Prepare for Class: “Read the Book” - Pearson Education · Algebra & Trigonometry Enhanced with...

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Chapter-Opening Topic & Project

Each chapter begins with a discussion of a topic of current interest and ends with a related project.

In the concluding project, you will apply what you have learned to solve a problem related to the topic.

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Internet-Based Projects

These projects allow for the integration of spreadsheet technology that you will need to be a productive member of the workforce.

The projects give you an opportunity to collaborate and use mathematics to deal with issues of current interest.

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Every Section begins with . . .

LEARNING OBJECTIVES Each section begins with a list of objectives. Individual objectives also appear in the text where they are covered.

These objectives focus your studying by emphasizing what’s most important and where to find it.

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Sections contain . . .

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Most sections begin with a list of key concepts to review, with page numbers.

Ever forget what you’ve learned? This feature highlights previously learned material to be used in this section. Review it, and you’ll always be prepared to move forward.

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Now Work the ‘Are You Prepared?’ Problems

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Work the ‘Are You Prepared?’ problems. If you get one wrong, you’ll know exactly what you need to review and where to review it!

446, 458

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We learn best by doing. You’ll solidify your understanding of examples if you try a similar problem right away, to be sure you understand what you’ve just read.

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Explorations and Seeing the Concept

These graphing utility activities foreshadow a concept or reinforce a concept just presented.

You will obtain a deeper and more intuitive understanding of theorems and definitions.

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Why didn’t you say that in the first place? This feature translates math into plain English.

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CalculusThis symbol appears next to information essential for the study of calculus.

Foreshadowing calculus now will make the material easier later.

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With each step presented on the left and the mathematics displayed on the right, you can immediately see how each step is employed.

358–359

Model It! Examples and Problems

These examples and problems require you to build a mathematical model from either a verbal description or data. The homework Model It! problems are marked by purple problem numbers.

It is rare for a problem to come in the form “Solve the following equation.” Rather, the equation must be developed based on an explanation of the problem. These problems require you to develop models that will enable you to describe the problem mathematically and suggest a solution to the problem.

472, 504

NEW! These margin notes provide a just-in-time reminder of a concept needed now, but covered in an earlier section of the book. Each note is back-referenced to the chapter, section and page where the concept was originally discussed.

Sometimes as you read, you encounter a word or concept you know you’ve seen before, but don't remember exactly what it means. This feature will point you to where you first learned the word or concept. A quick review now will help you see the connection to what you are learning for the first time and make remembering easier the next time.

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Prepare for Class: “Read the Book”

Need to Review?

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Practice: “Work the Problems”

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‘Are You Prepared?’ Problems

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These short-answer questions, mainly fill-in-the-blank, multiple-choice, and true/false items, assess your understanding of key definitions and concepts in the current section.

It is difficult to learn math without knowing the language of mathematics. These problems test your understanding of the formulas and vocabulary.

458–459

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These problems give you ample opportunity to dig in and develop your skills.

459–461

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461

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These problems have been added in most sections and appear at the end of the Application and Extensions exercises. They are intended to be thought-provoking, requiring some ingenuity to solve.

Challenge problems can be used for group work or to challenge your students. Solutions to Challenge Problems are in the Annotated Instructor’s Edition or in the Instructor’s Solution Manual (online).

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“Discussion and Writing” problem numbers are colored red. They support class discussion, verbalization of mathematical ideas, and writing and research projects.

To verbalize an idea, or to describe it clearly in writing, shows real understanding. These problems nurture that understanding. Many are challenging, but you’ll get out what you put in.

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These problems allow you to practice content learned earlier in the course.

Remembering how to solve all the different kinds of problems that you encounter throughout the course is difficult. This practice helps you remember previously learned skills.

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Many examples refer you to a related homework problem. These related problems are marked by and orange problem numbers.

If you get stuck while working problems, look for the closest Now Work problem, and refer to the related example to see if it helps.

454, 456, 457

NEW!Interactive Figure Exercises

Exercises that require you manipulate an interactive figure to solve. These exercises are labeled with the icon .

These exercises help you visualize important concepts and develop a “feel” for them. The figures are housed at bit.ly/2MibgaO and were developed in GeoGebra by author Michael Sullivan III.

458, 459, 473, 474

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Work these problems to ensure that you understand all the skills and concepts employed in the chapter. Think of it as a comprehensive review of the chapter. All answers to Chapter Review problems appear in the back of the text.

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527–528

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Practice makes perfect. These problems combine exercises from all sections, giving you a comprehensive review in one place.

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Be prepared. Take the sample practice test under test conditions. This will get you ready for your instructor’s test. If you get a problem wrong, you can watch the Chapter Test Prep Video.

531–532

Cumulative Review These problem sets appear at the end of each chapter, beginning with Chapter 2. They combine problems from previous chapters, providing an ongoing cumulative review. When you use them in conjunction with the Retain Your Knowledge problems, you will be ready for the final exam.

These problem sets are really important. Completing them will ensure that you are not forgetting anything as you go. This will go a long way toward keeping you primed for the final exam.

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Algebra & TrigonometryEnhanced with Graphing Utilities

Eighth Edition

Michael SullivanChicago State University

Michael Sullivan IIIJoliet Junior College

ANNOTATED INSTRUCTOR’S EDITION


Please contact https://support.pearson.com/getsupport/s/contactsupport with any queries on this content.

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Library of Congress Cataloging-in-Publication Data

Names: Sullivan, Michael, 1942- author. | Sullivan, Michael, III, 1967- Title: Algebra & trigonometry : enhanced with graphing utilities / Michael Sullivan (Chicago State University), Michael Sullivan, III (Joliet Junior College). Other titles: Algebra and trigonometry Description: Eighth Edition | Hoboken, NJ : Pearson Education, Inc., [2021] | Includes index. | Summary: “This textbook approaches college algebra and trigonometry using a right triangle approach. Graphing techniques are emphasized”-- Provided by publisher. Identifiers: LCCN 2019049457 | ISBN 9780135812846 (hardcover) Subjects: LCSH: Algebra--Textbooks. | Trigonometry--Textbooks. | Algebra--Graphic methods. | Trigonometry--Graphic methods. Classification: LCC QA154.3 .S75 2021 | DDC 512/.13--dc23 LC record available at https://lccn.loc.gov/2019049457

ScoutAutomatedPrintCode

ISBN 10: 0135812828ISBN 13: 9780135812822ISBN 10: 0135812844ISBN 13: 9780135812846


For the family

Katy (Murphy) and Pat

Mike and Yola

Dan and Sheila

Colleen (O’Hara) and Bill

Shannon, Patrick, Ryan

Michael, Kevin, Marissa

Maeve, Sean, Nolan

Kaleigh, Billy, Timmy


ix

ContentsThree Distinct Series xix

The Enhanced with Graphing Utilities Series xx

Preface to the Instructor xxi

Resources for Success xxviii

Applications Index xxix

To the Student xxxiv

R Review 1

R.1 Real Numbers 2Work with Sets • Classify Numbers • Evaluate Numerical Expressions • Work with Properties of Real Numbers

R.2 Algebra Essentials 18Graph Inequalities • Find Distance on the Real Number Line • Evaluate Algebraic Expressions • Determine the Domain of a Variable • Use the Laws of Exponents • Evaluate Square Roots • Use a Calculator to Evaluate Exponents • Use Scientific Notation

R.3 Geometry Essentials 31Use the Pythagorean Theorem and Its Converse • Know Geometry Formulas • Understand Congruent Triangles and Similar Triangles

R.4 Polynomials 41Recognize Monomials • Recognize Polynomials • Add and Subtract Polynomials • Multiply Polynomials • Know Formulas for Special Products • Divide Polynomials Using Long Division • Work with Polynomials in Two Variables

R.5 Factoring Polynomials 51Factor the Difference of Two Squares and the Sum and Difference of Two Cubes • Factor Perfect Squares • Factor a Second-Degree Polynomial: x2 + Bx + C • Factor by Grouping • Factor a Second-Degree Polynomial: Ax2 + Bx + C, A ≠ 1 • Complete the Square

R.6 Synthetic Division 59Divide Polynomials Using Synthetic Division

R.7 Rational Expressions 63Reduce a Rational Expression to Lowest Terms • Multiply and Divide Rational Expressions • Add and Subtract Rational Expressions • Use the Least Common Multiple Method • Simplify Complex Rational Expressions

R.8 nth Roots; Rational Exponents 74Work with nth Roots • Simplify Radicals • Rationalize Denominators and Numerators • Simplify Expressions with Rational Exponents

1 Graphs, Equations, and Inequalities 83

1.1 Graphing Utilities; Introduction to Graphing Equations 84Graph Equations by Plotting Points • Graph Equations Using a Graphing Utility • Use a Graphing Utility to Create Tables • Find Intercepts from a Graph • Use a Graphing Utility to Approximate Intercepts

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1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations 95Solve Equations Using a Graphing Utility • Solve Linear Equations • Solve Rational Equations • Solve Problems That Can Be Modeled by Linear Equations

1.3 Quadratic Equations 106Solve a Quadratic Equation by Factoring • Solve a Quadratic Equation Using the Square Root Method • Solve a Quadratic Equation by Completing the Square • Solve a Quadratic Equation Using the Quadratic Formula • Solve Problems That Can Be Modeled by Quadratic Equations

1.4 Complex Numbers; Quadratic Equations in the Complex Number System 118Add, Subtract, Multiply, and Divide Complex Numbers • Solve Quadratic Equations in the Complex Number System

1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations 127Solve Radical Equations • Solve Equations Quadratic in Form • Solve Equations Involving Absolute Value • Solve Equations by Factoring

1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications 135Translate Verbal Descriptions into Mathematical Expressions • Solve Interest Problems • Solve Mixture Problems • Solve Uniform Motion Problems • Solve Constant Rate Job Problems

1.7 Solving Inequalities 145Use Interval Notation • Use Properties of Inequalities • Solve Linear Inequalities Algebraically and Graphically • Solve Combined Inequalities Algebraically and Graphically • Solve Absolute Value Inequalities Algebraically and Graphically

Chapter Review 156

Chapter Test 160

Chapter Projects 160

x Contents

2 Graphs 162

2.1 The Distance and Midpoint Formulas 163Use the Distance Formula • Use the Midpoint Formula

2.2 Intercepts; Symmetry; Graphing Key Equations 170Find Intercepts Algebraically from an Equation • Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin • Know How to Graph Key Equations

2.3 Lines 179Calculate and Interpret the Slope of a Line • Graph Lines Given a Point and the Slope • Find the Equation of a Vertical Line • Use the Point-Slope Form of a Line; Identify Horizontal Lines • Use the Slope-Intercept Form of a Line • Find the Equation of a Line Given Two Points • Graph Lines Written in General Form Using Intercepts • Find Equations of Parallel Lines • Find Equations of Perpendicular Lines

2.4 Circles 195Write the Standard Form of the Equation of a Circle • Graph a Circle by Hand and by Using a Graphing Utility • Work with the General Form of the Equation of a Circle

2.5 Variation 202Construct a Model Using Direct Variation • Construct a Model Using Inverse Variation • Construct a Model Using Joint Variation


