.2 Introduction to Polynomial Functions 254

Section 2.3 Division of Polynomials and the Remainder and Factor Theorems 270

Section 2.4 Zeros of Polynomials 283

Section 2.5 Rational Functions 299

Problem Recognition Exercises: Polynomial and Rational Functions 322

Section 2.6 Polynomial and Rational Inequalities 323

Problem Recognition Exercises: Solving Equations and Inequalities 336

Section 2.7 Variation 337

Key Concepts 345

Review Exercises 348

Test 351

Cumulative Review Exercises 353

CHAPTER 3 Exponential and Logarithmic Functions 355

Section 3.1 Inverse Functions 356

Section 3.2 Exponential Functions 368

Section 3.3 Logarithmic Functions 381

Problem Recognition Exercises: Analyzing Functions 396

Section 3.4 Properties of Logarithms 397

Section 3.5 Exponential and Logarithmic Equations and Applications 406

Section 3.6 Modeling with Exponential and Logarithmic Functions 420

Key Concepts 436

Review Exercises 439

Test 441

Cumulative Review Exercises 443

CHAPTER 4 Trigonometric Functions 445

Section 4.1 Angles and Their Measure 446

Section 4.2 Trigonometric Functions Deﬁned on the Unit Circle 462

Section 4.3 Right Triangle Trigonometry 481

Section 4.4 Trigonometric Functions of Any Angle 497

Section 4.5 Graphs of Sine and Cosine Functions 508

Section 4.6 Graphs of Other Trigonometric Functions 527

Problem Recognition Exercises: Comparing Graphical Characteristics of Trigonometric Functions 539

Section 4.7 Inverse Trigonometric Functions 540

Key Concepts 556

Review Exercises 561

Test 564

Cumulative Review Exercises 566

CHAPTER 5 Analytic Trigonometry 567

Section 5.1 Fundamental Trigonometric Identities 568

Section 5.2 Sum and Difference Formulas 578

Section 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 591

Section 5.4 Product-to-Sum and Sum-to-Product Formulas 601

Section 5.5 Trigonometric Equations 607

Problem Recognition Exercises: Trigonometric Identities and Trigonometric Equations 622

Key Concepts 623

Review Exercises 625 Test 627

Cumulative Review Exercises 628

CHAPTER 6 Applications of Trigonometric Functions 629

Section 6.1 Applications of Right Triangles 630

Section 6.2 The Law of Sines 642

Section 6.3 The Law of Cosines 656

Problem Recognition Exercises: Solving Triangles Using a Variety of Tools 666

Section 6.4 Harmonic Motion 667

Key Concepts 677

Review Exercises 679 Test 681

Cumulative Review Exercises 683

CHAPTER 7 Trigonometry Applied to Polar Coordinate Systems and Vectors 685

Section 7.1 Polar Coordinates 686

Section 7.2 Graphs of Polar Equations 697

Problem Recognition Exercises: Comparing Equations in Polar and Rectangular Form 711

Section 7.3 Complex Numbers in Polar Form 713

Section 7.4 Vectors 726

Section 7.5 Dot Product 743

Key Concepts 757

Review Exercises 759 Test 762

Cumulative Review Exercises 763

CHAPTER 8 Systems of Equations and Inequalities 765

Section 8.1 Systems of Linear Equations in Two Variables and Applications 766

Section 8.2 Systems of Linear Equations in Three Variables and Applications 780

Section 8.3 Partial Fraction Decomposition 791

Section 8.4 Systems of Nonlinear Equations in Two Variables 801

Section 8.5 Inequalities and Systems of Inequalities in Two Variables 810

Problem Recognition Exercises: Equations and Inequalities in Two Variables 821

Section 8.6 Linear Programming 821

Key Concepts 830

Review Exercises 832 Test 834

Cumulative Review Exercises 835

CHAPTER 9 Matrices and Determinants and Applications 837

Section 9.1 Solving Systems of Linear Equations Using Matrices 838

Section 9.2 Inconsistent Systems and Dependent Equations 849

Section 9.3 Operations on Matrices 859

Section 9.4 Inverse Matrices and Matrix Equations 876

Section 9.5 Determinants and Cramer’s Rule 886

Problem Recognition Exercises: Using the Multiple Methods to Solve Systems of Linear Equations 899

Key Concepts 899

Review Exercises 901 Test 904

Cumulative Review Exercises 905

CHAPTER 10

Analytic Geometry 907

Section 10.1 The Ellipse 908

Section 10.2 The Hyperbola 925

Section 10.3 The Parabola 941

Problem Recognition Exercises: Comparing Equations of Conic Sections and the General Equation 954

Section 10.4 Rotation of Axes 956

Section 10.5 Polar Equations of Conics 969

Section 10.6 Plane Curves and Parametric Equations 979

Key Concepts 994

Review Exercises 997 Test 1001

Cumulative Review Exercises 1003

Section 11.1 Sequences and Series 1006

Section 11.2 Arithmetic Sequences and Series 1017

Section 11.3 Geometric Sequences and Series 1028

Problem Recognition Exercises: Comparing Arithmetic and Geometric Sequences and Series 1041

Section 11.4 Mathematical Induction 1041

Section 11.5 The Binomial Theorem 1048

Section 11.6 Principles of Counting 1054

Section 11.7 Introduction to Probability 1066

Key Concepts 1080

Review Exercises 1083 Test 1086

Cumulative Review Exercises 1088

CHAPTER 12 Preview of Calculus (Online)

Section 12.1 Introduction to Limits Through Tables and Graphs

Section 12.2 Algebraic Properties of Limits

Problem Recognition Exercises: Limits and Continuity

Section 12.3 The Tangent Problem: Introduction to Derivatives

Section 12.4 Limits at Inﬁnity and Limits of Sequences

Section 12.5 Area Under a Curve

Key Concepts Review Exercises Test

Additional Topics Appendix A-1 (Online)

Student Answer Appendix SA-1

Instructor Answer Appendix IA-1 (AIE only)

Credits C-1

Index I-1

Key Features

Clear, Precise Writing

Because a diverse group of students take this course, Julie Miller and Donna Gerken have written this manuscript to use simple and accessible language. Through their friendly and engaging writing style, students are able to understand the material easily.

Exercise Sets

The exercises at the end of each section are graded, varied, and carefully organized to maximize student learning:

• Prerequisite Review Exercises begin the section-level exercises and ensure that students have the foundational skills to complete the homework sets successfully.

• Concept Connections prompt students to review the vocabulary and key concepts presented in the section.

• Core Exercises are presented next and are grouped by objective. These exercises are linked to examples in the text and direct students to similar problems whose solutions have been stepped-out in detail.

• Mixed Exercises do not refer to specific examples so that students can dip into their mathematical toolkit and decide on the best technique to use.

• Write About It exercises are designed to emphasize mathematical language by asking students to explain important concepts.

• Technology Connections require the use of a graphing utility and are found at the end of exercise sets. They can be easily skipped for those who do not encourage the use of calculators.

• Expanding Your Skills Exercises challenge and broaden students’ understanding of the material.

Problem Recognition Exercises

Problem Recognition Exercises appear in strategic locations in each chapter of the text. These exercises provide students with an opportunity to synthesize multiple concepts and decide which problem-solving technique to apply to a given problem.

Exercises for Calculus

• Algebra for Calculus exercises specifically target the skills students use in calculus such as the simplification of a limit, and the simplification after taking a derivative.

• Equations and Inequalities for Calculus is another exercise set that provide sample equations and inequalities seen in calculus. These include the important skills of finding the values that make an expression zero or undefined to find the critical numbers in calculus.

Examples

• The examples in the textbook are stepped-out in detail with thorough annotations at the right explaining each step.

• Following each example is a similar Skill Practice exercise to engage students by practicing what they have just learned.

• For the instructor, references to an even-numbered exercise are provided next to each example. These exercises are highlighted with blue circles in the exercise sets and mirror the related examples. With increased demands on faculty time, this has been a popular feature that helps faculty write their lectures and develop their presentation of material. If an instructor presents all of the highlighted exercises, then each objective of that section of text will be covered.

Modeling and Applications

One of the most important tools to motivate our students is to make the mathematics they learn meaningful in their lives. The textbook is filled with robust applications and numerous opportunities for mathematical modeling for those instructors looking to incorporate these features into their course.

Callouts

Throughout the text, popular tools are included to highlight important ideas. These consist of:

• Tip boxes that offer additional insight to a concept or procedure.

• Avoiding Mistakes boxes that fend off common mistakes.

• Point of Interest boxes that offer interesting and historical mathematical facts.

• Instructor Notes to assist with lecture preparation.

Graphing Calculator Coverage

Material is presented throughout the book illustrating how a graphing utility can be used to view a concept in a graphical manner. The goal of the calculator material is not to replace algebraic analysis, but rather, to enhance understanding with a visual approach. Graphing calculator examples are placed in self-contained boxes and may be skipped by instructors who choose not to implement the calculator. Similarly, the graphing calculator exercises are found at the end of the exercise sets and may also be easily skipped.

End-of-Chapter Materials

The textbook has the following end-of-chapter materials for students to review before test time:

• Brief summary with references to key concepts. A detailed summary is located at www.mhhe.com/millerprecalculus.

• Chapter review exercises.

• Chapter test.

