Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition

Preview (16 of 1597 Pages)

100%

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 1 preview image

Loading page ...

SOLUTIONSMANUALTIMBRITTJackson State Community CollegeALGEBRA ANDTRIGONOMETRYENHANCED WITHGRAPHINGUTILITIESEIGHTHEDITIONMichael SullivanChicago State UniversityMichael Sullivan IIIJoliet Junior College

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 2 preview image

Loading page ...

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 3 preview image

Loading page ...

Table of ContentsChapter RReviewR.1Real Numbers .......................................................................................................................... 1R.2Algebra Essentials ................................................................................................................... 5R.3Geometry Essentials .............................................................................................................. 11R.4Polynomials ........................................................................................................................... 16R.5Factoring Polynomials ........................................................................................................... 23R.6Synthetic Division ................................................................................................................. 28R.7Rational Expressions ............................................................................................................. 30R.8nth Roots; Rational Exponents .............................................................................................. 40Chapter 1Graphs, Equations, and Inequalities1.1Graphing Utilities; Introduction to Graphing Equations ....................................................... 501.2Solving Equations Using a Graphing Utility; Linear and Rational Equations....................... 571.3Quadratic Equations .............................................................................................................. 711.4Complex Numbers; Quadratic Equations in the Complex Number System .......................... 901.5Radical Equations; Equations Quadratic in Form; Absolute Value Equations;Factorable Equations ............................................................................................................. 961.6Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs.................. 1171.7Solving Inequalities ............................................................................................................. 125Chapter Review............................................................................................................................ 137Chapter Test ................................................................................................................................. 147Chapter Projects ........................................................................................................................... 151Chapter 2Graphs2.1The Distance and Midpoint Formulas ................................................................................. 1522.2Intercepts; Symmetry; Graphing Key Equations ................................................................. 1652.3Lines .................................................................................................................................... 1822.4Circles.................................................................................................................................. 2002.5Variation .............................................................................................................................. 215Chapter Review............................................................................................................................ 220Chapter Test ................................................................................................................................. 226Cumulative Review...................................................................................................................... 228Chapter Projects ........................................................................................................................... 230Chapter 3Functions and Their Graphs3.1Functions ............................................................................................................................. 2313.2The Graph of a Function...................................................................................................... 2493.3Properties of Functions ........................................................................................................ 2583.4Library of Functions; Piecewise-defined Functions ............................................................ 2753.5Graphing Techniques: Transformations .............................................................................. 2873.6Mathematical Models: Building Functions.......................................................................... 305Chapter Review............................................................................................................................ 313Chapter Test ................................................................................................................................. 320Cumulative Review...................................................................................................................... 323Chapter Projects ........................................................................................................................... 327

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 4 preview image

Loading page ...

Chapter 4Linear and Quadratic Functions4.1Properties of Linear Functions and Linear Models.............................................................. 3294.2Building Linear Models from Data...................................................................................... 3404.3Quadratic Functions and Their Properties ........................................................................... 3464.4Build Quadratic Models from Verbal Descriptions and from Data ..................................... 3704.5Inequalities Involving Quadratic Functions......................................................................... 378Chapter Review............................................................................................................................ 397Chapter Test ................................................................................................................................. 405Cumulative Review...................................................................................................................... 408Chapter Projects ........................................................................................................................... 411Chapter 5Polynomial and Rational Functions5.1Polynomial Functions .......................................................................................................... 4145.2The Graph of a Polynomial Function; Models .................................................................... 4255.3The Real Zeros of a Polynomial Function ........................................................................... 4455.4Complex Zeros; Fundamental Theorem of Algebra ............................................................ 4825.5Properties of Rational Functions ......................................................................................... 4915.6The Graph of a Rational Function ....................................................................................... 5015.7Polynomial and Rational Inequalities .................................................................................. 557Chapter Review............................................................................................................................ 579Chapter Test ................................................................................................................................. 593Cumulative Review...................................................................................................................... 597Chapter Projects ........................................................................................................................... 602Chapter 6Exponential and Logarithmic Functions6.1Composite Functions ........................................................................................................... 6036.2One-to-One Functions; Inverse Functions........................................................................... 6216.3Exponential Functions ......................................................................................................... 6446.4Logarithmic Functions......................................................................................................... 6656.5Properties of Logarithms ..................................................................................................... 6876.6Logarithmic and Exponential Equations.............................................................................. 6966.7Financial Models ................................................................................................................. 7176.8Exponential Growth and Decay Models; Newton’s Law; Logistic Growthand Decay Models ............................................................................................................... 7256.9Building Exponential, Logarithmic, and Logistic Models from Data ................................. 736Chapter Review............................................................................................................................ 741Chapter Test ................................................................................................................................. 763Cumulative Review...................................................................................................................... 757Chapter Projects ........................................................................................................................... 760