Contents xi

3 Functions and Their Graphs 212

3.1 Functions 213Describe a Relation • Determine Whether a Relation Represents a Function • Use Function Notation; Find the Value of a Function • Find the Difference Quotient of a Function • Find the Domain of a Function Defined by an Equation • Form the Sum, Difference, Product, and Quotient of Two Functions

3.2 The Graph of a Function 229Identify the Graph of a Function • Obtain Information from or about the Graph of a Function

3.3 Properties of Functions 239Identify Even and Odd Functions from a Graph • Identify Even and Odd Functions from an Equation • Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant • Use a Graph to Locate Local Maxima and Local Minima • Use a Graph to Locate the Absolute Maximum and the Absolute Minimum • Use a Graphing Utility to Approximate Local Maxima and Local Minima and to Determine Where a Function Is Increasing or Decreasing • Find the Average Rate of Change of a Function

3.4 Library of Functions; Piecewise-defined Functions 253Graph the Functions Listed in the Library of Functions • Analyze a Piecewise-defined Function

3.5 Graphing Techniques: Transformations 265Graph Functions Using Vertical and Horizontal Shifts • Graph Functions Using Compressions and Stretches • Graph Functions Using Reflections about the x-Axis or y-Axis

3.6 Mathematical Models: Building Functions 279Build and Analyze Functions

Chapter Review 284

Chapter Test 288

Cumulative Review 289


4 Linear and Quadratic Functions 291

4.1 Properties of Linear Functions and Linear Models 292Graph Linear Functions • Use Average Rate of Change to Identify Linear Functions • Determine Whether a Linear Function Is Increasing, Decreasing, or Constant • Build Linear Models from Verbal Descriptions

4.2 Building Linear Models from Data 302Draw and Interpret Scatter Plots • Distinguish between Linear and Nonlinear Relations • Use a Graphing Utility to Find the Line of Best Fit

4.3 Quadratic Functions and Their Properties 310Graph a Quadratic Function Using Transformations • Identify the Vertex and Axis of Symmetry of a Parabola • Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts • Find a Quadratic Function Given Its Vertex and One Other Point • Find the Maximum or Minimum Value of a Quadratic Function

Chapter Review 208

Chapter Test 210


Chapter Project 211


4.4 Building Quadratic Models from Verbal Descriptions and from Data 324Build Quadratic Models from Verbal Descriptions • Build Quadratic Models from Data

4.5 Inequalities Involving Quadratic Functions 332Solve Inequalities Involving a Quadratic Function

Chapter Review 336

Chapter Test 338



xii Contents

5 Polynomial and Rational Functions 341

5.1 Polynomial Functions 342Identify Polynomial Functions and Their Degree • Graph Polynomial Functions Using Transformations • Identify the Real Zeros of a Polynomial Function and Their Multiplicity

5.2 The Graph of a Polynomial Function; Models 357Analyze the Graph of a Polynomial Function • Build Cubic Models from Data

5.3 The Real Zeros of a Polynomial Function 366Use the Remainder and Factor Theorems • Use Descartes’ Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function • Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function • Find the Real Zeros of a Polynomial Function • Solve Polynomial Equations • Use the Theorem for Bounds on Zeros • Use the Intermediate Value Theorem

5.4 Complex Zeros; Fundamental Theorem of Algebra 381Use the Conjugate Pairs Theorem • Find a Polynomial Function with Specified Zeros • Find the Complex Zeros of a Polynomial Function

5.5 Properties of Rational Functions 388Find the Domain of a Rational Function • Find the Vertical Asymptotes of a Rational Function • Find the Horizontal or Oblique Asymptote of a Rational Function

5.6 The Graph of a Rational Function 399Analyze the Graph of a Rational Function • Solve Applied Problems Involving Rational Functions

5.7 Polynomial and Rational Inequalities 411Solve Polynomial Inequalities Graphically and Algebraically • Solve Rational Inequalities Graphically and Algebraically

Chapter Review 418

Chapter Test 421



6 Exponential and Logarithmic Functions 424

6.1 Composite Functions 425Form a Composite Function • Find the Domain of a Composite Function


6.2 One-to-One Functions; Inverse Functions 433Determine Whether a Function Is One-to-One • Determine the Inverse of a Function Defined by a Mapping or a Set of Ordered Pairs • Obtain the Graph of the Inverse Function from the Graph of a One-to-One Function • Verify that a Function Defined by an Equation Is an Inverse Function • Find the Inverse of a Function Defined by an Equation

6.3 Exponential Functions 446Evaluate Exponential Functions • Graph Exponential Functions • Define the Number e • Solve Exponential Equations

6.4 Logarithmic Functions 465Change Exponential Statements to Logarithmic Statements and Logarithmic Statements to Exponential Statements • Evaluate Logarithmic Expressions • Determine the Domain of a Logarithmic Function • Graph Logarithmic Functions • Solve Logarithmic Equations

6.5 Properties of Logarithms 479Work with the Properties of Logarithms • Write a Logarithmic Expression as a Sum or Difference of Logarithms • Write a Logarithmic Expression as a Single Logarithm • Evaluate Logarithms Whose Base Is Neither 10 Nor e • Graph a Logarithmic Function Whose Base is Neither 10 Nor e

6.6 Logarithmic and Exponential Equations 488Solve Logarithmic Equations • Solve Exponential Equations • Solve Logarithmic and Exponential Equations Using a Graphing Utility

6.7 Financial Models 497Determine the Future Value of a Lump Sum of Money • Calculate Effective Rates of Return • Determine the Present Value of a Lump Sum of Money • Determine the Rate of Interest or the Time Required to Double a Lump Sum of Money

6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 507Model Populations That Obey the Law of Uninhibited Growth • Model Populations That Obey the Law of Uninhibited Decay • Use Newton’s Law of Cooling • Use Logistic Models

6.9 Building Exponential, Logarithmic, and Logistic Models from Data 518Build an Exponential Model from Data • Build a Logarithmic Model from Data • Build a Logistic Model from Data

Chapter Review 526

Chapter Test 531



7 Trigonometric Functions 534

7.1 Angles, Arc Length, and Circular Motion 535Angles and Degree Measure • Convert between Decimal and Degree, Minute, Second Measures for Angles • Find the Length of an Arc of a Circle • Convert from Degrees to Radians and from Radians to Degrees • Find the Area of a Sector of a Circle • Find the Linear Speed of an Object Traveling in Circular Motion

7.2 Right Triangle Trigonometry 548Find the Values of Trigonometric Functions of Acute Angles • Use Fundamental Identities • Find the Values of the Remaining Trigonometric Functions, Given the Value of One of Them • Use the Complementary Angle Theorem

Contents xiii


7.3 Computing the Values of Trigonometric Functions of Acute Angles 561Find the Exact Values of the Trigonometric Functions of

p

4= 45° • Find

the Exact Values of the Trigonometric Functions of p

6= 30° and

p

3= 60°

• Use a Calculator to Approximate the Values of the Trigonometric Functions of Acute Angles • Model and Solve Applied Problems Involving Right Triangles

7.4 Trigonometric Functions of Any Angle 572Find the Exact Values of the Trigonometric Functions for Any Angle • Use Coterminal Angles to Find the Exact Value of a Trigonometric Function • Determine the Signs of the Trigonometric Functions of an Angle in a Given Quadrant • Find the Reference Angle of an Angle • Use a Reference Angle to Find the Exact Value of a Trigonometric Function • Find the Exact Values of the Trigonometric Functions of an Angle, Given Information about the Functions

7.5 Unit Circle Approach; Properties of the Trigonometric Functions 583Find the Exact Values of the Trigonometric Functions Using the Unit Circle • Know the Domain and Range of the Trigonometric Functions • Use Periodic Properties to Find the Exact Values of the Trigonometric Functions • Use Even-Odd Properties to Find the Exact Values of the Trigonometric Functions

7.6 Graphs of the Sine and Cosine Functions 596Graph the Sine Function y = sin x and Functions of the Form y = A sin1vx2 • Graph the Cosine Function y = cos x and Functions of the Form y = A cos1vx2 • Determine the Amplitude and Period of Sinusoidal Functions • Graph Sinusoidal Functions Using Key Points • Find an Equation for a Sinusoidal Graph

7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 612Graph the Tangent Function y = tan x and the Cotangent Function y = cot x • Graph Functions of the Form y = A tan 1vx2 + B and y = A cot 1vx 2 + B • Graph the Cosecant Function y = csc x and the Secant Function y = sec x • Graph Functions of the Form y = A csc 1vx 2 + B and y = A sec 1vx 2 + B

7.8 Phase Shift; Sinusoidal Curve Fitting 620Graph Sinusoidal Functions of the Form y = A sin1vx - f2 + B • Build Sinusoidal Models from Data

Chapter Review 631

Chapter Test 637



xiv Contents

8 Analytic Trigonometry 640

8.1 The Inverse Sine, Cosine, and Tangent Functions 641Define the Inverse Sine Function • Find the Value of an Inverse Sine Function • Define the Inverse Cosine Function • Find the Value of an Inverse Cosine Function • Define the Inverse Tangent Function • Find the Value of an Inverse Tangent Function • Use Properties of Inverse Functions to Find Exact Values of Certain Composite Functions • Find the Inverse Function of a Trigonometric Function • Solve Equations Involving Inverse Trigonometric Functions


8.2 The Inverse Trigonometric Functions (Continued) 656Define the Inverse Secant, Cosecant, and Cotangent Functions • Find the Value of Inverse Secant, Cosecant, and Cotangent Functions • Find the Exact Value of Composite Functions Involving the Inverse Trigonometric Functions • Write a Trigonometric Expression as an Algebraic Expression

8.3 Trigonometric Equations 662Solve Equations Involving a Single Trigonometric Function • Solve Trigonometric Equations Using a Calculator • Solve Trigonometric Equations Quadratic in Form • Solve Trigonometric Equations Using Fundamental Identities • Solve Trigonometric Equations Using a Graphing Utility

8.4 Trigonometric Identities 672Use Algebra to Simplify Trigonometric Expressions • Establish Identities

8.5 Sum and Difference Formulas 680Use Sum and Difference Formulas to Find Exact Values • Use Sum and Difference Formulas to Establish Identities • Use Sum and Difference Formulas Involving Inverse Trigonometric Functions • Solve Trigonometric Equations Linear in Sine and Cosine

8.6 Double-angle and Half-angle Formulas 693Use Double-angle Formulas to Find Exact Values • Use Double-angle Formulas to Establish Identities • Use Half-angle Formulas to Find Exact Values

8.7 Product-to-Sum and Sum-to-Product Formulas 704Express Products as Sums • Express Sums as Products

Chapter Review 708

Chapter Test 711



9 Applications of Trigonometric Functions 714

9.1 Applications Involving Right Triangles 715Solve Right Triangles • Solve Applied Problems

9.2 The Law of Sines 721Solve SAA or ASA Triangles • Solve SSA Triangles • Solve Applied Problems

9.3 The Law of Cosines 732Solve SAS Triangles • Solve SSS Triangles • Solve Applied Problems

9.4 Area of a Triangle 739Find the Area of SAS Triangles • Find the Area of SSS Triangles

9.5 Simple Harmonic Motion; Damped Motion; Combining Waves 745Build a Model for an Object in Simple Harmonic Motion • Analyze Simple Harmonic Motion • Analyze an Object in Damped Motion • Graph the Sum of Two Functions