• Cumulative review exercises. These exercises cover concepts in the current chapter as well as all preceding chapters.

Supplement Package

Supplements for the Instructor

Author-Created Digital Media

Digital assets were created exclusively by the author team to ensure that the author voice is present and consistent throughout the supplement package.

• Donna Gerken ensures that each algorithm in the online homework has a stepped-out solution that matches the textbook’s writing style.

• Julie Miller created video content (lecture videos, exercise videos, graphing calculator videos, and Excel videos) to give students access to classroomlike instruction by the author.

• Julie Miller constructed over 50 dynamic math animations to accompany the text. The animations are diverse in scope and give students an interactive approach to conceptual learning. The animated content illustrates difficult concepts by leveraging the use of on-screen movement where static images in the text may fall short. They are organized in Connect hosted by ALEKS by chapter and section.

The Instructor’s Resource Manual (IRM) is a printable electronic supplement put together by the author team. The IRM includes Guided Lecture Notes, Classroom Activities using Wolfram Alpha, and Group Activities.

• The Guided Lecture Notes are keyed to the objectives in each section of the text. The notes step through the material with a series of questions and exercises that can be used in conjunction with lecture.

scramble questions and answer keys for multiple versions of a single test. Hundreds of text-specific, open-ended, and multiple-choice questions are included in the question bank.

Annotated Instructor’s Edition

• Answers to exercises appear adjacent to each exercise set, in a color used only for annotations.

• Instructors will find helpful notes within the margins to consider while teaching.

• References to even-numbered exercises appear in the margin next to each example for the instructor to use as Classroom Examples.

Power Points present key concepts and definitions with fully editable slides that follow the textbook. An instructor may project the slides in class or post to a website in an online course.

• The Classroom Activities using Wolfram Alpha promote active learning in the classroom by using a powerful online resource.

• A Group Activity is available for each chapter of the book to promote classroom discussion and collaboration.

The Instructor’s Solution Manual provides comprehensive, worked-out solutions to all exercises in the section exercises, review exercises, problem recognition exercises, chapter tests, and cumulative reviews. The steps shown in the solutions match the style and methodology of solved examples in the textbook.

TestGen is a computerized test bank utilizing algorithmbased testing software to create customized exams quickly. This user-friendly program enables instructors to search for questions by topic, format, or difficulty level; to edit existing questions, or to add new ones; and to

Supplements for the Student

Student Worksheets including guided lecture notes that step through the key objectives and Problem Recognition Exercise worksheets.

ALEKS® Prep for Precalculus

ALEKS Prep for Precalculus focuses on prerequisites and introductory material for Precalculus. These prep products can be used during the first 3 weeks of a course to prepare students for future success in the course and to increase retention and pass rates.

Connect Math® Hosted by ALEKS

Connect Math Hosted by ALEKS Corp. is an exciting, new assignment and assessment ehomework platform. Starting with an easily viewable, intuitive interface, students will be able to access key information, complete homework assignments, and utilize an integrated, mediarich eBook.

Smartbook® is the first and only adaptive reading experience available for the higher education market. Powered by the intelligent and adaptive LearnSmart engine, SmartBook facilitates the reading process by identifying what content a student knows and doesn’t know. As a student reads, the material continously adapts to ensure the student is focused on the content he or she needs the most to close specific knowledge gaps.

Detailed Chapter Summaries are available at www.mhhe.com/millerprecalculus.

Efficient. Easy to Use. Effective. Engaging. Gives Your Students the ALEKS Advantage

Are your students prepared for your course? Do they learn at different paces? Is there inconsistency between homework and test scores? ALEKS successfully addresses these core challenges and more.

With decades of scientiﬁc research behind its creation, ALEKS offers the most advanced adaptive learning technology that is proven to increase student success in math.

Optimized, Structured Learning

Using adaptive artiﬁcial intelligence, ALEKS identiﬁes precisely what each student knows and doesn’t know, and prescribes an individualized learning plan tailored to their unique strengths and weaknesses:

• Targets critical knowledge gaps

• Open-response environment

• Motivates student learning

• Presents only topics students are ready to learn

• Enhances learning with interactive resources

• Provides a structured learning path

Student-Friendly Learning Experience

ALEKS is designed to meet the needs of today’s students. A clean, modern, mobile-ready interface allows students to easily navigate their learning, track their progress and manage their assignments from anywhere.

“ I evaluated many different options, and ALEKS provided, by far, the best cycle of assessment and learning that allows for individualized instructional paths . . . no other program matches ALEKS.”

—Professor Eliza Gallagher, Clemson University, SC

THE ALEKS Instructor Module includes intuitive customization and management features that help save you valuable time and effort. Easily manage your courses and track student progress, all through one simple interface.

• Create learning goals with due dates that align with your textbook/syllabi and to pace student learning

• Implementation services and training help make setup simple and timely

• 100% mobile-ready allows you to manage your classes from anywhere

• LMS integration offers single sign-on and gradebook sync capabilities

ALEKS Reporting provides detailed data on student progress, allowing you to quickly identify intervention needs and to better understand student learning behaviors. View data for individual students up to the multi-campus level.

View a daily breakdown of how students learn in ALEKS, including the exact problems they attempt and their answers. This will help you to identify common mistakes and understand their behavior pattern, such as when they study and how frequently.

View student progress in a course area or at the individual topic level, including which topics students are struggling with the most.

Use this data to inform your teaching, group students based on similar knowledge levels, and shape a meaningful learning experience for your students.

Connect Math Hosted by ALEKS

Built By Today’s Educators, For Today’s Students

Fewer clicks means more time for you...

Change assignment dates right from the home page.

Teaching multiple sections? Easily move from one to another.

Online Exercises were carefully selected and developed to provide a seamless transition from textbook to technology.

Edit, print, and view assignments in just one click.

...and your students.

For consistency, the guided solutions match the style and voice of the original text as though the author is guiding the students through the problems.

Quality Content For Today’s Online Learners

Why SmartBook? Because it’s more than just words on a page.

Students today thrive on efficiency, mobility, and motivation. And SmartBook delivers. SmartBook is the first adaptive reading experience designed to change the way students learn. Students and instructors can enjoy access to SmartBook anywhere, anytime (now available offline) with a new and improved mobile interface. If students still prefer holding a text as they study, they can order a loose-leaf copy of their textbook for a significant discount.

SmartBook breaks down the learning experience into four stages: Preview, Read, Practice, and Recharge. Each stage provides personalized guidance and just-in-time remediation to ensure students stay focused and learn as efficiently as possible. With LearnSmart technology, questions are designed to foster critical thinking and conceptual learning.

Reports are also available to both students and instructors that track progress and show each student’s strengths and weaknesses. What does this mean for you? Teach a more informed classroom and provide more personalized guidance.

The ALEKS ® Initial Assessment is an artificially intelligent (AI), diagnostic assessment that identifies precisely what a student knows. Instructors can then use this information to make more informed decisions on what topics to cover in more detail with the class.

Our Commitment to Market Development and Accuracy

McGraw-Hill’s Development Process is an ongoing, never-ending, market-oriented approach to building accurate and innovative print and digital products. We begin developing a series by partnering with authors who desire to make an impact within their discipline to help students succeed. Next, we share these ideas and manuscript with instructors for review for feedback and to ensure that the authors’ ideas represent the needs within that discipline. Throughout multiple drafts, we help our authors adapt to incorporate ideas and suggestions from reviewers to ensure that the series carries the same pulse as today’s classrooms. With any new series, we commit to accuracy across the series and its supplements. In addition to involving instructors as we develop our content, we also utilize accuracy checks through our various stages of development and production. The following is a summary of our commitment to market development and accuracy:

1. 3 drafts of author manuscript

2. 2 rounds of manuscript review

3. 3 rounds of accuracy checking

4. 3 rounds of proofreading and copyediting

5. Toward the final stages of production, we incorporate additional rounds of quality assurance from instructors as they help contribute toward our digital content and print supplements

This process then will start again immediately upon publication in anticipation of the next edition. With our commitment to this process, we are confident that our series has the most developed content the industry has to offer, thus pushing our desire for quality and accurate content that meets the needs of today’s students and instructors.

Acknowledgments:

Paramount to the development of Precalculus was the invaluable feedback provided by the instructors from around the country who reviewed the manuscript or attended a market development event over the course of the several years the text was in development.

A Special Thanks to All of the Event Attendees Who Helped Shape Precalculus.

Focus groups and symposia were conducted with instructors from around the country to provide feedback to editors and the authors and ensure the direction of the text was meeting the needs of students and instructors.