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 5 preview image

Loading page ...

Chapter 7Trigonometric Functions7.1Angles, Arc Length, and Circular Motion ........................................................................... 7637.2Right Triangle Trigonometry............................................................................................... 7727.3Computing the Values of Trigonometric Functions of Acute Angles ................................. 7887.4Trigonometric Functions of Any Angle............................................................................... 8017.5Unit Circle Approach; Properties of the Trigonometric Functions...................................... 8177.6Graphs of the Sine and Cosine Functions............................................................................ 8267.7Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions................................... 8487.8Phase Shift; Sinusoidal Curve Fitting.................................................................................. 858Chapter Review............................................................................................................................ 871Chapter Test ................................................................................................................................. 880Cumulative Review...................................................................................................................... 884Chapter Projects ........................................................................................................................... 888Chapter 8Analytic Trigonometry8.1The Inverse Sine, Cosine, and Tangent Functions............................................................... 8918.2The Inverse Trigonometric Functions (Continued) ............................................................. 9058.3Trigonometric Equations ..................................................................................................... 9178.4Trigonometric Identities ...................................................................................................... 9388.5Sum and Difference Formulas ............................................................................................. 9518.6Double-Angle and Half-Angle Formulas ............................................................................ 9768.7Product-to-Sum and Sum-to-Product Formulas................................................................. 1004Chapter Review.......................................................................................................................... 1017Chapter Test ............................................................................................................................... 1032Cumulative Review.................................................................................................................... 1037Chapter Projects ......................................................................................................................... 1043Chapter 9Applications of Trigonometric Functions9.1Applications Involving Right Triangles ............................................................................ 10479.2The Law of Sines............................................................................................................... 10559.3The Law of Cosines ........................................................................................................... 10709.4Area of a Triangle.............................................................................................................. 10829.5Simple Harmonic Motion; Damped Motion; Combining Waves ...................................... 1092Chapter Review.......................................................................................................................... 1102Chapter Test ............................................................................................................................... 1108Cumulative Review.................................................................................................................... 1111Chapter Projects ......................................................................................................................... 1117Chapter 10Polar Coordinates; Vectors10.1 Polar Coordinates .............................................................................................................. 112110.2 Polar Equations and Graphs............................................................................................... 113010.3 The Complex Plane; De Moivre’s Theorem...................................................................... 115910.4 Vectors............................................................................................................................... 117210.5 The Dot Product................................................................................................................. 1185Chapter Review.......................................................................................................................... 1191Chapter Test ............................................................................................................................... 1200Cumulative Review.................................................................................................................... 1203Chapter Projects ......................................................................................................................... 1205

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 6 preview image

Loading page ...