Chapter Review 755

Chapter Test 757



Contents xv

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11 Analytic Geometry 825

11.1 Conics 826Know the Names of the Conics

11.2 The Parabola 827Analyze Parabolas with Vertex at the Origin • Analyze Parabolas with Vertex at (h, k) • Solve Applied Problems Involving Parabolas

11.3 The Ellipse 837Analyze Ellipses with Center at the Origin • Analyze Ellipses with Center at (h, k) • Solve Applied Problems Involving Ellipses

11.4 The Hyperbola 850Analyze Hyperbolas with Center at the Origin • Find the Asymptotes of a Hyperbola • Analyze Hyperbolas with Center at (h, k) • Solve Applied Problems Involving Hyperbolas

11.5 Rotation of Axes; General Form of a Conic 865Identify a Conic • Use a Rotation of Axes to Transform Equations • Analyze an Equation Using a Rotation of Axes • Identify Conics without Rotating the Axes

11.6 Polar Equations of Conics 873Analyze and Graph Polar Equations of Conics • Convert the Polar Equation of a Conic to a Rectangular Equation

xvi Contents

10 Polar Coordinates; Vectors 760

10.1 Polar Coordinates 761Plot Points Using Polar Coordinates • Convert from Polar Coordinates to Rectangular Coordinates • Convert from Rectangular Coordinates to Polar Coordinates • Transform Equations between Polar and Rectangular Forms

10.2 Polar Equations and Graphs 771Identify and Graph Polar Equations by Converting to Rectangular Equations • Graph Polar Equations Using a Graphing Utility • Test Polar Equations for Symmetry • Graph Polar Equations by Plotting Points

10.3 The Complex Plane; De Moivre’s Theorem 788Plot Points in the Complex Plane • Convert a Complex Number between Rectangular Form and Polar Form or Exponential Form • Find Products and Quotients of Complex Numbers • Use De Moivre’s Theorem • Find Complex Roots

10.4 Vectors 798Graph Vectors • Find a Position Vector • Add and Subtract Vectors Algebraically • Find a Scalar Multiple and the Magnitude of a Vector • Find a Unit Vector • Find a Vector from Its Direction and Magnitude • Model with Vectors

10.5 The Dot Product 812Find the Dot Product of Two Vectors • Find the Angle between Two Vectors • Determine Whether Two Vectors Are Parallel • Determine Whether Two Vectors Are Orthogonal • Decompose a Vector into Two Orthogonal Vectors • Compute Work

Chapter Review 820

Chapter Test 823




12 Systems of Equations and Inequalities 899

12.1 Systems of Linear Equations: Substitution and Elimination 900Solve Systems of Equations by Substitution • Solve Systems of Equations by Elimination • Identify Inconsistent Systems of Equations Containing Two Variables • Express the Solution of a System of Dependent Equations Containing Two Variables • Solve Systems of Three Equations Containing Three Variables • Identify Inconsistent Systems of Equations Containing Three Variables • Express the Solution of a System of Dependent Equations Containing Three Variables

12.2 Systems of Linear Equations: Matrices 914Write the Augmented Matrix of a System of Linear Equations • Write the System of Equations from the Augmented Matrix • Perform Row Operations on a Matrix • Solve a System of Linear Equations Using Matrices

12.3 Systems of Linear Equations: Determinants 929Evaluate 2 by 2 Determinants • Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables • Evaluate 3 by 3 Determinants • Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables • Know Properties of Determinants

12.4 Matrix Algebra 940Find the Sum and Difference of Two Matrices • Find Scalar Multiples of a Matrix • Find the Product of Two Matrices • Find the Inverse of a Matrix • Solve a System of Linear Equations Using an Inverse Matrix

12.5 Partial Fraction Decomposition 957

Decompose PQ

where Q Has Only Nonrepeated Linear Factors

• Decompose PQ

where Q Has Repeated Linear Factors • Decompose PQ

where Q Has a Nonrepeated Irreducible Quadratic Factor • Decompose PQ

where Q Has a Repeated Irreducible Quadratic Factor

12.6 Systems of Nonlinear Equations 966Solve a System of Nonlinear Equations Using Substitution • Solve a System of Nonlinear Equations Using Elimination

12.7 Systems of Inequalities 976Graph an Inequality by Hand • Graph an Inequality Using a Graphing Utility • Graph a System of Inequalities

12.8 Linear Programming 985Set Up a Linear Programming Problem • Solve a Linear Programming Problem

Chapter Review 992

Chapter Test 996



Contents xvii

11.7 Plane Curves and Parametric Equations 880Graph Parametric Equations by Hand • Graph Parametric Equations Using a Graphing Utility • Find a Rectangular Equation for a Plane Curve Defined Parametrically • Use Time as a Parameter in Parametric Equations • Find Parametric Equations for Plane Curves Defined by Rectangular Equations

Chapter Review 894

Chapter Test 897




14 Counting and Probability 1048

14.1 Counting 1049Find All the Subsets of a Set • Count the Number of Elements in a Set • Solve Counting Problems Using the Multiplication Principle

14.2 Permutations and Combinations 1054Solve Counting Problems Using Permutations Involving n Distinct Objects • Solve Counting Problems Using Combinations • Solve Counting Problems Using Permutations Involving n Nondistinct Objects

14.3 Probability 1063Construct Probability Models • Compute Probabilities of Equally Likely Outcomes • Find Probabilities of the Union of Two Events • Use the Complement Rule to Find Probabilities

Chapter Review 1073

Chapter Test 1075



Answers AN1

Challenge Problem Solutions CP1

Photo Credits C1

Subject Index I1

13 Sequences; Induction; the Binomial Theorem 999

13.1 Sequences 1000List the First Several Terms of a Sequence • List the Terms of a Sequence Defined by a Recursive Formula • Use Summation Notation • Find the Sum of a Sequence Algebraically and Using a Graphing Utility • Solve Annuity and Amortization Problems Using Recursive Formulas

13.2 Arithmetic Sequences 1014Determine Whether a Sequence Is Arithmetic • Find a Formula for an Arithmetic Sequence • Find the Sum of an Arithmetic Sequence

13.3 Geometric Sequences; Geometric Series 1020Determine Whether a Sequence Is Geometric • Find a Formula for a Geometric Sequence • Find the Sum of a Geometric Sequence • Determine Whether a Geometric Series Converges or Diverges • Solve Annuity Problems Using Formulas

13.4 Mathematical Induction 1032Prove Statements Using Mathematical Induction

13.5 The Binomial Theorem 1036

Evaluate a nj b • Use the Binomial Theorem

Chapter Review 1043

Chapter Test 1045



xviii Contents


xix

Students have different goals, learning styles, and levels of preparation. Instructors have different teaching philosophies, styles, and techniques. Rather than write one series to fit all, the Sullivans have written three distinct series. All share the same goal—to develop a high level of mathematical understanding and an appreciation for the way mathematics can describe the world around us. The manner of reaching that goal, however, differs from series to series.

Enhanced with Graphing Utilities SeriesThis series provides a thorough integration of graphing utilities into topics, allowing students to explore mathematical concepts and encounter ideas usually studied in later courses. Many examples show solutions using algebra side-by-side with graphing techniques. Using technology, the approach to solving certain problems differs from the Contemporary (Flagship) or Concepts through Functions Series, while the emphasis on understanding concepts and building strong skills is maintained. Texts in this series are College Algebra, Algebra & Trigonometry, and Precalculus.

Flagship SeriesThe Flagship Series is the most traditional in approach, yet modern in its treatment of precalculus mathematics. In each text, needed review material is included and is referenced when it is used. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor. Texts in this series are College Algebra, Algebra & Trigonometry, Trigonometry: A Unit Circle Approach, and Precalculus.

Concepts through Functions SeriesThis series differs from the others, utilizing a functions approach that serves as the organizing principle tying concepts together. Functions are introduced early in various formats. This approach supports the Rule of Four, which states that functions are represented symbolically, numerically, graphically, and verbally. Each chapter introduces a new type of function and then develops all concepts pertaining to that particular function. The solutions of equations and inequalities, instead of being developed as stand-alone topics, are developed in the context of the underlying functions. Graphing utility coverage is optional and can be included or excluded at the discretion of the instructor. Texts in this series are College Algebra; Precalculus, with a Unit Circle Approach to Trigonometry; Precalculus, with a Right Triangle Approach to Trigonometry.

Three Distinct Series to Meet Varied Instructional Needs

xix


The Enhanced with Graphing Utilities Series

College Algebra, Eighth EditionThis text provides an approach to college algebra that completely integrates graphing technology without sacrificing mathematical analysis and conceptualization. The text has three chapters of review material preceding the chapter on functions. Graphing calculator usage is integrated throughout. After completing this text, a student will be prepared for trigonometry, finite mathematics, and business calculus.

Algebra & Trigonometry, Eighth EditionThis text contains all the material in College Algebra, but it also develops the trigonometric functions using a right triangle approach and shows how that approach is related to the unit circle approach. Graphing techniques are emphasized, including a thorough discussion of polar coordinates, parametric equations, and conics using polar coordinates. Vectors in the plane, including the dot product, sequences, induction, and the binomial theorem are also presented. After completing this text, a student will be prepared for finite mathematics, business calculus, and engineering calculus.

Precalculus, Eighth EditionThis text contains a review chapter before covering the traditional precalculus topics of functions and their graphs, polynomial and rational functions, and exponential and logarithmic functions. The trigonometric functions are introduced using a unit circle approach and show how it is related to the right triangle approach. Graphing techniques are emphasized, including a thorough discussion of polar coordinates, parametric equations, and conics using polar coordinates. Vectors in the plane and in space, including the dot and cross products, sequences, induction, and the binomial theorem are also presented. Graphing calculator usage is integrated throughout. The final chapter provides an introduction to calculus, with a discussion of the limit, the derivative, and the integral of a function. After completing this text, a student will be prepared for finite mathematics, business calculus, and engineering calculus.

xx

COLLEGE ALGEBRAEnhanced with Graphing Utilities

Eighth Edition

Sullivan & Sullivan

Enhanced with Graphing UtilitiesEighth Edition

ALGEBRA andTRIGONOMETRY

Sullivan & Sullivan

PRECALCULUSEnhanced with Graphing Utilities

Eighth Edition

Sullivan & Sullivan


Now Work 1. Modeling 1. Writing/Discussion

Calculus Preview Interactive Figure

Preface to the Instructor

As professors at an urban university (Michael Sullivan) and a community college (Michael Sullivan III), we are aware of the varied needs of students in this

course. Such students range from those who have little mathematical background and are fearful of mathematics courses to those with a strong mathematical education and a high level of motivation. For some of your students, this will be their last course in mathematics, whereas others will further their mathematical education. We have written this text with both groups in mind.