Halina Adamska, Broward College–Central

Mary Beth Angeline, West Virginia University

Colleen Beaudoin, University of Tampa

Rachel Black, Central New Mexico Community College

Tony Bower, Saint Phillips College

Bowen Brawner, Tarleton State University

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Manuscript Reviewers

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Carl Clark, Indian River State College

Beth Clickner, Hillsborough Community College

Thomas Cooper, University of North Georgia

Christina Cornejo, Erie Community College

Jim Cotter, Truckee Meadows Community College

Cindy Cummins, Ozarks Technical Community College

Leslie Dalrymple, Texas State University–San Marcos

Hall Dave, Portland Community College

Nelson De La Rosa, Miami Dade College

Jerry Degroot, Purdue University

Noemi DeHerrera, Houston Community College

Reynolds Dennis, Portland Community College

Alan Dinwiddie, Front Range Community College

Christy Dittmar, Austin Community College–Rio Grande

Ginger Eaves, Bossier Parish Community College

Steven Edwards, Southern Polytechnic State University

Keith Erickson, Georgia Gwinnett College

Dihema Ferguson, Georgia Perimeter College

Barbara Finnegan, Del Mar Community College

Acknowledgments

Elise Fischer, Johnson County Community College

Stephanie Fitch, Missouri University of Science and Technology

Marion Foster, Houston Community College

Lana Fredrickson, Front Range Community College

John Fulk, Georgia Perimeter College

Darren Funk-Neubauer, Colorado State University

Ed Gallo, Sinclair Community College

Valdez Gant, North Lake College

David George, Ohio State University

Kevin Gibbs, University of Toledo

Vijaya Gompam, Troy University

Jennifer Gorman, College of Southern Nevada

William Griffiths, Southern Polytechnic State University

Barry Griffiths, University of Central Florida

Jeff Gutliph, Georgia Perimeter College

Sylvia Gutowska, Community College of Baltimore County–Essex

Ryan Hansen, West Virginia University

Debbie Hanus, Brookhaven College

Craig Hardesty, Hillsborough Community College

Jason Hasbrouck, College of Lake County

Tom Hayes, Montana State University

Mary Beth Headlee, State College of Florida Manatee

James Hearl, Pasco-Hernando Community College

Beata Hebda, University of North Georgia

Christy Hediger, Lehigh Carbon Community College

Matthew Henes, Pasadena City College

Jean Hindie, Community College of Denver

Gangadhar Hiremath, University of North Carolina

Linda Ho, El Camino College

Lori Hodges, University of New Orleans

Sarah Holliday, Southern Polytechnic State University

Heidi Howard, Florida State College

Keith Hubbard, Stephen F. Austin State University

Sharon Jackson, Brookhaven College

David James, Howard University

Erin Joseph, Central New Mexico Community College

Brian Kahl, Community College of Baltimore County–Essex

Chandra Karnati, University of North Georgia

Susan Keith, Georgia Perimeter College

Lynette Kenyon, Collin College Plano

Raja Khoury, Collin College–Plano

Minsu Kim, University of North Georgia

Christopher King, College of Southern Nevada

Sandra Kingan, Brooklyn College

Russell Kohl, University of Maryland

Daniel Kopsas, Ozarks Technical Community College

Elena Kravchuk, University of Alabama

Ramesh Krishnan, South Plains College

Bohdan Kunciw, Salisbury University

Weiling Landers, Windward Community College

Viktoriya Lanier, Middle Georgia State College

Rick Leborne, Tennessee Technological University

Sungwook Lee, University of Southern Mississippi

Deb Lehman, State Fair Community College

Xuhui Li, California State University–Long Beach

Folberg Lisa, Portland Community College

Domingo Litong, Houston Community College

Tammy Louie, Portland Community College

Rene Lumampao, Austin Community College–Rio Grande

Phil Maclean, Columbus State Community College

Edmund MacPherson, Tyler Junior College

Anna Madrid-Larranaga, Central New Mexico Community College

Crepin Mahop, Howard University

Jason Malozzi, Lehigh Carbon Community College

Cynthia Martinez, Temple College

Shawna Masters, Collin College–Plano

Ramon Mata-Toledo, James Madison University

Janet Mayeux, SE Louisiana University

Michael Mays, West Virginia University

Roderick McBane, Houston Community College

Cynthia McGinnis, Northwest Florida State College

Christine McKenna, University of Nevada Las Vegas

Tim McNicholl, Iowa State University

Mary Merchant, Cedar Valley College

Robert Mitchell, Pennsylvania College of Technology

Chris Mizell, Northwest Florida State College

Val Mohanakumar, Hillsborough Community College

Monica Montalvo, Collin College–Plano

Candy Moraczewski, Delaware County Community College

Malika T. Morris, Houston Community College

Dorothy Muhammad, Houston Community College

Linda Myers, Harrisburg Community College

Julie Nation, Mississippi State University

Chris Nazelli, Wayne State University

Mandri Obeyesekere, Houston Community College

Victor Obot, Texas Southern University

Charles Odion, Houston Community College

Chinenye Ofodile, Howard University

Donald Orr, Miami Dade College

Victor Pambuccian, Arizona State University–West

Stan Perrine, Georgia Gwinnett College

Haberman Peter, Portland Community College

Shawn Peterson, Texas State University–San Marcos

Gerri Petty, Oklahoma State University

David Platt, Front Range Community College

Wendy Pogoda, Hillsborough Community College

John Polhill, Bloomsburg University of Pennsylvania

Jonathan Poritz, Colorado State University

Didi Quesada, Miami Dade College

Brooke Quinlan, Hillsborough Community College

Mohammed Rajah, Miracosta College

Don Ransford, Edison College–Fort Myers

Carolynn Reed, Austin Community College–Rio Grande

Denise Reid, Valdosta State University

Nancy Resseguie, Arapahoe Community College

Shelia Rivera, University of West Georgia

Ken Roblee, Troy University

Michael Rosenthal, Florida International University

Bill Rosenthal, Laguardia Community College

Sean Rule, Central Oregon Community College

Haazim Sabree, Georgia Perimeter College

Fatemeh Salehibakhsh, Houston Community College

Fary Sami, Harford Community College

Jared Schlieper, Armstrong Atlantic State University

Julie Schmidt, Central Oregon Community College

Linda Schott, Ozarks Technical Community College

Mary Schuster, University of Cinncinatti

Mohammad Shakil, Miami Dade College

Lisa Shannon, Meridian Community College

Kenneth Shiskowski, Eastern Michigan University

Giorgi Shonia, Ohio University

Andrew Siefker, Angelo State University

Jennifer Siegel, Broward College–Central

Randell Simpson, Temple College

Premjit Singh, Ohio University

Sounny Slitine, Saint Philips College

David Slutzky, University of North Georgia

Shawn Smith, Nicholls State University

Author Acknowledgments:

Cindy Soderstrom, Salt Lake Community College

Mary Ann Sojda, Montana State University

Shannon Solis, San Jacint College

Scott Sorrell, University of Louisiana Lafayette

Greg Stiffler, Community College of Baltimore County–Essex

Malgorzata Surowiec, Texas Tech University

Vic Swaim, SE Louisiana University

Paula Talley, Temple College

Mary Ann Teel, University of North Texas

Alain Togbe, Purdue University

Rae Tree, Oklahoma State University

Danielle Truszkowski, Community College of Baltimore County–Essex

Chris Turner, Pensacola State College

Joan Van Glabek, Edison College–Fort Myers

Phil Veer, Johnson County Community College

Sue Wall, Wake Tech Community College

Karen Walters, Nova Community College

James Wan, Long Beach City College

Walter Wang, Baruch College

Bingwu Wang, Eastern Michigan University

Jason Wetherington, Pasco-Hernando Community College

Emily Whaley, Georgia Perimeter College

Mark White, University of North Carolina

Dr. Bob Wieman, Virginia State University

Rebecca Wong, West Valley College

Jane-Marie Wright, Suffolk County Community College

Changyong Zhong, Georgia State University

An editor once told us that publishing a book is like making a movie because there are so many people behind the scenes that make the final product a success. Words cannot begin to express our heartfelt thanks to all of you, but we’ll do our best. First and foremost, we want to thank our editor Emily Windelborn who started with us on this project when it was just idea, and then lent her unwavering, day-to-day support through final publication. Without Emily, we’d still be on page 1. To Ryan Blankenship, Marty Lange, Kurt Strand, we are forever grateful for the amazing opportunities you and McGraw-Hill have given us.

To our brand manager, Caroline Celano, as the pilot on this long journey you set the standard for leadership. Each day, you lead by example to unlock our full potential and inspire our best work. You’re strong but not rude; kind, but not weak; humble, but not timid. To the marketing team Michelle Greco, Leigh Jacka, Simon Wong, Megan Farber, Sara Swangard, Ashley Swafford, Jill Gordon, and Alex Gay: Your artistry and creative ideas for our project are 90% inspiration, 90% innovation, and 100% perspiration. Thank you for making us shine.

Our heartfelt gratitude goes to the content project manager Peggy Selle for steering the ship and keeping us all on task. To Laurie Janssen and David Hash, many thanks for a beautiful design, and to Carrie Berger for the beautiful photos and art. The book is gorgeous.

Special thanks to the digital team, Rob Brieler and Victor Pareja, for keeping the digital train on the tracks. Thank you for overseeing the enormous job of managing digital content and ensuring consistency of the author voice. Along these lines, we must express our utmost gratitude to digital authors Tim Chappell, Meghan Clovis, Vanessa Coffelt, Alina Coronel, Lizette Foley, Lance Gooden, Jeffrey Guild, Esmarie Kennedy, Michael Larkin,

Acknowledgments

Nathalie Vega-Rhodes, and Stephen Toner for their diligence working on digital content. All of you are amazing. To Jason Wetherington and Mary Beth Headlee thank you so much for your work on SmartBook and for the additional pairs of eyes on our manuscript. To Beth Clickner, many, many thanks for the beautiful and thorough PowerPoint presentations of our material. To our colleague and friend Kimberly Alacan, we’re so grateful for your creativity in preparing the chapter openers and the group activities. To Nora Devlin, thank you for managing the solutions manual projects, lecture notes, and Internet Activities. No doubt, many instructors and students thank you as well.