Chapter 11Analytic Geometry11.2 The Parabola ...................................................................................................................... 120911.3 The Ellipse......................................................................................................................... 122511.4 The Hyperbola ................................................................................................................... 124211.5 Rotation of Axes; General Form of a Conic ...................................................................... 126211.6 Polar Equations of Conics ................................................................................................. 127511.7 Plane Curves and Parametric Equations ............................................................................ 1284Chapter Review.......................................................................................................................... 1299Chapter Test ............................................................................................................................... 1308Cumulative Review.................................................................................................................... 1313Chapter Projects ......................................................................................................................... 1315Chapter 12Systems of Equations and Inequalities12.1 Systems of Linear Equations: Substitution and Elimination ............................................. 131912.2 Systems of Linear Equations: Matrices ............................................................................. 134212.3 Systems of Linear Equations: Determinants...................................................................... 136712.4 Matrix Algebra .................................................................................................................. 138112.5 Partial Fraction Decomposition ......................................................................................... 140012.6 Systems of Nonlinear Equations........................................................................................ 141912.7 Systems of Inequalities ...................................................................................................... 144712.8 Linear Programming.......................................................................................................... 1462Chapter Review.......................................................................................................................... 1476Chapter Test ............................................................................................................................... 1491Cumulative Review.................................................................................................................... 1499Chapter Projects ......................................................................................................................... 1503Chapter 13Sequences; Induction; the Binomial Theorem13.1 Sequences .......................................................................................................................... 150513.2 Arithmetic Sequences ........................................................................................................ 151913.3 Geometric Sequences; Geometric Series........................................................................... 152813.4 Mathematical Induction ..................................................................................................... 153913.5 The Binomial Theorem...................................................................................................... 1549Chapter Review.......................................................................................................................... 1556Chapter Test ............................................................................................................................... 1560Cumulative Review.................................................................................................................... 1563Chapter Projects ......................................................................................................................... 1566Chapter 14Counting and Probability14.1 Counting ............................................................................................................................ 156914.2 Permutations and Combinations ........................................................................................ 157214.3 Probability ......................................................................................................................... 1577Chapter Review.......................................................................................................................... 1584Chapter Test ............................................................................................................................... 1586Cumulative Review.................................................................................................................... 1587Chapter Projects ......................................................................................................................... 1590

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 7 preview image

Loading page ...

1Chapter RReviewSection R.11.rational2.45 634303313.Distributive4.c5.a6.b7.True8.False; The Zero-Product Property states that if aproduct equals 0, then at least one of the factorsmust equal 0.9.False; 6 is the Greatest Common Factor of 12and 18. The Least Common Multiple is thesmallest value that both numbers will divideevenly. The LCM for 12 and 18 is 36.10.True11.1, 3, 4,5, 92, 4, 6, 7,81, 2,3, 4, 5, 6, 7,8, 9AB12.1, 3, 4,5, 91, 3, 4, 61, 3, 4, 5, 6, 9AC13. 1, 3, 4,5, 92, 4, 6, 7,84AB14.1, 3, 4,5, 91, 3, 4, 61, 3, 4AC15.()1, 3, 4,5, 92, 4, 6, 7,81,3, 4, 61, 2,3, 4,5, 6, 7,8,91,3, 4, 61, 3, 4, 6ABC16. ()1, 3, 4,5, 92, 4, 6, 7,81,3, 4, 641, 3, 4, 61,3, 4, 6ABC17.0, 2, 6, 7, 8A18.0, 2, 5, 7, 8, 9C19. 1, 3, 4, 5, 92, 4, 6, 7, 840, 1, 2, 3, 5, 6, 7, 8, 9AB20.2, 4, 6, 7, 81, 3, 4, 61, 2, 3, 4, 6, 7, 80, 5, 9BC21.0, 2, 6, 7, 80, 1, 3, 5, 90, 1, 2, 3, 5, 6, 7, 8, 9AB22.0, 1, 3, 5, 90, 2, 5, 7, 8, 90, 5, 9BC23.a.2,5b.6, 2,5c.16,,1.333...1.3, 2,52 d. e.16,,1.333...1.3,, 2,52 24.a. 1b.0,1c.5 , 2.060606...2.06,1.25, 0,13d.5

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 8 preview image

Loading page ...