As a teacher, and as an author of precalculus, engineering calculus, finite mathematics, and business calculus texts, Michael Sullivan understands what students must know if they are to be focused and successful in upper-level math courses. As an instructor and an author of a developmental mathematics series, Michael’s son and co-author, Michael Sullivan III, understands the trepidations and skills that students bring to the Algebra and Trigonometry course. As the father of current college students, Michael III realizes that today’s college students demand a variety of media to support their education. This text addresses that demand by providing technology and video support that enhances understanding without sacrificing math skills. Together, we have taken great pains to ensure that the text offers solid, student-friendly examples and problems, as well as a clear and seamless writing style.

A tremendous benefit of authoring a successful series is the broad-based feedback we receive from teachers and students. We are sincerely grateful for their support. Virtually every change in this edition is the result of their thoughtful comments and suggestions. We are confident that, building on the success of the first seven editions and incorporating many of these suggestions, we have made Algebra & Trigonometry Enhanced with Graphing Utilities, 8th Edition, an even better tool for learning and teaching. We continue to encourage you to share with us your experiences teaching from this text.

Features in the Eighth EditionA descriptive list of the many special features of Algebra & Trigonometry can be found in the front of this text. This list places the features in their proper context as building blocks of an overall learning system that has been carefully crafted over the years to help students get the most out of the time they put into studying. Please take the time to review this and to discuss it with your students at the beginning of your course. Our experience is that when students utilize these features, they are more successful in the course.

New to the Eighth Edition

New Within the TextbookAll of the exercises and examples in the text have been reviewed and analyzed, and we have incorporated feedback from users of the text. All time-sensitive problems have been updated to the most recent information available. Here are the new features of this edition:

• Challenge Problems – These problems appear in the Applications and Extensions part of the section exercises and are designed to challenge students. Full solutions are in the back of the Annotated Instructor’s Edition and in the Instructor’s Solution Manual.

• “Need to Review?” feature – We placed reminders in the margin for key review topics. The reminders point students to the location of the review material in the textbook.

• Chapter Projects – The projects have been enhanced to give students an up-to-the-minute experience. Many of these projects require the student to research information online in order to solve problems.

• Interactive Figure Exercises – We have added this new category of exercises that require students to manipulate an interactive figure to solve. The interactive figures may be found at bit.ly/2MibgaO or in the Video and Resource Library of MyLab Math, and were created by author Michael Sullivan III in GeoGebra. These exercises are labeled with the icon .

• Expanded! Retain Your Knowledge Problems – These problems, which were new to the previous edition, are based on learning research, including a study of precalculus students at University of Louisville entitled “Spaced retrieval practice increases college students’ short- and long-term retention of mathematics knowledge” (Hopkins et al, 2016). The Retain Your Knowledge problems were so well received that we have expanded them in this edition. Moreover, while the focus remains to help students maintain their skills, in most sections, problems were chosen that preview skills required to succeed in subsequent sections or in calculus ( ). All answers to Retain Your Knowledge problems are given in the back of the text and these problems are available in the prebuilt assignments in the Assignment Manager in MyLab Math.

• Key to Exercise Types – To help you navigate the features of the exercise sets, we’ve included a key at the bottom of the first page of each section’s exercises.

xxi


• Graphing Utility Screen Captures – In several instances we have added Desmos screen captures along with the TI-84 Plus CE screen captures. These updated screen captures provide alternative ways of visualizing concepts and making connections between equations, data, and graphs in full color.

Content ChangesChapter R• Section R.8 Objective 3 now includes rationalizing the

numerator. Problems 69–76 provide practice.

Chapter 1• Section 1.1 has been reorganized to only include an

introduction to graphing and graphing utilities.

Chapter 2• NEW Section 2.1 The Distance and Midpoint Formulas

• NEW Section 2.2 Example 5 Testing an Equation for Symmetry

Chapter 3• NEW Section 3.1 Objective 1 Describe a Relation

NEW Example 1 Describing a Relation demonstrates using the Rule of Four to express a relation numerically, as a mapping, and graphically given a verbal description.

• NEW Section 3.2 Example 4 Expending Energy

Chapter 4• Section 4.3 now introduces the concept of concavity for

a quadratic function.

• NEW Section 4.3 Example 3 Graphing a Quadratic Function Using Its Vertex, Axis, and Intercepts

• Section 4.3 Example 8 Analyzing the Motion of a Projectile (formerly in Section 4.4)

• NEW Section 4.4 Example 4 Fitting a Quadratic Function to Data

Chapter 5• Previous Section 5.1 has been revised and split into two

sections:

5.1 Polynomial Functions

5.2 Graphing Polynomial Functions; Models

• NEW Section 5.2 Example 2 Graphing a Polynomial Function (a 4th degree polynomial function)

Chapter 6• NEW Section 6.2 Objective Verify a Function Defined

by an Equation is an Inverse Function

Chapter 7• NEW Section 7.1 Example 6 Field Width of a Digital

Lens Reflex Camera Lens

• NEW Section 7.5 Example 5 Using Symmetry to Find Exact Values of Trigonometric Functions

• Sections 7.6 and 7.7 were reorganized for increased clarity. Two new objectives were added to Section 7.7.

Chapter 8• Sections 8.1 and 8.2 were reorganized for increased

clarity. Four new objectives were added to Section 8.1. The objectives in Section 8.2 were reordered.

Chapter 10• Section 10.3 DeMoivre’s Theorem was rewritten to

support the exponential form of a complex number.

Euler’s Formula is introduced to express a complex number in exponential form. The exponential form is used to compute products and quotients.

DeMoivre’s Theorem is expressed using the exponential form of a complex number. The exponential form is used to find complex roots.

Chapter 12• NEW Section 12.5 Example 1 Identifying Proper and

Improper Rational Expressions

Chapter 13• NEW Section 13.3 Objective 5 Solving Annuity Problems

Using Formulas

New Within MyLab Math• Setup & Solve Exercises require students to show how

they set up a problem as well as the solution, better mirroring what is required of them on tests. We have included both the “traditional” and Setup & Solve versions of exercise within MyLab to provide you with more options for assessing students.

• Integrated Review content and assessments help you provide students with the remediation they need, when they need it. Integrated Review consists of:

Skills Check Quizzes by chapter assess the prerequisite skills students need for that chapter.

Skills Review Homework, again by chapter, is personalized (based on the results of the Skills Check Quiz) to provide students with help on the prerequisite skills they are lacking. Students receive just the help they need—no more, no less.

Intermediate Algebra eText, Exercises, Videos, and Worksheets—For students who need more help (or for co-requisite courses), we’ve included the contents of a streamlined Intermediate Algebra course within this MyLab course. There’s no need to go elsewhere for remediation.

• Interactive Figures (formerly titled Guided Visualizations) have been expanded to support teaching and learning. The figures (created in GeoGebra by author Michael Sullivan III) illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently.

• Enhanced Sample Assignments are pre-made section-level assignments that address key concepts within the section and help keep previously learned skills fresh with RetainYour Knowledge questions. They are assignable and editable.

xxii Preface to the Instructor


Using the Eighth Edition Effectively with Your SyllabusTo meet the varied needs of diverse syllabi, this text contains more content than is likely to be covered in an Algebra and Trigonometry course. As the chart illustrates, this text has been organized with flexibility of use in mind. Within a given chapter, certain sections are optional (see the details that follow the accompanying figure) and can be omitted without loss of continuity.

2

1

3

R

11.1�11.4

11.5�11.7

10.1�10.3

4 5 6 7 13

12 14

8

9

10.4�10.5

Chapter R ReviewThis chapter consists of review material. It may be used as the first part of the course or later as a just-in-time review when the content is required. Specific references to this chapter occur throughout the text to assist in the review process.

Chapter 1 Equations and InequalitiesPrimarily a review of intermediate algebra topics, this material is a prerequisite for later topics. The coverage of complex numbers and quadratic equations with a negative discriminant is optional and may be postponed or skipped entirely without loss of continuity.

Chapter 2 GraphsThis chapter lays the foundation for functions. Section 2.5 is optional.

Chapter 3 Functions and Their GraphsThis is perhaps the most important chapter. Section 3.6 is optional.

Chapter 4 Linear and Quadratic FunctionsTopic selection depends on your syllabus. Sections 4.2 and 4.4 may be omitted without loss of continuity.

Chapter 5 Polynomial and Rational FunctionsTopic selection depends on your syllabus.

Chapter 6 Exponential and Logarithmic FunctionsSections 6.1–6.6 follow in sequence. Sections 6.7, 6.8, and 6.9 are optional.

Chapter 7 Trigonometric FunctionsSection 7.8 may be omitted in a brief course.

Chapter 8 Analytic TrigonometrySections 8.2, 8.6, and 8.7 may be omitted in a brief course.

Chapter 9 Applications of Trigonometric FunctionsSections 9.4 and 9.5 may be omitted in a brief course.

Chapter 10 Polar Coordinates; VectorsSections 10.1–10.3 and Sections 10.4–10.5 are independent and may be covered separately.

Chapter 11 Analytic GeometrySections 11.1–11.4 follow in sequence. Sections 11.5, 11.6, and 11.7 are independent of each other, but each requires Sections 11.1–11.4.

Chapter 12 Systems of Equations and InequalitiesSections 12.2–12.7 may be covered in any order, but each requires Section 12.1. Section 12.8 requires Section 12.7.

Chapter 13 Sequences; Induction; The Binomial TheoremThere are three independent parts: Sections 13.1–13.3, Section 13.4, and Section 13.5.

Chapter 14 Counting and ProbabilityThe sections follow in sequence.

AcknowledgmentsTexts are written by authors, but they evolve from idea to final form through the efforts of many people.

Thanks are due to the following people for their assistance and encouragement during the preparation of this edition:

• From Pearson Education: Dawn Murrin, for her substantial support, dedication, and energy; Jeff Weidenaar for his attention to detail, experience, editorial expertise, and genuine interest in this project; Peggy McMahon for directing the always difficult production process; Rose Kernan for handling liaison between the compositor and author; Stacey Sveum and Jordan Longoria for their creative and enthusiastic marketing this text; Marcia Horton for her continued support and genuine interest; Paul Corey for his leadership and commitment to excellence; and Peggy Lucas and the Pearson sales team for their continued confidence and personal support of our texts.

• Accuracy checkers: Roger Lipsett read the entire manuscript and checked the accuracy of answers. Timothy Britt created the Solutions Manuals and accuracy-checked answers.

• Michael Sullivan III would like to thank his colleagues at Joliet Junior College for their support and feedback.

Finally, we offer our sincere thanks to the dedicated users and reviewers of our texts, whose collective insights form the backbone of each text revision.

The list of those to whom we are indebted continues to grow. If we’ve forgotten anyone, please accept our apology. Thank you to all.