To Patricia Steele, the best copy editor ever, thank you for mentoring us and for ensuring consistency throughout our work. To Elka Block, Jennifer Blue, and the team at DiacriTech, many thanks for doing multiple levels of accuracy checking. Your talents are absolutely amazing. Additional thanks to Julie Kennedy and Carey Lange for their tireless attention to detail proofreading pages.

Finally, to the dedicated people in the McGraw-Hill sales force, thank you so much for your continued confidence, encouragement, and support.

Most importantly, we want to give special thanks to all the students and instructors who use Precalculus in their classes.

—Julie Miller and Donna Gerken

Applications Index

Agriculture/Gardening/ Landscaping

Corn plants per acre for maximum yield, 352

Costs for farmer to run tractor, 380

Crop acreage and maximum profits, 830

Dimensions and area of corrals/chicken coops, 247, 251, 348

Dimensions and area of garden in yard, 251

Dimensions of garden based on area, 334

Farm stand’s vegetables sold and price per pound, 868

Fencing for farm pens and dimensions of, 94

Fertilizer solution, 89

Garden, dimensions of triangular portions of, 119, 664, 681

Garden and measurements of triangular portions, 117

Garden dimension, based on fencing length, 104

Height of tree and age, 435

Lawn mower sale price, 11

Nursery’s inventory and profits, 829

Palm tree and estimate of leaning, 654

Plant fertilizer makeup, 789

Seeds selected from package, good vs. defective, 1065

Sprinkler: area watered and angle of rotation, 561, 663, 696

Sunflower height, 14

Time for pump to drain pond, 115

Time to mow lawn alone vs. together, 91

Weed-cutter and angular and linear speed, 461

Animals/Pets

Animal’s mass in relation to tidal volume, 367

Animal’s mass in relation to weight of heart, 350

Cattle feeding trough and metal sheeting, 600

Deer population, 442

Dog’s “accident” being on rug, probability of, 1079

Gestation and longevity for selected animals, 179, 181

Girl’s average height by age and projections, 180

Girl’s height and weight from age 2 to 10, 179

Human hearing and sound waves, 589

Pea plant color probabilities (Mendel), 1077

Probability of being left-handed, 348

Symmetry of bird, human face and flower, 197

Boats/Marine

Boat/kayak speed in still water, 85, 90

Sail measurements, 87, 91

Shoreline points for boats to reach, 94

Speeds of two boats, based on distance apart, 115

Two ships’ speeds and time they will be certain distance apart, 94

Business

Advertising campaign and new sales, 419

Aluminum and cylindrical drink mix container, 336

Kitten’s weight, progression of, 1025

Puppy’s weight increase in days/months after adoption, 178–180

Rabbit population in wildlife area, 352

Spay/neuter costs for shelter, 827

Veterinarian X-ray machine resale value, 380

Astronomy/Space Travel

Gravitational force between Earth and person at sea level, 28

Gravitational force between Jupiter and Earth, 28

Miles from Proxima Centauri to Earth, 26

Biology

Bacteria population in culture, 250–253, 334, 336, 424–427, 432, 434, 442, 444, 809

Bass population in lake, 441

Blood alcohol level and rate of change, 157–158

Concentration of drug in bloodstream, 320, 336

Deer population, 442

Gender probability, 1065, 1074, 1076

Arrangement of commercials during half-hour show, 1065

Car prices, 872

Change in T-shirt cost from manufacturer, 205

Cleaning company’s average cost per house call, 315

Coffee shop’s production costs and prices for two hot drinks, 872

Companies/businesses’ costs, revenue and break-even point, 774, 777, 778, 832

Company expenses for one year and subsequent years, 1016

Company’s trucks and use of to minimize cost, 827, 829

Concession stand sales, 858

Cookbook prices and supply and demand, 778

Cookbook sales and relation to price, 343

Cookie maker’s costs, revenue and profits, 178 Costs for business stationery, 227

Customer service survey and number of ways it be can filled in, 1063, 1087

Dance studio’s costs, revenue and profits for private lessons, 234

Math textbook sales cycle, 627

Maximum profit for companies, 250

Maximum profit for companies and business owners, 252, 825–826, 829

Medical device resale value, 1037

Movie theater’s concession sales, 902

New book sales trend, 435

New product sales, 433

Number of handshakes at meeting, 1016

Pennant flags and cost to make based on measurements, 654

Power company and costs for air pollutant control, 320

Printing company’s average costs, 319

Sporting goods store’s inventory and profits, 829

Sports trainer’s average costs, 319, 350

Street vendor’s drinks sold and price per unit, 872

Surf shop inventory, 755

Ticket earnings and types sold, 858

Tourism value to local economy, 1038, 1084, 1087

Tractor resale value, 380

Wait time for customer service, 1088

Winter coat sales, 620

X-ray machine resale value, 380

Decreased dimensions and volume of cereal box, 298

Delivery truck route possibilities, 1064

Diner’s profits on tea and coffee, 827

Donut shop profits, 835

Employee task possibilities, 1065

Food market’s monthly sales, 365

Full-time and part-time employees, numbers of, 822, 824

Gas station’s revenue and profits, 872

Grocer and amount spent on various advertising, 848

Inflation and company’s monthly costs, 435

Labor costs, 829, 873

Lawn company’s costs, revenue and profits for maintenance calls, 178

Lemonade vendor’s costs, revenue and profits, 171–172

Manufacturer’s production costs and profits, 828, 829

Chemistry

Acid mixtures, 116, 786

Antifreeze mixture, 56, 119, 776, 777

Bleach mixture, 52, 772–773

pH levels, 394, 419, 440

Saline solution mixture, 56, 776

Construction/Building

Amount of wire left based on wire used, 150 Bookcase and frame’s diagonal brace, 553

Bridge cables, 953

Circular cross section of vent pipe with roof, 923

Circular saw and linear and angular speed, 461

Concrete mixture, 90, 92, 114

Condominiums and maximizing ocean view from, 641

Crane’s cable, length of, 663

Elliptical concrete pipe design, 998

Floor dimensions, 807

Front face of house, dimensions of rectangular portion, 91

Gravel roads and angle of depression for, 637

Home’s diagonal beam and angle to frame base, 548

Location of foci to make elliptical table, 921

Location of foci to make elliptical window, 921

Maximum volume of solar oven, 268

Mountain cabin, porch and slope’s angle of inclination, 653

Parking lot dimensions, 246–247

Pitch of a roof, 162

Pitch of roof, 164, 632

Plywood costs, 833

Pool’s volume at certain depth when being filled, 108

Power drill cost, 232

Railroad bridge height, from roadway, 636

Rates of lumber cut, 789

Residential buildings and heights of, 653

Robotic painting arm and area of, 462

Roof truss and lengths of triangular sides, 91

Roof truss triangles, lengths and area of, 87, 600

Semiellipse of road tunnel/bridge arch, 917, 997, 1001

Sewer line slope and angle of depression for, 637

Slope of storm drainage pipe, 162

Storage shed and angle of roof, 640

Tile, what is needed and costs of, 59, 346, 1087

Time/rate for pump(s) to drain pond, 116, 847

Tree house height, 636

Tree removal chain and work done, 755

Velocity of fluid through drainage pipe, 252

Water pipe installation on island, 641

Water volume carried by gutter, 251

Wheelchair ramp and ADA compliance on slope, 553

Wind pressure on wall, 352

Wooden beam size and strength, 344

Consumer Spending

Amounts borrowed from various sources, 847, 901

Book cost based on markup after publisher cost, 147

Car depreciation rate, 28

Car financing, 148

Car loans and interest, 378, 395, 439

Car rental costs, 343, 345, 826

Cell phone costs based on age of user, 348

Cell phone plan costs, 170, 172, 212, 214, 873

City parking garage costs, 177

Commuter’s toll costs, 683

Cost to carpet room based on size, 344

Cost to download music from website, 222

Decreased dimensions and volume of cereal box, 298

Dining room table prices, 903

Discount on grill, 14

Electric bill, 14

Federal income tax, 215

First-class postage costs, 212

Grocery store payment types and gender, 1088

Home loan and interest, 395

Homeowner’s electric bills, 1019

Home value and appreciation over time, 1037

Hotel costs comparison, 104

Kitchen tile costs based on length and width of room, 344

Monthly power bills, 524

Online ticket purchases for dance show, 227

Phone card minutes left, 150

Power drill cost, 232

Property taxes, 177, 367

Restaurant bill and tipping, 147

Restaurant tipping, 11

Retirement planning, 378, 380, 417, 419, 820

Student loans and simple interest, 56, 120, 777

Television services spending, 173

Vehicle depreciation, 436

Video games spending per person, 148

Water bill, 14

Watercolor paint price at online shop, 223

Distance/Speed/Time

Acceleration of rocket versus time after launch, 268, 352

Airplane’s altitude, speed and distance, 367

Airplane’s distance in nautical miles, 634

Airplane’s speed and speed of wind, 832

Airplane’s velocity, wind velocity and ground speed and bearing of plane, 735, 741, 762

Average speed of two planes, 90, 117

Bicycle and angular and linear speed, 457, 461, 463, 561

Boat/kayak speed in still water, 85

Boat’s distance in nautical miles, 634–635

Boats/ships and various factors of distance and bearing, 638, 639, 662, 663, 680, 682, 741