Chapter R:Review2e.5 , 2.060606...2.06,1.25, 0,1,5325.a. 1b.0,1c.1 1 10,1,,,2 3 4d.Nonee.1 1 10,1,,,2 3 426.a.Noneb.1c.1.3,1.2,1.1,1d.Nonee.1.3,1.2,1.1,127.a.Noneb.Nonec.Noned.12,,21,2e.12,,21,228.a.Noneb.Nonec.110.32d.2,2e.12,2,10.3229.a.18.953b.18.95230.a.25.861b.25.86131.a.28.653b.28.65332.a.99.052b.99.05233.a.0.063b.0.06234.a.0.054b.0.05335.a.9.999b.9.99836.a.1.001b.1.00037.a.0.429b.0.42838.a.0.556b.0.55539.a.34.733b.34.73340.a.16.200b.16.20041.32542.5 21043.23 4x44.322y45.312y46.24 6x47.26x48.26y49.62x50.26x51.94252752.64323553.64 36126 54.84 288055.185 21810856.10010 2100208057.112113433358.14132222

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 9 preview image

Loading page ...

Section R.1:Real Numbers359. 63 52326152161711 60.2834232836328183210320323   61.4956 73414423564231431762.14 3221122211211 63. 1062 283210645210252107210144 64.25 46342206118618612     65.1153212266.1154933367.4812653268.2421532 69.3 103 2 535215 3 7255327770.535 359 103 3 5 2333516271.6102 3 5 22325275 5 3 952553445972.21 1003 7 4 25325325 37 4252532873.321582345202074.418311326675.7449328187565676.8151613515192181877.51103131812363678.2864046159454579.5825643913241512012040  80.329451421424281.329812015606082.631215335147070 83.5185275 9 35918119 2 111127 3915222 1184.5215355 7 5572127 3 2235 572563 2

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 10 preview image

Loading page ...

Chapter R:Review485.1417417211372121212186.24122 22222235635 3 235 3 2315252102102123515151515154 34 345 35 3587.33233636232 481484842812312315888888.513513 513 513 621623 223 22515142222289.64624xx90.4 2184xx91.244xxxx92.243412xxxx93.31312 3222242422 222 32312222xxxxx94.21213 23333363633 23 231233 22xxxxx95.222442868xxxxxxx96.22515565xxxxxxx97.2292727186321163xxxxxxx98.2231531553145xxxxxxx99.228228161016xxxxxxx100.224224868xxxxxxx101.2223 (5 )36031536015604 xxkxxxxkxxxkxk102.2222222222222()(3 )41233412(3)3412(3)3412(2 )3412242xkxkxxxkxkxkxxxxkkkxxxxkkkxxxxkkxxkk103.23232355xxxxxxx104.23 421214since multiplication comes before addition in theorder of operations for real numbers.2345 420since operations inside parentheses come beforemultiplication in the order of operations for realnumbers.105.2 3 42 1224  2 32 46848106.4371257, but434 53 220626132.6251010105107.Subtraction is not commutative; forexample:231132 .

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 11 preview image

Loading page ...

Section R.2:Algebra Essentials5108.Subtraction is not associative; forexample:52124521.109.Division is not commutative; for example:2332.110.Division is not associative; forexample:1222623, but122212112.111.The Symmetric Property implies that if 2 =x,thenx= 2.112.From theprinciple of substitution,if5x, then  222552525530xxxxxxx113.There are no real numbers that are both rationaland irrational, since an irrational number, bydefinition, is a number that cannot be expressedas the ratio of two integers; that is, not a rationalnumberEvery real number is either a rational number oran irrational number, since the decimal form of areal number either involves an infinitelyrepeating pattern of digits or an infinite, non-repeating string of digits.114.The sum of an irrational number and a rationalnumber must be irrational. Otherwise, theirrational number would then be the difference oftwo rational numbers, and therefore would haveto be rational.115.Answers will vary.116.Since 1 day = 24 hours, we compute12997541.541624.Now we only need to consider the decimal partof the answer in terms of a 24 hour day. That is,0.54162413hours. So it must be 13 hourslater than 12 noon, which makes the time 1 AMCST.117.Answers will vary.Section R.21.variable2.origin3.strict4.base; exponent (or power)5.31.2345678106.d7.a8.b9.True10.False; the absolute value of a real number isnonnegative.00which is not a positivenumber.11.False; a number in scientific notation isexpressed as the product of a number, x,110xor101x , and a power of 10.12.True13.523414.13322315.10216.5617.12 18.532 19.3.14 20.21.41