Preface to the Instructor xxiii


James Africh, College of DuPageSteve Agronsky, Cal Poly State UniversityGererdo Aladro, Florida International

UniversityGrant Alexander, Joliet Junior CollegeDave Anderson, South Suburban CollegeWes Anderson, Northwest Vista CollegeRichard Andrews, Florida A&M UniversityJoby Milo Anthony, University of Central

FloridaJames E. Arnold, University of

Wisconsin-MilwaukeeAdel Arshaghi, Center for Educational MeritCarolyn Autray, University of West GeorgiaAgnes Azzolino, Middlesex County CollegeWilson P. Banks, Illinois State UniversitySudeshna Basu, Howard UniversityTimothy Bayer, Virginia Western CCDale R. Bedgood, East Texas State UniversityBeth Beno, South Suburban CollegeCarolyn Bernath, Tallahassee Community

CollegeRebecca Berthiaume, Edison State CollegeWilliam H. Beyer, University of AkronAnnette Blackwelder, Florida State UniversityRichelle Blair, Lakeland Community CollegeKevin Bodden, Lewis and Clark CollegeJeffrey Boerner, University of Wisconsin-StoutConnie Booker, Owensboro Community and

Technical CollegeBarry Booten, Florida Atlantic UniversityLaurie Boudreaux, Nicholls State UniversityLarry Bouldin, Roane State Community

CollegeBob Bradshaw, Ohlone CollegeTrudy Bratten, Grossmont CollegeTim Bremer, Broome Community CollegeTim Britt, Jackson State Community CollegeHolly Broesamle, Oakland CC-Auburn HillsMichael Brook, University of DelawareTimothy Brown, Central Washington

UniversityJoanne Brunner, Joliet Junior CollegeWarren Burch, Brevard Community CollegeMary Butler, Lincoln Public SchoolsMelanie Butler, West Virginia UniversityJim Butterbach, Joliet Junior CollegeRoberto Cabezas, Miami Dade CollegeWilliam J. Cable, University of

Wisconsin-Stevens PointLois Calamia, Brookdale Community CollegeJim Campbell, Lincoln Public SchoolsRoger Carlsen, Moraine Valley Community

CollegeElena Catoiu, Joliet Junior CollegeMathews Chakkanakuzhi, Palomar CollegeTim Chappell, Penn Valley Community

CollegeJohn Collado, South Suburban CollegeAmy Collins, Northwest Vista CollegeAlicia Collins, Mesa Community CollegeNelson Collins, Joliet Junior CollegeRebecca Connell, Troy UniversityJim Cooper, Joliet Junior CollegeDenise Corbett, East Carolina UniversityCarlos C. Corona, San Antonio CollegeTheodore C. Coskey, South Seattle

Community CollegeRebecca Connell, Troy UniversityDonna Costello, Plano Senior High SchoolRebecca Courter, Pasadena City CollegeGarrett Cox, The University of Texas at San

AntonioPaul Crittenden, University of Nebraska at

LincolnJohn Davenport, East Texas State UniversityFaye Dang, Joliet Junior CollegeAntonio David, Del Mar College

Stephanie Deacon, Liberty UniversityDuane E. Deal, Ball State UniversityJerry DeGroot, Purdue North CentralTimothy Deis, University of

Wisconsin–PlattevilleJoanna DelMonaco, Middlesex Community

CollegeVivian Dennis, Eastfield CollegeDeborah Dillon, R. L. Turner High SchoolGuesna Dohrman, Tallahassee Community

CollegeCheryl Doolittle, Iowa State UniversityKaren R. Dougan, University of FloridaJerrett Dumouchel, Florida Community

College at JacksonvilleLouise Dyson, Clark CollegePaul D. East, Lexington Community CollegeDon Edmondson, University of Texas-AustinErica Egizio, Joliet Junior CollegeJason Eltrevoog, Joliet Junior CollegeChristopher Ennis, University of MinnesotaKathy Eppler, Salt Lake Community CollegeRalph Esparza, Jr., Richland CollegeGarret J. Etgen, University of HoustonScott Fallstrom, Shoreline Community CollegePete Falzone, Pensacola Junior CollegeArash Farahmand, Skyline CollegeSaid Fariabli, San Antonio CollegeW.A. Ferguson, University of Illinois-Urbana/

ChampaignIris B. Fetta, Clemson UniversityMason Flake, student at Edison Community

CollegeTimothy W. Flood, Pittsburg State UniversityRobert Frank, Westmoreland CountyCommunity CollegeMerle Friel, Humboldt State UniversityRichard A. Fritz, Moraine ValleyCommunity CollegeDewey Furness, Ricks CollegeMary Jule Gabiou, North Idaho CollegeRandy Gallaher, Lewis and Clark CollegeTina Garn, University of ArizonaDawit Getachew, Chicago State UniversityWayne Gibson, Rancho Santiago CollegeLoran W. Gierhart, University of Texas at San

Antonio and Palo Alto CollegeRobert Gill, University of Minnesota DuluthNina Girard, University of Pittsburgh at

JohnstownSudhir Kumar Goel, Valdosta State UniversityAdrienne Goldstein, Miami Dade College,

Kendall CampusJoan Goliday, Sante Fe Community CollegeLourdes Gonzalez, Miami Dade College,

Kendall CampusFrederic Gooding, Goucher CollegeDonald Goral, Northern Virginia Community

CollegeSue Graupner, Lincoln Public SchoolsMary Beth Grayson, Liberty UniversityJennifer L. Grimsley, University of CharlestonKen Gurganus, University of North CarolinaIgor Halfin, University of Texas-San AntonioJames E. Hall, University of Wisconsin-

MadisonJudy Hall, West Virginia UniversityEdward R. Hancock, DeVry Institute of

TechnologyJulia Hassett, DeVry Institute, DupageChristopher Hay-Jahans, University of South

DakotaMichah Heibel, Lincoln Public SchoolsLaRae Helliwell, San Jose City CollegeCeleste Hernandez, Richland CollegeGloria P. Hernandez, Louisiana State

University at EuniceBrother Herron, Brother Rice High School

Robert Hoburg, Western Connecticut State University

Lynda Hollingsworth, Northwest Missouri State University

Deltrye Holt, Augusta State UniversityCharla Holzbog, Denison High SchoolLee Hruby, Naperville North High SchoolMiles Hubbard, St. Cloud State UniversityKim Hughes, California State College-San

BernardinoStanislav, Jabuka, University of Nevada, RenoRon Jamison, Brigham Young UniversityRichard A. Jensen, Manatee Community

CollegeGlenn Johnson, Middlesex Community

CollegeSandra G. Johnson, St. Cloud State UniversityTuesday Johnson, New Mexico State

UniversitySusitha Karunaratne, Purdue University North

CentralMoana H. Karsteter, Tallahassee Community

CollegeDonna Katula, Joliet Junior CollegeArthur Kaufman, College of Staten IslandThomas Kearns, North Kentucky UniversityJack Keating, Massasoit Community CollegeShelia Kellenbarger, Lincoln Public SchoolsRachael Kenney, North Carolina State

UniversityPenelope Kirby, Florida State UniversityJohn B. Klassen, North Idaho CollegeDebra Kopcso, Louisiana State UniversityLynne Kowski, Raritan Valley Community

CollegeYelena Kravchuk, University of Alabama at

BirminghamRay S. Kuan, Skyline CollegeKeith Kuchar, Manatee Community CollegeTor Kwembe, Chicago State UniversityLinda J. Kyle, Tarrant Country Jr. CollegeH.E. Lacey, Texas A & M UniversityDarren Lacoste, Valencia College-West

CampusHarriet Lamm, Coastal Bend CollegeJames Lapp, Fort Lewis CollegeMatt Larson, Lincoln Public SchoolsChristopher Lattin, Oakton Community

CollegeJulia Ledet, Lousiana State UniversityWayne Lee, St. Phillips CCAdele LeGere, Oakton Community CollegeKevin Leith, University of HoustonJoAnn Lewin, Edison CollegeJeff Lewis, Johnson County Community

CollegeJanice C. Lyon, Tallahassee Community

CollegeJean McArthur, Joliet Junior CollegeVirginia McCarthy, Iowa State UniversityKarla McCavit, Albion CollegeMichael McClendon, University of Central

OklahomaTom McCollow, DeVry Institute of

TechnologyMarilyn McCollum, North Carolina State

UniversityJill McGowan, Howard UniversityWill McGowant, Howard UniversityAngela McNulty, Joliet Junior CollegeLisa Meads, College of the AlbemarleLaurence Maher, North Texas State UniversityJay A. Malmstrom, Oklahoma City

Community CollegeRebecca Mann, Apollo High SchoolLynn Marecek, Santa Ana CollegeSherry Martina, Naperville North High SchoolRuby Martinez, San Antonio College

xxiv Preface to the Instructor


Alec Matheson, Lamar UniversityNancy Matthews, University of OklahomaJames Maxwell, Oklahoma State

University-StillwaterMarsha May, Midwestern State UniversityJames McLaughlin, West Chester UniversityJudy Meckley, Joliet Junior CollegeDavid Meel, Bowling Green State UniversityCarolyn Meitler, Concordia UniversitySamia Metwali, Erie Community CollegeRich Meyers, Joliet Junior CollegeEldon Miller, University of MississippiJames Miller, West Virginia UniversityMichael Miller, Iowa State UniversityKathleen Miranda, SUNY at Old WestburyChris Mirbaha, The Community College of

Baltimore CountyVal Mohanakumar, Hillsborough Community

CollegeThomas Monaghan, Naperville North High

SchoolMiguel Montanez, Miami Dade College,

Wolfson CampusMaria Montoya, Our Lady of the Lake

UniversitySusan Moosai, Florida Atlantic UniversityCraig Morse, Naperville North High SchoolSamad Mortabit, Metropolitan State

UniversityPat Mower, Washburn UniversityTammy Muhs, University of Central FloridaA. Muhundan, Manatee Community CollegeJane Murphy, Middlesex Community CollegeRichard Nadel, Florida International

UniversityGabriel Nagy, Kansas State UniversityBill Naegele, South Suburban CollegeKarla Neal, Lousiana State UniversityLawrence E. Newman, Holyoke Community

CollegeDwight Newsome, Pasco-Hernando

Community CollegeDenise Nunley, Maricopa Community

CollegesJames Nymann, University of Texas-El PasoMark Omodt, Anoka-Ramsey Community

CollegeSeth F. Oppenheimer, Mississippi State

UniversityLeticia Oropesa, University of MiamiLinda Padilla, Joliet Junior CollegeSanja Pantic, University of Illinois at ChicagoE. James Peake, Iowa State UniversityKelly Pearson, Murray State UniversityDashamir Petrela, Florida Atlantic UniversityPhilip Pina, Florida Atlantic UniversityCharlotte Pisors, Baylor UniversityMichael Prophet, University of Northern IowaLaura Pyzdrowski, West Virginia UniversityCarrie Quesnell, Weber State University

Neal C. Raber, University of AkronThomas Radin, San Joaquin Delta CollegeAibeng Serene Radulovic, Florida Atlantic

UniversityKen A. Rager, Metropolitan State CollegeTraci Reed, St. Johns River State CollegeKenneth D. Reeves, San Antonio CollegeElsi Reinhardt, Truckee Meadows Community

CollegeJose Remesar, Miami Dade College, Wolfson

CampusJane Ringwald, Iowa State UniversityDouglas F. Robertson, University of

Minnesota, MPLSStephen Rodi, Austin Community CollegeWilliam Rogge, Lincoln Northeast High

SchoolHoward L. Rolf, Baylor UniversityMike Rosenthal, Florida International

UniversityPhoebe Rouse, Lousiana State UniversityEdward Rozema, University of Tennessee at