Braking distance and speed, 252, 334, 343

Camper’s distance from ranger station, 680

Car’s acceleration and deceleration, 211, 228

Car’s velocity and time to reach certain speed, 92

Catamaran and distance to lighthouse, 652

City locations and distances between, using longitude and latitude, 455–456, 460, 561

Coast Guard ship and distance to distressed ship, 659–660

Distance between home and school/work, based on average speeds, 90, 114–115

Distance between work and home, 114–115

Distance of bike ride and time, 147

Distance of bike ride based on bearing, 640

Distance of drive from Daytona Beach to Miami, 147

Distance of object in free fall over time, 1026

Distance of sailboat from shore, 480, 836

Distance to fire from observation platforms, 129, 136

Distance traveled by rolling/bouncing ball over time, 1026, 1039

Fireworks mortar, time to reach certain heights, 89, 115

Gas mileage at 60 mph, 233–235

Gas mileage compared with speed, 250, 251

Height and horizontal distance of water from firefighter hose, 250

Height of stone thrown from cliff, 245

Height of thrown football and time to reach receiver, 245

Helicopter as viewed from two observation points, 652

Helicopter’s distance and direction, 638

Light-year distance, 19–20

Maximum height and length of long jump, 250

Motorist’s average speed, 334

Observers on shore to boats on water, 680

Passing car and time to reach certain distance, 104

Plane’s round trip, average speed of, 53

Plane’s speed in still air, 90

Point of contact of kicked ball/rock, 808

Police car and motorist’s speed, 637

Revolutions of bike wheel and distance traveled, 227, 343

Runners’ distance from each other, 680

Runners’ speeds, 777, 834

Runners’ time to cover certain distance, 90

Satellite, distance traveled, 20

Ship/boat’s speed and bearing, 741, 1003

Ship in open ocean and ship and current’s velocity, 734–735

Ships: nautical miles traveled, distance from port and bearing for return, 638

Sled acceleration, 211

Soccer ball and vertical/horizontal distance; and kicking angle, 120, 600, 621

Speeding ticket cost, 170

Speed of boat in water, and speed of current, 90–91, 97, 773–774, 777

Speed of moving sidewalk vs. speed of walker, 777

Speeds of two boats, based on distance apart, 115

Stopping distance, 93

Toy rocket, time to reach certain heights, 88–89

Truck’s tires and linear and angular speed, 461

Two ships’ speeds and time they will be certain distance apart, 94

Velocity of fluid through drainage pipe, 252

Education/Schools

Arranging books on shelf and number of permutations, 1058

Book cost based on markup after publisher cost, 147

Cafeteria lineup possibilities, 1065

Campus safety survey and probability of certain answers, 1073

College application increase, 365

Course selection possibilities, 1085

Days to read book, 1087

Drama class participation possibilities, 1064, 1085

Elementary vocabulary lesson and testing, 419

Final exam grade probability, 1077

Math textbook sales cycle, 627

Multiple-choice questions and probability, 1078

Palindrome possibilities, 1065

Possible ways to misspell a word, 1085, 1087

Public college enrollment and projected enrollment, 179, 181

Selection of students for scholarships, 1080

Student government and committee positions, number of permutations, 1058, 1060–1061

Student loans and simple interest, 56, 120, 777

Study hours for various courses, 817, 819

Summer reading book selection possibilities, 1065

Test answers and possible variations, 1057, 1063, 1085

Test questions and possibilities, 1087

Test scores, 872

Test scores and overall average, 101, 103, 104

Tuition and fees at college, 15, 68

Tutoring hours, 828, 833

Employment

Hospital employee ID codes, 1063

Hourly wages, 777

Mail-order processing, rates working together, 86

Number of workers and time to complete job, 343

Salaries of two jobs over time, comparison of, 1040

Salaries plus commission, comparison of, 104

Salary, projected increases and total income over time period, 1023–1024, 1026, 1040

Salesperson’s weekly/monthly salary with commissions, 177, 179, 204–207, 212, 214, 683, 826, 1084

Soldier selection possibilities, 1065

Time to complete typesetting job, working together, 115

Total amount earned, 1039

Weekly salary, 56, 777

Environment

Atmospheric pressure and altitude, 379

Campers’ altitude, based on water’s boiling point, 68

Costs to remove waste from polluted river, 320

Distance between hikers in park, 129

Distance to fire from observation platforms, 129, 136

Earthquake and where could be felt, 820

Earthquake magnitude/intensity, 391, 393, 419

Geological study areas and earthquake epicenter, 136

Height of Pacific Ocean volcano since 1960, 234

Hurricane wind speed and barometric pressure, 178, 180, 367

Ocean waves and average rate of change in speed, 164

Pollution based on number of people, 343 Power company and costs for air pollutant control, 320

Water level in Everglades, 367, 369, 1018–1019

Water level in retention pond, 177, 212, 213

Weight of body above Earth surface, 352

Finance/Investments

Amount of counterfeit money “spent,” 1038

Amounts borrowed, based on interest paid, 83, 89

Annuity value, 1035–1036, 1039, 1084, 1087

Bonds, interest and yields, 340, 343, 417

Compound interest, 164, 166, 233, 235, 374, 376, 378, 380, 417, 419, 430, 432, 439, 441, 442, 444, 809, 836, 1035–1036

Currency denominations, 93

Federal income tax, 215

Home sales, 790, 848

Inflation and buying power, 379

Inheritance money spent and respent, 1038

Investment and interest earnings, 228, 378, 430

Investment in bond fund and yield, 406–407, 414–415

Investment rate of return, 422, 423, 430, 441, 442

Investments, original amounts, 83, 89, 114

Loan payments, 436

Loan principal, 89

Money market funds, 417

Mutual fund investments, 786

Principal investment amounts, 832, 847

Property taxes, 92, 177, 367

Retirement account and growth of, 1016

Retirement planning, 378, 380, 417, 419, 820

Simple interest, 11, 51, 56, 59, 83, 89, 114, 341, 343, 345, 378, 380, 439, 441, 777

Stock and mutual fund investments, 59, 116, 789

Stock fund and rate of return, 430

Stock investments, 834

Tax rebate money spent and multiplier effect of, 1034, 1038

Tractor resale value, 380, 382, 1037

Food/Nutrition

Almond croissant purchase in France, 227

Caffeine and biological half-life, 418

Calcium content, 832

Cereal boxes, content weights and variations in, 104

Cheesecake slice and area of, 462

Cookbook sales and relation to price, 343

Cooling rate of cake/pie from oven, 380, 418

Dinner menu variations at hospital, 1063

Ham and number of people it will serve, 343

Hamburgers’ caloric and cholesterol content, 179, 181

Ice cream fat content, 777

Nut mixture, 834

Pizza crusts and toppings, number of variations, 1055

Pizza slice and area of, 462

Probability of certain cookies selected from box, 1076

Protein powder content, 834, 835

Refrigerator temperature, 104

Restaurant bill and tipping, 147

Restaurant tipping, 11, 14

Sodium content in chips and soda, 777

Taco lunch and drinks and calories consumed, 755

Turkey baking time, 28

Geography/Points

of Interest

Arches of WW II airship hangars, 999

Bermuda Triangle and area of, 652

Big Ben and diameter of clock face, based on angle of elevation, 631

Brooklyn Bridge and cable heights, 999

Distances between cities, 455–456, 460, 561, 664, 682

Flatiron Building and angle of point, 663

Golden Gate Bridge and cable heights, 1002

Leaning Tower of Suurhusen (Germany), distance from base to top, 653

Roman Coliseum’s inner and outer ellipse, 922

Tram and angle of incline on Rendezvous Mountain, 637

Washington’s Ellipse, elliptical boundary and eccentricity of, 922

Health/Human Body

Body temperature range, Celsius to Fahrenheit conversion, 104

Cholesterol levels, 92

Drug’s concentration in bloodstream, 53

Heart rate, maximum recommended for adults, 11

Red blood cells, number of, 26

Saline solution, 90

Hobbies/Entertainment

Bingo game attendance, 237

Bread throw in Seinfeld episode, vertical position and time to reach, 92

Child’s wagon and work done, 755

Coin toss probabilities, 1040, 1065, 1078

College theater tickets, 820

Concert ticket costs, 684

Cost to download music from website, 222

Dance lesson demonstration possibilities, 1064

Dice rolling probabilities, 1069, 1076, 1078, 1086, 1088

Digital songs storage, 26

Distance of bike ride and time, 147

DVD/CD selection probabilities, 1080, 1085

Elliptical pool table, 924

Family’s time spent at two Disney parks, 817 Ferris wheel and position of riders, 669–670, 674, 681