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 12 preview image

Loading page ...

Chapter R:Review621.10.5222.10.33323.20.67324.10.25425.0x26.0z27.2x28.5y 29.1x30.2x31.Graph on the number line:2x 32.Graph on the number line:4x33.Graph on the number line:1x 34.Graph on the number line:7x35.(,)(0,1)1011d C Dd36.(,)(0,3)3033d C Ad37.(,)(1,3)3122d D Ed38.(,)(0,3)3033d C Ed39.(,)( 3,3)3( 3)66d A Ed 40.(,)(1,1)1122d D Bd41.222 3264xy  42.33(2)3633xy  43.525(2)(3)230228xy  44.22(2)(2)(3)462xxy   45.2(2)4242355xxy46.23112355xyxy 47.3(2)2(3)66320022355xyy48.2(2)343237333xy 49.3(2)11xy 50.3(2)55xy 51.32325xy 52.32321xy 53.33133xx54.22122yy 55.454(3)5(2)12102222xy56.323(3)2(2)9455xy57.454(3)5(2)1210121022xy 

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 13 preview image

Loading page ...

Section R.2:Algebra Essentials758.323 3223 32 29413xy59.21xxPart (c) must be excluded. The value0xmustbe excluded from the domain because it causesdivision by 0.60.21xxPart (c) must be excluded. The value0xmustbe excluded from the domain because it causesdivision by 0.61.2(3)(3)9xxxxxPart (a) ,3x, must be excluded because itcauses the denominator to be 0.62.29xxNone of the given values are excluded. Thedomain is all real numbers.63.221xxNone of the given values are excluded. Thedomain is all real numbers.64.332(1)(1)1xxxxxParts (b) and (d) must be excluded. The values1, and1xx must be excluded from thedomain because they cause division by 0.65.223510510(1)(1)xxxxx xxxxParts (b), (c), and (d) must be excluded. Thevalues0,1, and1xxx must be excludedfrom the domain because they cause division by0.66.22329191(1)xxxxxxx xPart (c) must be excluded. The value0xmustbe excluded from the domain because it causesdivision by 0.67.45x5xmust be exluded because it makes thedenominator equal 0.Domain5x x68.64x4x must be excluded sine it makes thedenominator equal 0.Domain4x x 69.4xx4x must be excluded sine it makes thedenominator equal 0.Domain4x x 70.26xx6xmust be excluded sine it makes thedenominator equal 0.Domain6x x71.555(32)(3232)(0)0 C999CF72.555(32)(21232)(180)100 C999CF73.555(32)(7732)(45)25 C999CF74.55(32)(432)995 ( 36)920 CCF 75.2( 9)( 9)( 9)81 76.224(4)16  77.22114164

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 14 preview image

Loading page ...

Chapter R:Review878.22114164  79.64642211333393 80.2323144444 81.131334446482.31313222883.2100101084.2366685.2444 86.2333 87.2242489981xxx88.122211444xxx 89.42222121422xx yxyx yy90.333113333yxyxyxyx91.2523541134xyyxyxyxx y92.22 11 231231xyxyxyx yx y 93.253533372723 1573222122(4)()16( 3)27162716271627   yx zy x zx y zx y zxyzx yzx zy94.21211344241 11621624()428481212xy zxyzx yx yxyzxyzx y z  95.22233266132223233923224yxxxxyyxyy96.3332222223326363255666562161255yxxyxyxxyy97.12 22241xxyy 98.13133322yxyx99.222221415xy 100. 2222214 14x y101.2222124xy 102. 2222111xy 103.222xx104.22xx105.222221415xy 106.2221213xyxy 107.1122yx

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 15 preview image

Loading page ...