ChattanoogaDennis C. Runde, Manatee Community

CollegePaul Runnion, Missouri University of Science

and TechnologyAmit Saini, University of Nevada-RenoLaura Salazar, Northwest Vista CollegeAlan Saleski, Loyola University of ChicagoSusan Sandmeyer, Jamestown Community

CollegeBrenda Santistevan, Salt Lake Community

CollegeLinda Schmidt, Greenville Technical CollegeIngrid Scott, Montgomery CollegeA.K. Shamma, University of West FloridaZachery Sharon, University of Texas at San

AntonioJoshua Shelor, Virginia Western CCMartin Sherry, Lower Columbia CollegeCarmen Shershin, Florida International

UniversityTatrana Shubin, San Jose State UniversityAnita Sikes, Delgado Community CollegeTimothy Sipka, Alma CollegeCharlotte Smedberg, University of TampaLori Smellegar, Manatee Community CollegeGayle Smith, Loyola BlakefieldCindy Soderstrom, Salt Lake Community

CollegeLeslie Soltis, Mercyhurst CollegeJohn Spellman, Southwest Texas State

UniversityKaren Spike, University of North CarolinaRajalakshmi Sriram, Okaloosa-Walton

Community CollegeKatrina Staley, North Carolina Agricultural

and Technical State UniversityBecky Stamper, Western Kentucky University

Judy Staver, Florida Community College-South

Robin Steinberg, Pima Community CollegeNeil Stephens, Hinsdale South High SchoolSonya Stephens, Florida A&M UniveristyPatrick Stevens, Joliet Junior CollegeJohn Sumner, University of TampaMatthew TenHuisen, University of North

Carolina, WilmingtonChristopher Terry, Augusta State UniversityDiane Tesar, South Suburban CollegeTommy Thompson, Brookhaven CollegeMartha K. Tietze, Shawnee Mission Northwest

High SchoolRichard J. Tondra, Iowa State UniversityFlorentina Tone, University of West FloridaSuzanne Topp, Salt Lake Community CollegeMarilyn Toscano, University of Wisconsin,

SuperiorMarvel Townsend, University of FloridaJim Trudnowski, Carroll CollegeDavid Tseng, Miami Dade College, Kendall

CampusRobert Tuskey, Joliet Junior CollegeMihaela Vajiac, Chapman University-OrangeJulia Varbalow, Thomas Nelson Community

College-LeesvilleRichard G. Vinson, University of South

AlabamaJorge Viola-Prioli, Florida Atlantic UniversityMary Voxman, University of IdahoJennifer Walsh, Daytona Beach Community

CollegeDonna Wandke, Naperville North High SchoolTimothy L.Warkentin, Cloud County

Community CollegeMelissa J. Watts, Virginia State UniversityHayat Weiss, Middlesex Community CollegeKathryn Wetzel, Amarillo CollegeDarlene Whitkenack, Northern Illinois

UniversitySuzanne Williams, Central Piedmont

Community CollegeLarissa Williamson, University of FloridaChristine Wilson, West Virginia UniversityBrad Wind, Florida International UniversityAnna Wiodarczyk, Florida International

UniversityMary Wolyniak, Broome Community CollegeCanton Woods, Auburn UniversityTamara S. Worner, Wayne State CollegeTerri Wright, New Hampshire Community

Technical College, ManchesterRob Wylie, Carl Albert State CollegeAletheia Zambesi, University of West FloridaGeorge Zazi, Chicago State UniversityLoris Zucca, Lone Star College-KingwoodSteve Zuro, Joliet Junior College

Michael SullivanChicago State UniversityMichael Sullivan IIIJoliet Junior College

Preface to the Instructor xxv


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Annotated Instructor’s EditionISBN - 0135812828 / 9780135812822Shorter answers are on the page beside the exercises. Longer answers are in the back of the text.

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Algebra ReviewISBN: 0131480065 / 9780131480063Four chapters of Intermediate Algebra review. Perfect for a corequisite course or for individual review. Available in print form; PDFs are also available within MyLab Math.


xxix

Acousticsamplifying sound, 530loudness of sound, 477, 532loudspeaker, 753tuning fork, 753whispering galleries, 845

Aerodynamicsmodeling aircraft motion, 824

Agriculturefarm management, 990–991farm workers in U.S., 517field enclosure, 974grazing area for cow, 744removing stump, 811watering a field, 116

Air travelbearing of aircraft, 719cost of transatlantic, 228, 236distance between two planes,

280–281frequent flyer miles, 729holding pattern, 610, 670intersection point for two planes,

280–281, 893parking at O’Hare International

Airport, 262revising a flight plan, 736speed and direction of aircraft, 806,

809–810

Archaeologyage of ancient tools, 510age of fossil, 516age of tree, 516date of prehistoric man’s death, 530

Architecturebrick staircase, 1019, 1045Burj Khalifa building, 33Flatiron Building, 743floor design, 1017, 1045football stadium seating, 1019mosaic design, 1019, 1045Norman window, 39, 329One World Trade Center, 570–571parabolic arch, 329racetrack design, 848special window, 330, 337stadium construction, 1019vertically circular building, 201window design, 329–330window dimensions, 116

Area. See also Geometryof Bermuda Triangle, 743of building ground, 743under a curve, 654of dodecagon, 692of isosceles triangle, 702of octagon, 701–702of sector of circle, 545of segment of circle, 756

Artfine decorative pieces, 570framing a painting, 159

Astronomyangle of elevation of Sun, 718distance from Earth to its

moon, 31distances of planets from Sun, 1012Halley’s comet, 879International Space

Station (ISS), 894light-year, 31parallax method of measuring

distance, 719planetary orbits, 845

Earth, 848elliptical, 848Jupiter, 848Mars, 848Mercury, 879Neptune, 898Pluto, 848, 898

Aviationfighter jet design, 743modeling aircraft motion, 824orbital launches, 911sonic boom, 864

Biologyalcohol and driving, 472, 477–478bacterial growth, 508–509

E. coli, 251, 293, 522blood types, 1053bone length, 337–338cancer, 462, 523cricket chirp rate and temperature,

330–331healing of wounds, 462, 476lung volume, 594maternal age versus Down

syndrome, 308muscle force, 811yeast biomass as function of time,

521–522

Businessadvertising, 193, 309, 338automobile production, 431, 927blending coffee, 142, 159candy bar size, 117checkout lines, 1072clothing store, 1075cookie orders, 995–996cost

of can, 406–407, 409of charter bus, 159of commodity, 431of manufacturing, 30, 142, 236,

417, 984marginal, 322, 337minimizing, 991–992of printing textbooks, 362–363of production, 251, 431, 955, 996

of theater ticket per student, 417of transporting goods, 263

cost equation, 192, 206cost function, 300, 301demand

for candy, 207demand equation, 337, 338, 422depreciation, 424, 1029

straight-line, 296–297, 301discounts, 105–106, 432drive-thru rate

at Burger King, 457at Citibank, 462, 476at McDonald’s, 462

expense computation, 143inventory management, 284Jiffy Lube’s car arrival

rate, 462, 477managing a meat market, 991milk production, 523mixing candy, 142mixing nuts, 142online purchases, 1072orange juice production, 927precision ball bearings, 30presale order, 912price markup, 105product design, 991production scheduling, 991product promotion, 193profit, 955

maximizing, 989, 990, 991profit function, 228rate of return on, 504restaurant management, 912revenue, 142, 322, 335

airline, 992of clothing store, 945daily, 322from digital music, 278maximizing, 322, 328–329monthly, 322online advertising, 524–525from seating, 1030of Tesla, Inc., 523theater, 913

revenue equation, 206RV rental, 338salary, 1019

gross, 227, 432increases in, 1029, 1045

salescommission on, 155, 337of movie theater ticket, 900,

905, 911net, 169

salvage value, 530supply and demand, 297–298, 300tax, 417theater attendance, 105toy truck manufacturing, 984transporting goods, 984truck rentals, 192unemployment, 1075wages

of car salesperson, 192hourly, 102–103, 105

Calculusarea under a curve, 278, 654area under graph, 251, 865, 880,

957, 1073average rate of change, 366, 446,

478, 496, 582, 595, 619, 655, 661, 672, 680, 731, 820, 837, 894, 914, 928, 1013

carrying a ladder around a corner, 670

concavity test, 323critical numbers, 1013difference quotient, 279, 331, 335,

387, 446, 464, 506, 548, 571, 691, 708, 849, 894, 928, 975, 1031

discontinuities, 410exact value calculations, 837factoring expressions, 59, 169, 252,

331, 478, 655, 914, 992first derivative, 548f1x2 = ex, 1012increasing/decreasing/constant

function, 323, 595, 611, 880, 985inequalities, 416, 464Intermediate Value Theorem,

380–381, 410, 985maximum-minimum problems,

302, 399, 518, 571rain gutter construction, 702

Mean Value Theorem, 252Newton’s Method, 398normal line, 965odd-even functions, 366partial fraction decomposition,

1020, 1036, 1054, 1063, 1073points of intersection, 399, 432polynomial functions, 380rationalizing numerator, 310, 496,

661, 940real zeros, 1020rectangular equation of plane

curve, 1031reduction of expressions to lowest

terms, 73rewriting expressions, 284, 310, 323,

518, 620, 693, 1063secant line equation, 302, 506, 672simplifying expressions, 229, 264,

284, 323, 335, 410, 432, 560, 721, 739, 873, 975

Simpson’s rule, 331slope of perpendicular line, 229tangent line, 559, 788turning points, 417, 548

Carpentry. See also Constructionpitch, 194

Chemistry, 105alpha particles, 864antifreeze solution, 202

Applications Index


decomposition reactions, 516drug concentration, 408–409gas laws, 207pH, 476purity of gold, 143radioactive decay, 515–516, 523,

530, 532, 992radioactivity from Chernobyl, 516reactions

self-catalytic, 322solutions, 912

salt, 143, 144, 159sugar molecules, 143volume of gas, 155

Combinatoricsairport codes, 1055binary codes, 1075birthday permutations, 1057, 1062,

1069, 1073, 1075blouses and skirts combinations,

1053book arrangements, 1062box stacking, 1061code formation, 1061combination locks, 1062committee formation, 1059,

1061–1062, 1075Senate committees, 1062

flag arrangement, 1060, 1075letter codes, 1055–1056license plate possibilities,

1062, 1075lining up people, 1056, 1061number formation, 1053, 1061,

1062, 1075objects selection, 1062seating arrangements, 1075shirts and ties combinations, 1053telephone numbers, 1075two-symbol codewords, 1052word formation, 1060, 1062, 1075

Communicationsdata plan, 212, 237, 289–290installing cable TV, 283phone charges, 300radar detection, 770satellite dish, 833, 836satellite receiver, 872smartphones, 106, 516social networking, 106, 517, 524spreading of rumors, 462, 477texting speed, 410Touch-tone phones, 707, 754

Computers and computingBlu-ray drive, 545graphics, 811, 956laser printers, 143tablets, 117, 262, 517website design, 956website map, 956