Film festival award possibilities, 1064

Fireworks vertical height, speed, and visibility, 334

Location of foci for boomerang, 938

Lottery combinations and probability, 1064, 1077, 1086

Movie screen and angle of elevation, 556

Online ticket purchases for dance show, 227

Possible arrangement of songs by DJ, 1085

Probability of certain cards drawn from deck, 1072, 1077–1078, 1080, 1086, 1090

Quilting and equation for flower design, 709

Raffle tickets and possible ways to win, 1061, 1087

Rock concert’s intensity and loudness, 415

Rock songs vs. country songs on playlist, 820

Roulette outcome probabilities, 1068, 1076

Shadow box dimensions and area, 251

Slot machine outcome probability, 1079

Speed of racing canoe, 344

Theater ticket pricing and seats sold, 789

Theater tickets and supply and demand, 778

Thrown ball’s speed and vertical position, 350

Toy rocket, time to reach certain heights, 88–89

Toy rocket’s position and time; and angle of elevation, 84–85, 270, 332–333, 628

Toy rocket’s vertical position and time, 268, 330–331

Video game players’ positions and speed, 129

Video games spending per person, 148

Watercolor paint price at online shop, 223

Home/Family

Backyard slide and extension of, 479

Ceiling fan and angular and linear speeds, 456, 463

Children in photo, possible ways to arrange, 1090

Elliptical rug from rectangular carpet, 921

Garage door remote sequence possibilities, 1063

Outfits, number of variations, 1063, 1087

Selecting batteries/lightbulbs, good vs. dead/ defective, 1065, 1076, 1086

Sock color selection probability, 1066

Three-digit number combinations for lock/code, 1065, 1085

Home Maintenance/Improvements

Patio, base and height of triangular portions, 91 Roof repair costs, 93

Time for pump/hose to fill swimming pool, 91, 117

Time to vacuum house, working together, 90

Toilet repair costs, 93

Measurements

Advertising balloon and cables’ angle with ground, 553

Alarm code and number of variations of, 1056

Aluminum and cylindrical drink mix container, 336

Aquarium dimensions, 808

Arranging books on shelf and number of permutations, 1066

Award ribbons at fair and number of permutations, 1059

Bermuda Triangle and area of, 652

Big Ben and diameter of clock face, based on angle of elevation, 631

Blimp and various measurements, 680

Block on spring and maximum/minimum height of, 619

Block on spring/bob on pendulum and harmonic motion, 673, 681–684

Buildings as hyperboloids and hyperbolic cross section and diameters of, 998, 1002

Building’s height, based on sun’s angle of inclination and shadow, 682

Cardboard dimensions, 93

Child’s swing and maximum/minimum height of, 619

Clocks’ second and minute hand measurements, 462, 464

Cube, length of diagonal through, 91

Dogsled pulled and work done, 752

Engines and various parts’ measurements, 654, 665, 674, 682

Flag and flagpole height and size, based on various factors, 564, 636

Flagpole on hill and angle of inclination, 650, 653

Floor dimensions, 807

Force on various objects and work done, 755, 761, 762

Forklift and freight on ramp, 754

Fountain’s water height, 649

Front face of house, dimensions of rectangular portion, 91

Gears and degrees in rotation, 462

“golden rectangle,” 94

Grocery store sign dimensions, 807

Height of lamppost, based on man’s shadow, 108

Height of palm tree, 475

Hill’s height based on angle of elevation, 652

Ladder and angle with ground and wall, 640

Ladder’s reach, 476, 479, 631

Lawnmower pushed and work done, 751–752

Length of pool based on depths and angle slope, 636

Light’s illumination, 639

Metronome’s pendulum arm swings, 519

Octagonal stained glass window, sides length of, 94

Paddle wheel and angular speed, 461

Patio, base and height of triangular portions, 91

Pendulum swings, 346, 675, 676, 1039, 1084

Plane distance to point on runway, 475–476

Plane’s height based on angle of elevation, 652

Pool’s volume at certain depth when being filled, 108

Pyramid of plastic cups, number in certain row and total, 1027

Quilt dimensions from its area, 334

Radius of underground gasoline storage tank, 297

Rental truck dimensions, 298

Right circular cone measurements, 28

Rocket liftoff and video camera, angle of elevation, 555

Sailboat and turn of the winch on, 460

Sundial and dial’s shadow, 589

Sun’s angle and building’s shadow, 640

Surveyor and various measurements, 461, 479, 652, 653, 680

Swings of a pendulum, 344

Tent dimensions, 297

Test tube in centrifuge and various positions of, 674

Theater seats, number in certain row and total, 1027

Tower height, 680, 682

Tower’s cable, length of, 664

Triangles, length of sides, 28, 87

Triangular face of gabled roof, area of, 652

Triangular region to be primed, 664

Triangular shade sail and materials cost, 682

TV screen, dimensions of, 117, 834

Washington Monument shadow and sun, 553, 636

Water depth at boat and distance between anchor and bow, 636

Water volume in trough, 108

Waterwheel and positions on, 674, 683

Wheels and pulleys, 460, 561, 563

Window dimensions, 807

Window’s vertical dimension, based on angle of elevation, 632

Medicine/Health

Aspheric eyeglass lenses, 938

Bacteria population in culture, 250–253, 334, 336, 424–427, 432, 434, 442, 444, 809

Blood pressure, 620, 674

Blood pressure probabilities, 1086

Blood type probabilities, 1079

Blood type transfusion-matching probabilities, 1079

Body mass index, 343, 345, 838

Breast cancer survival probability, 1078

Cholera epidemic and deaths, 419

Cholesterol levels, 57, 119, 1078

Concentration of drug in bloodstream, 320, 336

Doctor visits in relation to patient’s ages, 352

Drug concentration in bloodstream, 808

Ebola virus, 434

Flu outbreak and new cases, 164, 166, 1037

Girl’s height and weight from age 2 to 10, 179

Heart surgery mortality rate, 1077

Kidney stone position in lithotripsy procedure, 921

Leg bones and magnitude of force, 756

Medicine dosages and patients’ weight, 338, 339–340, 343

New AIDS cases in United States, 268

Participants in drug and alcohol rehabilitation program, 1025

Radioactive substances used in health care, 418, 420, 432, 434, 439–442, 808

Respiratory cycle and inhalations/exhalations, 522, 524

Sounds and hearing impairment, 419

Sounds and pain-causing intensity and loudness, 415

Systolic blood pressure by age, 173, 174–175

Ultrasound and frequency of, 673

Winter colds and probability of catching, 1075

Miscellaneous

Ages compared, 14

Cannon firing and path of the ball, 986

Committee formations possibilities and probabilities, 1064, 1070

Path of shell fired at firing range, 990

Pyrotechnic rocket and path of after launch, 1003

Motor Vehicles

Antifreeze mixture, 90, 117

Car depreciation rate, 28

Car’s velocity and time to reach certain speed, 92

Driver’s average speed in nice weather and in thunderstorm, 90

Gallons gas needed, 15

Miles driven, 92

Passing car and time to reach certain distance, 104

Rental truck’s cargo space, dimensions of, 93

Stopping distance, 93

Politics

Numbers of Senate Democrats and Republicans, 92

Political party probability, 1077

Poll and percentage of votes received, 105

U.S. senators and possible variations for committee formations, 1064

Real Estate/Housing

Apartment rental costs, plus deposits for animals, 15

Property taxes, 92

Science

Acid solution, 84, 114

Alternating current generator and harmonic motion, 675

Antifreeze mixture, 90

Ant’s path across picnic table, 984–985

Area of picture projected on wall, 343

Astronomical units and parsec and in relation to light year, 682

Atmospheric pressure and altitude, 379

Atomic particles path, 938

Bacteria culture and population in, 93

Bleach solution, 84

Boiling point of water and altitude, 68

Bulb in parabolic mirror of car headlight/ flashlight, 950

Caffeine and biological half-life, 418

Carbon-14 dating, 425–426, 431, 441

Cooling rate of cake/pie from oven, 380, 418

Cooling rate of water after heater shut off, 380

Daylight and darkness duration, 523, 524

Depth of water (in oceans and lakes) and intensity of light, 441

Distance between Earth and its moon, 922

Distance between Earth and various stars, 637

Distance between planets, 654

Distance between various planets and Sun at aphelion or at perihelion, 918, 922, 978, 997, 1001

Earth and moon, distance between, 561

Earth circumference, 463

Earthquake, distance from epicenter, 93

Earthquake magnitude/intensity, 391, 393, 419

Earth radius, 480

Earth’s orbit and linear speed, 462

Electric current based on voltage and resistance, 343

Electric power based on current and resistance, 351

Elliptical curve of lightbulb, 921

Equilibrium forces, 737–738, 779

Ethanol fuel mixture, 90

Fertilizer solution, 89

Freezing temperature versus time, 334

Frequencies of piano notes, 1039

Geological study areas and earthquake epicenter, 136

Gravitational force and planets, 338

Half-life of radioactive elements, 375, 379, 418, 432, 439–440

High and low tides and water levels, 518–519, 524, 562

Hurricane and kinetic energy, 341

Initial velocity and acceleration, 1025

Kepler’s third law, 345

Lightbulb intensity, 344

Light-year distance, 19–20

McNaught comet and distance from Sun, 938

Moon cycles and illumination of, 521, 562

Nuclear power cooling tower and diameter of, 938

Orbits of Halley’s and Hale-Bopp comets, 922

Orbits of Halley’s Comet and Earth, 922

Radiation intensity in relation to distance from source, 345

Resistance in parallel circuits, 319–320

Satellite dish as paraboloid and receiver placement, 948–950

Satellites and maximum distance along Earth’s surface, 638

Snell’s Law and angle of refraction, 620, 627

Solar cooker pot placement, 950, 952

Solar water heater’s tube, 952

Sound and damping factor, 676

Sound frequencies, 320

Sound heard by people in two positions and point of origination of, 934, 998, 1001