Section R.2:Algebra Essentials9108.211xy109.If2,x323223542 23 25 24161210410xxxIf1,x323223542 13 15 1423540xxx110.If1,x32324324 13 11243128xxxIf2,x32324324 23 22232122244xxx111.4444(666)666381222(222)112.333333331(0.1) (20)2 101012101028113.6(8.2)304, 006.671114.5(3.7)693.440115.3(6.1)0.004116.5(2.2)0.019117.6(2.8)481.890118.6(2.8)481.890 119.4(8.11)0.000120.4(8.11)0.000 121.2454.24.54210122.132.143.21410123.20.0131.310124.30.004214.2110125.432,1553.215510126.421, 2102.12110127.40.0004234.2310128.20.05145.1410129.46.151061,500130.39.7109700131.31.214100.001214132.49.88100.000988133.81.110110, 000, 000134.24.11210411.2135.28.1100.081136.16.453100.6453137.Alw138.2Plw139.Cd140.12Abh141.234Ax142.3Px143.343Vr

Solution Manual for Algebra and Trigonometry Enhanced with Graphing Utilities, 8th Edition - Page 16 preview image

Loading page ...

Chapter R:Review10144.24Sr145.3Vx146.26Sx147.a.If1000,x4000240002(1000)40002000$6000CxThe cost of producing 1000 watches is$6000.b.If2000,x4000240002(2000)40004000$8000CxThe cost of producing 2000 watches is$8000.148.210801202560325$98His balance at the end of the month was $98.149.We want the difference betweenxand 4 to be atleast 6 units. Since we don’t care whether thevalue forxis larger or smaller than 4, we takethe absolute value of the difference. We want theinequality to be non-strict since we are dealingwith an ‘at least’ situation. Thus, we have46x150.We want the difference betweenxand 2 to bemore than 5 units. Since we don’t care whetherthe value forxis larger or smaller than 2, wetake the absolute value of the difference. Wewant the inequality to be strict since we aredealing with a ‘more than’ situation. Thus, wehave25x151.a.110108110225x108 volts is acceptable.b.110104110665x104 volts isnotacceptable.152.a.220214220668x214 volts is acceptable.b.22020922011118x209 volts isnotacceptable.153.a.32.99930.0010.0010.01xA radius of 2.999 centimeters is acceptable.b.32.8930.110.110.01xA radius of 2.89 centimeters isnotacceptable.154.a.98.69798.61.61.61.5x97˚F is unhealthy.b.98.610098.61.41.41.5x100˚F isnotunhealthy.155.The distance from Earth to the Moon is about8410400, 000, 000meters.156.The height of Mt. Everest is about388488.84810meters.157.The wavelength of visible light is about75100.0000005meters.158.The diameter of an atom is about101100.0000000001meters.159.The diameter is about20.04034.0310inches.160.The tiniest motor is less than50.00004410millimeters tall.

Preview Mode

This document has 1597 pages. Sign in to access the full document!

Report

Study Now!

Document Details

Related Documents

Test Bank for Algebra and Trigonometry Enhanced with Graphing Utilities , 7th Edition

Precalculus - Polynomial and Rational Functions

Precalculus - Functions

Precalculus - Exponential and Logarithmic Functions

Math Word Problems - Translating Expressions

Math Word Problems - Equations

Algebra II – Word Problems

Algebra II – Sequences and Series

Algebra II - Segments Lines and Inequalities

Algebra II - Relations and Functions

Company

Explore

Study Tools