Constructionof border around a garden, 117of border around a pool, 117of box, 113–114, 116, 974

closed, 288open, 283

of brick staircase, 1045of can, 420of coffee can, 144of cylindrical tube, 974of enclosures

around garden, 143around pond, 143maximizing area of, 325–326,

329, 337of fencing, 325–326, 329,

337, 974minimum cost for, 409

of flashlight, 836of headlight, 836of highway, 570, 730, 756installing cable TV, 283patio dimensions, 117pitch of roof, 720of rain gutter, 329, 564–565, 702of ramp, 729

access ramp, 193of rectangular field enclosure, 329of stadium, 329–330, 1019of steel drum, 409of swimming pool, 39, 40of swing set, 738of tent, 743TV dish, 836vent pipe installation, 848of walk, 637

Cryptographymatrices in, 956passwords, 1062

DecoratingChristmas tree, 34

Demographicsbirth rate(s), 331, 1047

of unmarried women, 322death rates, 1047diversity index, 476living at parents’ home, 117marital status, 1054mosquito colony growth, 515population. See Populationpoverty rates, 364rabbit colony growth, 1011

Designof awning, 730of box with minimum surface

area, 409of fine decorative pieces, 570of Little League Field, 547of water sprinkler, 545

Directionof aircraft, 806, 809–810compass heading, 810for crossing a river, 810of fireworks display, 863of lightning strikes, 863of motorboat, 810of swimmer, 823

DistanceBermuda Triangle, 40bicycle riding, 238

from Chicago to Honolulu, 655circumference of Earth, 547depth of pool, 264between Earth and Mercury, 730between Earth and Venus, 731from Earth to a star, 719of explosion, 863height

of aircraft, 729, 730of bouncing ball, 1029, 1045of bridge, 729of building, 637, 719of cloud, 566of CN Tower, 569of Eiffel Tower, 569of embankment, 719of Ferris Wheel rider, 670of Great Pyramid of Cheops,

40, 730of helicopter, 756of hot-air balloon, 569of Lincoln’s caricature on

Mt. Rushmore, 569of mountain, 725–727, 729of Mt. Everest, 31of One World Trade Center,

570–571of statue on a building, 567of tower, 569of tree, 729of Washington Monument, 570of Willis Tower, 719

from home, 238from Honolulu to Melbourne,

Australia, 655of hot-air balloon

to airport, 757from intersection, 168

from intersection, 280–281, 282length

of guy wire, 569, 571, 737of lake, 636of ski lift, 728

limiting magnitude of telescope, 530

to the Moon, 729nautical miles, 546parallax method of measuring, 719pendulum swings, 1025, 1029to plateau, 569across a pond, 569range of airplane, 144reach of ladder, 569of rotating beacon, 619at sea, 729of search and rescue, 159from ship to Statue of Liberty, 637to shore, 569, 636, 730between skyscrapers, 719sound to measure, 134–135of storm, 159to tower, 730traveled by wheel, 39between two moving vehicles, 168

toward intersection, 282between two objects, 569visibility of Gibb’s Hill Lighthouse

beam, 40, 716–717, 720visual, 40walking, 238

widthof gorge, 569of Mississippi River, 719of river, 565–566, 636

EconomicsConsumer Price Index (CPI), 506demand equations, 422inflation, 505IS-LM model in, 912marginal propensity to

consume, 1030multiplier, 1030participation rate, 228per capita federal debt, 505poverty rates, 364poverty threshold, 169relative income of child, 956supply-side, 252unemployment, 1075

Educationage distribution of community

college, 1076college costs, 505, 955college value, 117computing grades, 156degrees awarded, 1051

doctorates, 1072education savings account, 1011faculty composition, 1073field trip, 417funding a college education, 530grades, 105learning curve, 463, 477maximum level achieved, 998multiple-choice test, 1062spring break, 991, 1008student loan

interest on, 955true/false test, 1061tuition, 530video games and grade-point

average, 308working students and GPA, 117

Electricity, 105alternating current (ac), 636alternating current (ac) circuits,

609, 628, 691alternating current (ac)

generators, 609charging a capacitor, 753cost of, 260current in RC circuit, 463current in RL circuit, 463, 477impedance, 127Kirchhoff’s Rules, 913, 927parallel circuits, 127

resistance in, 398rates for, 155, 193resistance, 71, 74, 207, 210, 398voltage

foreign, 30U.S., 30

Electronicsclock signal, 754comparing tablets, 117keyboard layout, 410

xxx Applications Index


loudspeakers, 753microphones, 178non-sinusoidal waves, 754sawtooth curve, 702, 753

Energyexpended while walking, 232–233nuclear power plant, 863solar, 178, 819solar heat, 836thermostat control, 278

Engineeringbridges

Golden Gate, 326–327parabolic arch, 337, 836semielliptical arch, 848, 896suspension, 329, 836

crushing load, 135drive wheel, 720electrical, 558Gateway Arch (St. Louis), 836grade of road, 194horsepower, 207lean of Leaning Tower of Pisa, 729maximum weight supportable by

pine, 204moment of inertia, 707piston engines, 569product of inertia, 702road system, 770rods and pistons, 738safe load for a beam, 207searchlight, 679, 836, 896tolerances, 155tunnel clearance, 610weld inspection, 558whispering galleries, 848

EntertainmentDemon Roller Coaster customer

rate, 462–463movie theater, 94, 654theater revenues, 913

Environmentendangered species, 462invasive species, 517lake pollution control laws, 1011oil leakage, 431

Finance, 105. See also Investment(s)annuity, 1026–1027, 1029balancing checking account, 30bills in wallet, 1075clothes shopping, 997comparing bank accounts, 505computer system purchase, 504concession markup, 105cost

of car, 105of car rental, 263of college, 505of data plan, 237, 289–290of driving a car, 192of electricity, 260of fast food, 912of land, 756minimizing, 409

of natural gas, 262of pizza, 106of printing textbooks, 362–363of transatlantic travel, 228, 236of triangular lot, 743

cost equation, 206cost function, 300, 301cost minimization, 322credit cards

balance on, 965debt, 1011interest on, 504payment, 263, 1011

depreciation, 462of car, 478, 495, 533

discounts, 432discretionary income, 117division of money, 105, 137–138electricity rates, 193expenditures, average annual,

327–328federal debt, 251financial planning, 137–138, 159,

912, 924, 927–928, 982, 984, 985–986, 991

foreign exchange, 432fraternity purchase, 117funding a college education, 530fundraising lottery, 408future value of money, 365gross salary, 227growth of investment, 519–520inheritance, 106life cycle hypothesis, 330loans, 142

amortization schedule, 161car, 1011home, 1011interest on, 137, 158, 160–161, 955repayment of, 504student, 955

mortgagesfees, 263interest rates on, 505, 506payments, 203, 206, 210, 1009second, 505

natural gas rates, 193price appreciation of homes, 504prices of fast food, 913price vs. quantity demanded, 300refunds, 912revenue equation, 206revenue maximization, 322,

324–325, 328–329rich man’s promise, 1030salary options, 1031sales commission, 155saving

for a car, 504for a computer, 1045for a home, 1029for spring break, 1008

savings accounts interest, 504selling price, 211sewer bills, 155sinking fund, 1029taxes, 300

federal income, 263, 445withholding, 432

used-car purchase, 504

Food and nutritionanimal, 992candy, 307color mix of candy, 1075cooler contents, 1076cooling time of pizza, 516fast food, 408, 912, 913fat content, 155Girl Scout cookies, 1072hospital diet, 913, 927hot dog and soda combinations, 301ice cream, 991number of possible meals, 1051–1052sodium content, 155warming time of beer stein, 516wine, 495

Forensicsblood spatter analysis, 558height as function of femur

length, 300height as function of humerus

length, 300height as function of tibia length, 478identifying remains, 737

Forestrywood product classification,

514–515

Gamesdie rolling, 1065, 1066–1067, 1076grains of wheat on a chess

board, 1030lottery, 1076, 1077

Gardens and gardening. See also Landscapingborder around, 117enclosure for, 143

Geographyarea of Bermuda Triangle, 743area of lake, 743, 756inclination of hill, 819inclination of mountain trail, 716,

756, 975

Geologyearthquakes, 477–478geysers, 1019

Geometryangle between two lines, 692balloon volume, 431circle

area of, 142, 743circumference of, 30, 142equation of, 939inscribed in square, 282length of chord of, 738radius of, 974

collinear points, 939cone volume, 207, 432cube

length of edge of, 380surface area of, 30volume of, 30

cylinderinscribing in cone, 283

inscribing in sphere, 282volume of, 207, 432

Descartes’ method of equal roots, 974–975

equation of line, 939ladder angle, 757octagon, 701–702polygon

area of, 939diagonals of, 117

Pythagorean Theorem, 116quadrilateral area, 743, 757rectangle

area of, 30, 227, 280, 288, 337dimensions of, 106, 116, 158, 974inscribed in a circle, 282inscribed in ellipse, 848inscribed in semicircle, 282, 703perimeter of, 30pleasing proportion for, 159semicircle inscribed in, 282

regular dodecagon, 692semicircle area, 743, 757sphere

surface area of, 30volume of, 30

squarearea of, 142perimeter of, 142

surface areaof balloon, 431of cube, 30of sphere, 30

tetrahedron, 939triangle

area of, 30, 939, 743circumscribing, 731equilateral, 30, 168inscribed in circle, 282isosceles, 168, 227, 559, 757, 974lengths of the legs, 159medians of, 168Pascal’s, 1012, 1042perfect, 744right, 568, 718sides of, 758

Governmentfederal debt, 251federal income tax, 228, 263, 445federal tax withholding, 155first-class mail, 264per capita federal debt, 505

Health. See also Medicineage versus total cholesterol, 525blood pressure, 670elliptical trainer, 849, 872exercising, 155expenditures on, 228heartbeats during exercise, 294ideal body weight, 445life cycle hypothesis, 330life expectancy, 155weight-height relation, 226

Home improvement. See also Constructionpainting a house, 913painting a room, 620

Applications Index xxxi


Housing. See also Real estateapartment rental, 330price appreciation of homes, 504prices for, 420

Investment(s), 105, 142, 159, 532allocation, 102, 264in bonds, 991

Treasuries, 927, 928, 982, 984, 985–986

zero-coupon, 502, 505in CDs, 501, 991comparing, 505compound interest on, 497–498,

499, 501diversified, 913doubling of, 502, 505education savings account, 1011finance charges, 504in fixed-income securities, 991401(k), 1029, 1045growth of, 519–520IRA, 505, 1011, 1029

Roth, 1011return on, 504, 991in stock

analyzing, 340appreciation, 504NASDAQ stocks, 1061NYSE stocks, 1061portfolios of, 1054price of, 1030

time to reach goal, 504, 506tripling of, 503, 505

Kinesiologymuscle force, 811

Landscaping, 144. See also Gardens and gardeningboulder movement, 812enclosures, 337height of tree, 729removing stump, 811tree planting, 927watering lawn, 545

Law and law enforcementmotor vehicle thefts, 1072violent crimes, 228

Leisure and recreationamusement park ride, 545cable TV, 283community skating rink, 289Ferris wheel, 201, 545, 610, 670,