Sound loudness and distance from source, 340

Sounds’ intensity, 394, 415

Sound waves, 607

Space Shuttle and angular and linear speed, 464

Star’s magnitude and harmonic motion, 675

Steel welding and temperature, 418

Sun’s angle of elevation, 640, 677, 679

Swings of a pendulum, 344

Telescopes’ parabolic mirrors, 952–953

Temperature of object in freezer at various time intervals, 53

Temperatures on conducting plate, 885

Total electrical resistance, 53

Velocity of dropped object at impact, 14

Vertical velocity of dropped object, 1025

Vinegar and water as cleaning agent, 777

Weight of body above Earth surface, 352 “whispering galleries” effect, 921

Sports/Recreation

Achilles tendon stretch and push against wall, 740

Arena seating, based on ticket sales, 832

Athlete’s workout and length of, 481

Baseball player and probability of getting a hit at bat, 1076, 1086

Basketball jumps, height and time to reach, 92

Basketball player possibilities to start game, 1065

Basketball player’s rebound jump, 334

Basketball player’s shots and free-throws, 789

Batting order possibilities, 1066

Biathlon, distance of city loop in, 90

Bowler’s handicap and average scores, 104

Calories burned during various types of exercise, 827, 873, 905

Chess matches, number possible, 1064

Daytona 500 finish possibilities, 1085

Distance between hikers in park, 129

Distance from baseball diamond’s home plate to second base, 91

Fast-pitch softball and distances on field, 663

Football punt, vertical height and time to reach, 92

Force to break board in karate, 350

Golf ball and path after being hit, 990

Golf score needed, 117

Gymnastics and minimum score needed, 103

Height of thrown football and time to reach receiver, 245

Hiker and estimated height of mountain, 653

Hikers and path’s angle of incline, 553

Hikers on circular path and distance between, 666

Hiking path’s angle of ascent, 632

Horse race winning possibilities, 1064

Kayaker, bearing and distance of travel, 742

Kick boxer and force on bag, 740

Kicked soccer ball and time to reach certain height, 117

Kite flying and height of kite from ground, 631, 680

Maximum height and length of long jump, 250

Motorcyclist’s jump over canyon, 991

NFL crossbars on goalposts, 479

Number of ways softball team can be formed, 1062

Olympic athletes and medals won, 232

Parasail height, based on angle of elevation, 680

Probability of making all free throws in basketball game, 1078

Radius and weight of exercise ball, 350

Roller coaster height, based on time, 213

Runners’ bearing from starting point and total time of run, 638, 639

Runners’ speeds, 777, 834

Runners’ time to cover certain distance, 90

Running and biking, average speeds in triathlon, 90

Running and biking speeds, 53, 779

Shot put and path of the shot, 985–986

Ski run’s angle of incline, 553

Sled acceleration, 211

Snow tubing hill and angle of incline, 553

Soccer ball and vertical/horizontal distance; and kicking angle, 120, 600, 621

Softball and path after being hit, 991

Softball/baseball and path after being hit, 991, 1000

Sports trainer’s average costs, 319, 350

Swimmer and various factors, 741, 742

Swimming and running speeds, 779

Teeter totter, angle and height of, 639

Tennis tournament match possibilities, 1064

Thrown ball and various factors, 734, 741

Thrown/kicked football and various factors, 88, 247, 621, 741, 762

Tightrope walker and factors affecting, 743

Time spent on treadmill after incremental increases, 1025

Touchdown passes, players compared, 14 Tour de France, 448

Triathlon and swim/run time based on various factors, 641

Triathlon swim and true speed of, 735–736

Wimbledon match probability, 1078

Winning carnival game probability, 1080 Zip line length, 479

Statistics/Demographics

Health insurance coverage probability, 1088

New AIDS cases in United States, 268

Number of ancestors over 12 generations, 1040

Number of men and women in jury pool, 55, 1076, 1087

Poll of trial viewers and probability, 1076

Population changes (of various towns, states, countries), 230, 381, 425–426, 433, 435, 438, 443, 684, 1089

Population changes (of various towns, states and countries), 228, 379, 423–424, 431, 433, 436, 441

Probability of being over 60 in China, 1077

Probability of births being twins/not twins, 1076

Probability of one-year survival at different ages, 1070, 1086

Probability of selecting two women, two men, 1090

Social Security numbers, number of possible combinations, 1065

U.S. population, 379, 432

Technology/Electronics

Cell phone costs based on age of user, 348

Cell phone display area, measurements of, 91

Cell phone plan costs, 170, 212

Cell tower on hill and angle of inclination, 649–650

Cell tower signal boundary, 136

Computer byte arrangements, 1063

Computer display area, measurements of, 91

Computer virus, 433

Digital songs storage, 26

Hard drive and angular speed, 461

Microphone placements to locate shooter, 937

Path of target on computer screen, 990, 1000

Radio station call letter possibilities, 1063

Tablet’s screen dimensions, 115

Tablets sold and total revenue and profit, 872

Total unread emails, 1025

Touch-tone phones and dual-tone multi-frequency signaling, 606

TV screen, dimensions of, 117, 834

Video game and player’s bearing at various points, 640

Video game and polar coordinates of target, 696

Web page, video storage on, 26

Website visitors, 442

Transportation/Travel

Airplane and bearing for various trips, 638, 640, 680

Airplane’s altitude, speed and distance, 367

Airplane’s altitude and various factors affecting, 118, 480, 636

Airplanes and paths over control tower, 991

Airplane’s distance and angle of elevation from radar tower, 537, 565

Airplane’s propeller as lemniscate and equation for, 709

Average speed of two planes, 90, 117

Bike ride, paved roads vs. off road, 664

Braking distance and speed, 252, 343

Car, skids and curve of road, 338

Car rental costs based on miles driven, 343

Car’s acceleration and deceleration, 201, 211, 228

Cars and paths as they approach intersection, 991

Car seating arrangement possibilities, 1065

City parking garage costs, 177

Distance between home and school/work, based on average speeds, 90, 114–115

Distance of bike ride, 147, 149, 640

Distance of drive from Daytona Beach to Miami, 147

Driver’s average speed in nice weather and in thunderstorm, 90

Engines various parts’ measurements, 621

Gallons gas needed, 15

Gas mileage, 50, 87, 233–237, 250–253, 790

Helicopter path from accident to hospital, 990

Incline railway and various factors, 479, 637

License plate variations, number of possibilities, 1063

Miles driven, 92

Miles driven by truck, 779

Miles driven in city vs. on highway, 779

Military supply plane and path of drop, 992

Motorist’s average speed, 334

Nights spent in various cities, based on total spent, 847

Number of routes to travel to work and school, 1085

Number of small vs. large rental buses for college, 824

Oversold airline seat selections, 1065

Path of stunt man’s car off cliff, 1000

Pickup trucks and force to pull stuck car, 742

Plane’s altitude, 115

Planes’ distance apart and bearing of, 663, 681

Plane’s round trip, average speed of, 53

Plane’s speed in still air, 90

Police radar detector and motorist’s actual speed, 105

Probability of being killed in vehicle crash, 1087

Probability of shortage of airline seats on certain route, 1079

Radar range of ship, 136

Red traffic light probability, 1078

Rental truck dimensions, 298, 300, 807

Revolutions of bike wheel and distance traveled, 227, 343

Ship location and radio signals on shore, 937

Slope of hill, 162

Sounds’ intensity (jet, traffic, motorcycle), 394

Speeding ticket cost, 170

Traffic flow rates, 854–855, 857–858, 902, 905

Tram and angle of incline on Rendezvous Mountain, 637

Vehicle depreciation, 436

Vehicles parked on hill and factors affecting, 749–750, 754, 761

Weather

Average monthly rainfall, 115

Average monthly snowfall, 101

Daily high and low temperatures, 228

Hurricane and kinetic energy, 341

Hurricane wind speed and barometric pressure, 178, 180, 367

Monthly high temperatures, 523

Precipitation, highs and lows, 523

Temperatures and average rate of change, 164

Weather balloon, distance from ground and length of tethering ropes, 637

Wind pressure on wall, 352

Wildlife Management

Bass population in lake, 93

Deer population, based on “mark-recapture,” 93 Deer population, growth of, 92

Review of Prerequisites

Chapter Outline

R.1 Sets and the Real Number Line 2

R.2 Exponents and Radicals 16

R.3 Polynomials and Factoring 29

Problem Recognition Exercises: Simplifying Algebraic Expressions 42

R.4 Rational Expressions and More Operations on Radicals 43

R.5 Equations with Real Solutions 54

R.6 Complex Numbers and More Quadratic Equations 71

R.7 Applications of Equations 82

R.8 Linear, Compound, and Absolute Value Inequalities 95

Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities 106

Algebra for Calculus 106

Equations and Inequalities for Calculus 107

Athletes know that in order to optimize their performance they need to pace themselves and be mindful of their target heart rate. For example, a 25-year-old with a maximum heart rate of 195 beats per minute should strive for a target heart rate zone of between 98 and 166 beats per minute. This correlates to between 50% and 85% of the individual’s maximum recommended heart rate (Source: American Heart Association, www. americanheart.org). The mathematics involved in finding maximum recommended heart rate and an individual’s target heart rate zone use a linear model relating age and resting heart rate. An introduction to modeling is presented here in Chapter R along with the standard order of operations used to carry out these calculations. Chapter R reviews skills and concepts required for success in college algebra. Just as an athlete must first learn the basics of a sport and build endurance and speed, a student studying mathematics must focus on necessary basic skills to prepare for the challenge ahead. Preparation for algebra is comparable to an athlete preparing for a sporting event. Putting the time and effort into the basics here in Chapter R will be your foundation for success in later chapters.