731, 753field trip, 417roller coaster, 630video games and grade-point

average, 308

Measurementoptical methods of, 679of rainfall, 819

Mechanics, 105. See also Physics

Mediafake news, 155YouTube usage, 1072

Medicine. See also HealthACL recovery, 581age versus total cholesterol, 525blood pressure, 610, 670cancer, 462, 523drug concentration, 251, 408–409drug medication, 462, 477healing of wounds, 462, 476lithotripsy, 849spreading of disease, 531

Meteorologyweather balloon height and

atmospheric pressure, 520–521

Miscellaneousbanquet seating, 991bending wire, 974biorhythms, 610carrying a ladder around a corner,

559, 619, 670citrus ladders, 1019coffee container, 533cross-sectional area of beam,

228, 236curve fitting, 909–910, 912, 927, 995diameter of wire, 31drafting error, 168Droste Effect, 1012Koch’s snowflake, 1030lamp shadow, 864Mandelbrot sets, 797mineral deposits in water pipe, 178motor, 31paper creases, 1035pet ownership, 1072sidewalk area, 560surface area of balloon, 431surveillance satellites, 720volume of balloon, 431water leak, 879wire enclosure area, 282

Mixtures. See also Chemistryblending coffees, 138–139, 142, 159,

984, 995blending teas, 142cement, 144mixed nuts, 142, 911, 984, 996mixing candy, 142solutions, 912water and antifreeze, 143

Motion, 753. See also Physicscatching a train, 896on a circle, 545of Ferris Wheel rider, 670of golf ball, 236, 670minute hand of clock, 545, 635

objects approaching intersection, 892–893

of pendulum, 754, 757revolutions of circular disk, 39simulating, 887tortoise and the hare race, 974uniform, 139–140, 142, 892–893

Motor vehiclesalcohol and driving, 472, 477–478approaching intersection, 892automobile production, 431, 927average car speed, 144brake repair with tune-up, 1075braking load, 819, 823cost of driving a car, 192crankshafts, 730depreciation, 424, 478, 495, 533with Global Positioning System

(GPS), 530loans for, 1011runaway car, 335spin balancing tires, 546stopping distance, 228, 322, 445towed, 300used-car purchase, 504windshield wiper, 545

Musicrevenues from, 278

Navigationavoiding a tropical storm, 736bearing, 717, 736, 756

of aircraft, 719of ship, 719

charting a course, 810commercial, 729compass heading, 810crossing a river, 810error in

correcting, 734–735, 756time lost due to, 729

rescue at sea, 726–727, 729revising a flight plan, 736sailing, 787

Oceanographytides, 610, 630

Opticsangle of refraction, 671bending light, 671DSLR camera lens field width, 541index of refraction, 671intensity of light, 207laser beam, 718laser projection, 702lensmaker’s equation, 74light obliterated through glass, 461measurement using, 679mirrors, 864, 1013parabolic reflector, 897reflecting telescope, 836

Pediatricsheight vs. head circumference, 445

Petsdog roaming area, 547

Pharmacyvitamin intake, 912, 928

Photographycamera distance, 570field width of lens, 541, 545, 581

Physics, 105angle of elevation of Sun, 718bouncing balls, 1045braking load, 819damped motion, 756–757deflection of board, 880density of a gas, 226diameter of atom, 31Doppler effect, 409effect of elevation on weight, 236escape velocity, 880falling objects, 206force, 142, 809

frictional, 719, 810to hold a wagon on a hill,

816–818resultant, 809of wind on a window, 205, 207

gravity, 398, 417on Earth, 227, 445on Jupiter, 228

harmonic motion, 747, 756–757heat loss, 204, 210heat transfer, 670Hooke’s Law, 301horsepower, 207inclination of mountain trail, 716inclined ramp, 810–811intensity of light, 159, 207kinetic energy, 142, 207maximum weight supportable by

pine, 204missile trajectory, 340moment of inertia, 707motion of object, 747–748Newton’s laws, 206, 511, 516pendulum motion, 135, 545, 754,

757, 1025period, 82, 278, 445simple pendulum, 206

pressure, 142, 207product of inertia, 702projectile motion, 116, 279, 322,

335, 568, 581, 670, 697, 702, 707, 885–886, 892, 896

artillery, 335, 661, 893distance, 582thrown object, 892

rotational inertia, 229safe load for a beam, 207simulating motion, 887sound

to measure distance, 134–135sonic boom, 864speed of, 155

static equilibrium, 807, 810, 811, 823strain, 365

xxxii Applications Index


stress of materials, 207stretching a spring, 206, 756tension, 807, 810–811, 823, 1036thrown object, 159

ball, 330, 335, 805truck pulls, 811uniform motion, 139–140, 142, 144,

159, 282, 892–893, 896velocity down inclined planes, 82vertically propelled object, 335vibrating string, 206wavelength of visible light, 31weight, 207, 210

of a boat, 810of a car, 810of a piano, 806

work, 142

Playswinging, 758wagon pulling, 809, 819

Population. See also Demographicsbacterial, 515decline in, 515E. coli growth, 251, 293of endangered species, 517of fruit fly, 513–514as function of age, 228growth in, 515, 517insect, 398, 515, 517of predators, 595of trout, 1010of United States, 495, 524, 1047of world, 495, 524, 530, 999

Probabilitycheckout lines, 1072coin toss, 1065colored candy, 1064exponential, 457, 462, 476–477household annual income, 1072Poisson, 462–463Price is Right games, 1072of same birthday in roomful of

people, 517standard normal density

function, 278of winning lottery, 1048, 1073

Publishingtextbook printing cost, 362–363

Pyrotechnicsfireworks display, 863

Rate. See also Speedof car, 545catching a bus, 892catching a train, 892

current of stream, 912of emptying

oil tankers, 144a pool, 144

of filling, 144, 159to keep up with the Sun, 546revolutions per minute

of bicycle wheels, 545of water consumption during

shower, 279

Real estatecommission, 155cost of triangular lot, 743land cost, 756mortgage fees, 263property area, 743saving for a home, 1029selling price of, 211value of, 162

Recreationbungee jumping, 417Demon Roller Coaster customer

rate, 462–463

Securitysecurity cameras, 719

Seismologycalibrating instruments, 896

Sequences. See also Combinatoricsceramic tile floor design, 1017Drury Lane Theater, 1018football stadium seating, 1019seats in amphitheater, 1018

Societyideal mate, 478

Speed. See also Rateof aircraft, 144, 809–810angular, 545, 635average, 144of current, 142, 546, 996of cyclists going in opposite

directions, 144as function of time, 238, 282linear, 543

on Earth, 546of Moon, 546of motorboat, 142of moving walkways, 142revolutions per minute of

pulley, 546of rotation of lighthouse

beacons, 636of sound, 155of swimmer, 823of truck, 718

of wheel pulling cable cars, 546wind, 912of wind turbine, 545

Sportsbaseball, 893, 1062, 1075

diamond, 168dimensions of home plate, 743field, 737, 738homeruns, 309Little League, 168, 547on-base percentage, 302–303World Series, 1062

basketball, 1062free throws, 235–236, 720granny shots, 235

biathlon, 144bungee jumping, 417calculating pool shots, 570cycling, 94–95, 144, 547discus throw, 94exacta betting, 1075football, 143, 848, 1062

angle of pursuit, 559field design, 117

golf, 236, 525, 670, 885–886, 892distance to the green, 736sand bunkers, 661

hammer throw, 637kayaking, 680marathon runners, 279, 729Olympic heroes, 144races, 143, 159, 971–972, 974relay runners, 1075shot-put throw, 94soccer, 737swimming, 757, 823tennis, 143, 365, 409

Surveyingland dimensions, 729

Surveysof appliance purchases, 1053data analysis, 1050, 1053stock portfolios, 1054of summer session attendance,

1053of TV sets in a house, 1072

Temperatureof air parcel, 1019body, 31, 155conversion of, 432, 445cooling time of pizza, 516cricket chirp rate and, 330–331measuring, 193after midnight, 364–365monthly, 610, 629–630, 636relationship between scales, 278sinusoidal function from, 624–625of skillet, 530

warming time of beer stein, 516wind chill factor, 531

Timefor beer stein to warm, 516for block to slide down inclined

plane, 568–569Ferris Wheel rider height as

function of, 670to go from an island to a town, 283hours of daylight, 423, 534, 610,

626–627, 630, 638–639, 653–654for pizza to cool, 516for rescue at sea, 159of sunrise, 546, 654of trip, 558–559, 570waiting, for fast food, 408

Transportationde-icing salt, 661high-speed walkways, 143Niagara Falls Incline Railway, 719sailing, 787

Travel. See also Air travel; Navigationdrivers stopped by the police,

532–533driving to school, 207parking at O’Hare International

Airport, 262

Volumeof gasoline in tank, 82of ice in skating rink, 289of water in cone, 283

Weaponsartillery, 335, 661, 893cannons, 340

Weatheratmospheric pressure, 462, 476avoiding a tropical storm, 736cooling air, 1019forecasting, 1068hurricanes, 308, 364, 629lightning and thunder, 159lightning strikes, 860–861, 863rainfall measurement, 819relative humidity, 463tornadoes, 307wind chill, 263–264, 531

Work, 819computing, 816–818, 823constant rate jobs, 996pulling a wagon, 819ramp angle, 819wheelbarrow push, 809working together, 141, 143,

144, 159

Applications Index xxxiii


To the StudentAs you begin, you may feel anxious about the number of theorems, definitions, procedures, and equations you encounter. You may wonder if you can learn it all in time. Don’t worry, your concerns are normal. This text was written with you in mind. If you attend class, work hard, and read and study effectively, you will build the knowledge and skills you need to be successful. Here’s how you can use the text to your benefit.

Read CarefullyWhen you get busy, it’s easy to skip reading and go right to the problems. Don’t! The text provides a large number of examples and clear explanations to help you break down the mathematics into easy-to-understand steps. Reading will provide you with a clearer understanding, beyond simple memorization. Read before class (not after) so you can ask questions about anything you didn’t understand. You’ll be amazed at how much more you’ll get out of class when you do this.

Use the FeaturesWe use many different methods in the classroom to communicate. Those methods, when incorporated into the text, are called “features.” The features serve many purposes, from supplying a timely review of material you learned before (just when you need it), to providing organized review sessions to help you prepare for quizzes and tests. Take advantage of the features and you will master the material.

To make this easier, we’ve provided a brief guide to getting the most from this book. Refer to the “Prepare for Class,” “Practice,” and “Review” guidelines on the first three pages of this book. Spend fifteen minutes reviewing the guide and familiarizing yourself with the features by flipping to the page numbers provided. Then, as you read, use them. This is the best way to make the most of your text. In this edition, we’ve also added a handy key to the labeling of the homework exercises so that you know what the colors and icons mean:

Now Work 1. Modeling 1. Writing/Discussion Calculus Preview Interactive Figure

xxxiv

Please do not hesitate to contact us via [email protected] with any questions, comments, or suggestions about ways to improve this text. We look forward to hearing from you, and good luck with all of your studies.

Best Wishes!Michael SullivanMichael Sullivan III


Prepare for Class: “Read the Book” - Pearson Education · Algebra & Trigonometry Enhanced with...

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