SECTION R.1

OBJECTIVES

1. Identify Subsets of the Set of Real Numbers

2. Use Inequality Symbols and Interval Notation

3. Find the Union and Intersection of Sets

4. Evaluate Absolute Value Expressions

5. Use Absolute Value to Represent Distance

6. Apply the Order of Operations

7. Simplify Algebraic Expressions

8. Write Algebraic Models

Sets and the Real Number Line

1. Identify Subsets of the Set of Real Numbers

A hybrid vehicle gets 48 mpg in city driving and 52 mpg on the highway. The formula A 5 1 48 c 1 1 52 h gives the amount of gas A (in gal) for c miles of city driving and h miles of highway driving. In the formula, A, c, and h are called variables and these represent values that are subject to change. The values 1 48 and 1 52 are called constants because their values do not change in the formula.

For a trip from Houston, Texas, to Dallas, Texas, a motorist travels 36 mi of city driving and 91 mi of highway driving. The amount of fuel used by this hybrid vehicle is given by

A 5 1 48 1 36 2 1 1 52 1 91 2 5 2.5 gal

The numbers used in day-to-day life such as those used to determine fuel consumption come from the set of real numbers, denoted by R. A set is a collection of items called elements. The braces { and } are used to enclose the elements of a set. For example, {gold, silver, bronze} represents the set of medals awarded to the top three finishers in an Olympic event. A set that contains no elements is called the empty set (or null set) and is denoted by { } or [ . When referring to individual elements of a set, the symbol [ means “is an element of,” and the symbol ” means “is not an element of.” For example,

5 [ {1, 3, 5, 7} is read as “5 is an element of the set of elements 1, 3, 5, and 7.”

6 ” {1, 3, 5, 7} is read as “6 is not an element of the set of elements 1, 3, 5, and 7.”

A set can be defined in several ways. Listing the elements in a set within braces is called the roster method. Using the roster method, the set of the even numbers between 0 and 10 is represented by {2, 4, 6, 8}. Another method to define this set is by using set-builder notation. This uses a description of the elements of the set. For example, 5 x x is an even number between 0 and 10 6

The set of all x such that x is an even number between 0 and 10

In our study of college algebra, we will often refer to several important subsets (parts of) the set of real numbers (Table R-1).

TIP

Notice that the first five letters of the word rational spell ratio. This will help you remember that a rational number is a ratio of integers.

Table R-1 Subsets of the Set of Real Numbers, R Set Definition

Natural numbers, N {1, 2, 3, …}

Whole numbers, W {0, 1, 2, 3, …}

Integers, Z {… , 3, 2, 1, 0, 1, 2, 3, …}

Rational numbers, Q e p q p, q [ Z and q ﬁ 0 f

• Rational numbers can be expressed as a ratio of integers where the denominator is not zero.

Examples: 6 11 (ratio of 6 and 11) and 9 (ratio of 9 and 1).

• All terminating and repeating decimals are rational numbers. Examples: 0.71 (ratio of 71 and 100), 0.6 5 0.666 (ratio of 2 and 3).

Irrational numbers, H Irrational numbers are real numbers that cannot be expressed as a ratio of integers. The decimal form of an irrational number is nonterminating and nonrepeating. Examples: π and 12

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exclaimed,—O thou who beyond recovery hast captivated my soul, the glance of thine eye has opened a wound in my bosom which will not be cured to the end of my life!

I love, I love an adolescent, and my passion burns like a flame at the bottom of my heart. When love glided into my bosom, scarcely did the tender down shade the cheek of my lover. Oh, I love! and it is for thee, my well-beloved, that my tears flow; and I swear by Him who created love, that my heart has never known tenderness but for thee! I offer to thee my first flame.

When the night deepens its shadows, it is to imitate the blackness of thy curling locks; when the day shines in its purest splendour, it is to recall to mind the dazzling brightness of thy countenance: the exhalations of the aloes are less sweet than the perfume of thy breath; and the lover, enamoured of thy charms, shall pass his life in recounting thy praises.

My best-beloved comes forth, but her countenance is veiled; yet at sight of her all minds are bewildered. The slender branch in the Valley of Camels becomes jealous of her flexible and attractive form. Suddenly she raises her hand and removes the curious veil which concealed her, and the inhabitants of the land utter cries of surprise. Is it a flash of lightning, say they, which illuminates our dwellings? or have the Arabs lighted fires in the desert?

Aly Douhi Eben Sammir

Adgham Eben Ali

Fedghem Eben Sarraage

Sakhrer Sellamé Eben Fakhrer

Drayhy Eben Chahllan

Fares El-Harba

Auad Eben Giandal

Selam Eben Mehgiel

Zarrak

Zarrak Ebn Fakhrer

Giarah Eben Mehgiel

Zehayran Eben Houad

Motlac Eben Fayhan

Faress Eben Aggib

[A] According to Arab law, murder is compensated by money; and the sum is fixed according to circumstances.

[B] This bottle was taken with all the rest into Egypt.

[C] An Arabic expression implying extent of dominion.

[D] A title of a Turkish officer, used in derision by the Bedouins.

[E] Turban of ceremony, (Turkish.)

[F] Destroyer of the Turks.

[G] Every Bedouin accustoms his horse to some sign when it is to put out all its speed He employs it only on pressing occasions, and never confides the secret even to his own son

[H] A pun not easy to translate: Serah means gone; Serhan, wolf.

[I] When a Bedouin voluntarily gives up his horse to his adversary, he may neither kill him nor make him prisoner

[J] Ebn Sihoud, King of the Wahabees, is often called by this name.

[K] This imaginary princess was no other than lady Hester Stanhope

[L] The ceremony is called the hasnat.

[M] These chiefs were, Zarack Ebn Fahrer, chief of the tribe El Gioullan; Giarah Ebn Meghiel, chief of the tribe El Giahma; Ghaleb Ebn Ramdoun, chief of the tribe El Ballahiss; and Fares Ebn Nedged, chief of the tribe El Maslekher.

[N] Female camels of the most beautiful species

[O] An equestrian exercise with sticks, called djerids, which are lanced like javelins.

[P] The tribe El Krassa, whose chief was Zahaman Ebn Houad; the tribe El Mahlac, with its chief Ebn Habed; the tribe El Meraikhrat, its chief Roudan Ebn Abed; and the tribe El Zeker, its chief Matlac Ebn Fayhan

[Q] Fares Ebn Aggib, chief of the tribe El Bechakez, with five hundred tents; Cassan Ebn Unkban, chief of the tribe El Chiamssi, one thousand tents; Selame Ebn Nahssan, chief of the tribe El Fuaher, six hundred tents; Mehanna el Saneh, chief of the tribe El Salba, eight hundred tents

[R] The tribe of El Fedhan, composed of five thousand tents; that of El Sabha, four thousand tents; El Fekaka, one thousand five hundred; El Messahid, three thousand five hundred; El Salca, three thousand; finally, that of Benni Dehabb, five thousand

[S] The tribe of Beny Tay, composed of 4,000 tents; that of El Hamarnid, 1,500 tents; of El Daffir, 2,500 tents; of El Hegiager, 800 tents; and lastly, that of El Khresahel, 3,000.

[T] At Maktal El Abed, we met two tribes, that of Berkaje, commanded by Sahdoun Ebn Wuali, 1300 tents strong, and that of Mahimen, commanded by Fahed Ebn Salche, of 300 tents Crossing the Euphrates before Haiff, we concluded an alliance with Alayan Ebn Nadjed, chief of the tribe of Bouharba, which reckoned 500 tents.

[U] Published by Abel Ledoux.

[V] The celebrated treatise on medicine by Ebn Sina.

[W] This Arabic letter is of a bent form

[X] A stringed instrument.

Transcriber’s note

Minor punctuation errors have been changed without notice. Inconsistencies in hyphenation have been standardized. Spelling has been retained as published.

The spelling of the tribe El Hassnnée was standardized to include the accent mark.

CHANGED FROM TO

Page 11: “manners are every thing” “manners are everything”

Page 47: “M F”

“M F”

Page 69: “Nabbee was armed with” “Nabee was armed with”

Page 71: “Damascus for merchandize” “Damascus for merchandise”

Page 76: “me for my weaknes” “me for my weakness”

Page 104: “des rous of securing” “desirous of securing”

Page 110: “arrived at a spot were” “arrived at a spot where”

Page 136: “the prayer Faliha” “the prayer Fatiha”

Page 137: “enemies be extingushed” “enemies be extinguished”

Page 149: “cafia (handkercheif)” “cafia (handkerchief)”

Page 153: “Drayhy ordered the Hatfé” “Drayhy ordered the hatfé”

Page 158: “enthusiastically rece ved” “enthusiastically received”

Page 204: “Chatti Eben Faress 15,00” “Chatti Eben Faress 1,500”

Page 204: “Auad Eben Motlac 23,00” “Auad Eben Motlac 2,300”

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