CramX Logo
RegisterLog in
Solution Manual for Precalculus, 8th Edition - Document preview page 1

Solution Manual for Precalculus, 8th Edition - Page 1

Document preview content for Solution Manual for Precalculus, 8th Edition

Solution Manual for Precalculus, 8th Edition

Take the stress out of textbook problems with Solution Manual for Precalculus, 8th Edition, a complete guide to solving every question.

Samuel Clark
Contributor
4.0
0
12 months ago
Preview (16 of 1468 Pages)
100%
Log in to unlock
Page 1 of 16
Solution Manual for Precalculus, 8th Edition - Page 1 preview image’SSOLUTIONSMANUALTIMBRITTJackson State Community CollegePRECALCULUSNINTHEDITIONMichael SullivanChicago State University
Page 2 of 16
Solution Manual for Precalculus, 8th Edition - Page 2 preview image
Page 3 of 16
Solution Manual for Precalculus, 8th Edition - Page 3 preview imageTable of ContentsPrefaceChapter 1Graphs1.1 The Distance and Midpoint Formulas......................................................................................... 11.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................ 121.3 Lines ......................................................................................................................................... 241.4 Circles....................................................................................................................................... 41Chapter Review ............................................................................................................................... 52Chapter Test..................................................................................................................................... 62Chapter Projects............................................................................................................................... 64Chapter 2Functions and Their Graphs2.1 Functions .................................................................................................................................. 662.2 The Graph of a Function........................................................................................................... 802.3 Properties of Functions ............................................................................................................. 872.4 Library of Functions; Piecewise-defined Functions ............................................................... 1022.5 Graphing Techniques: Transformations ................................................................................. 1132.6 Mathematical Models: Building Functions............................................................................. 129Chapter Review ............................................................................................................................. 135Chapter Test................................................................................................................................... 148Cumulative Review ....................................................................................................................... 152Chapter Projects............................................................................................................................. 155Chapter 3Linear and Quadratic Functions3.1 Linear Functions and Their Properties.................................................................................... 1573.2 Linear Models: Building Linear Functions from Data ........................................................... 1673.3 Quadratic Functions and Their Properties .............................................................................. 1723.4 Build Quadratic Models from Verbal Descriptions and from Data ........................................ 1903.5 Inequalities Involving Quadratic Functions............................................................................ 198Chapter Review ............................................................................................................................. 216Chapter Test................................................................................................................................... 229Cumulative Review........................................................................................................................ 230Chapter Projects............................................................................................................................. 233Chapter 4Polynomial and Rational Functions4.1 Polynomial Functions and Models.......................................................................................... 2364.2 Properties of Rational Functions............................................................................................. 2584.3 The Graph of a Rational Function .......................................................................................... 2654.4 Polynomial and Rational Inequalities ..................................................................................... 3124.5 The Real Zeros of a Polynomial Function .............................................................................. 3284.6 Complex Zeros; Fundamental Theorem of Algebra ............................................................... 355Chapter Review ............................................................................................................................. 362Chapter Test................................................................................................................................... 391Cumulative Review........................................................................................................................ 395Chapter Projects............................................................................................................................. 400
Page 4 of 16
Solution Manual for Precalculus, 8th Edition - Page 4 preview imageChapter 5Exponential and Logarithmic Functions5.1 Composite Functions .............................................................................................................. 4025.2 One-to-One Functions; Inverse Functions .............................................................................. 4185.3 Exponential Functions ............................................................................................................ 4375.4 Logarithmic Functions............................................................................................................ 4565.5 Properties of Logarithms ........................................................................................................ 4765.6 Logarithmic and Exponential Equations................................................................................. 4845.7 Financial Models .................................................................................................................... 5015.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growthand Decay Models .................................................................................................................... 5085.9 Building Exponential, Logarithmic, and Logistic Models from Data .................................... 515Chapter Review ............................................................................................................................. 520Chapter Test................................................................................................................................... 540Cumulative Review........................................................................................................................ 544Chapter Projects............................................................................................................................. 548Chapter 6Trigonometric Functions6.1 Angles and Their Measure...................................................................................................... 5506.2 Trigonometric Functions: Unit Circle Approach.................................................................... 5576.3 Properties of the Trigonometric Functions ............................................................................. 5726.4 Graphs of the Sine and Cosine Functions ............................................................................... 5846.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions...................................... 6036.6 Phase Shift; Sinusoidal Curve Fitting ..................................................................................... 611Chapter Review ............................................................................................................................. 622Chapter Test................................................................................................................................... 637Cumulative Review........................................................................................................................ 640Chapter Projects............................................................................................................................. 644Chapter 7Analytic Trigonometry7.1 The Inverse Sine, Cosine, and Tangent Functions.................................................................. 6487.2 The Inverse Trigonometric Functions (Continued) ................................................................ 6587.3 Trigonometric Equations ........................................................................................................ 6697.4 Trigonometric Identities ......................................................................................................... 6887.5 Sum and Difference Formulas ................................................................................................ 6997.6 Double-angle and Half-angle Formulas.................................................................................. 7217.7 Product-to-Sum and Sum-to-Product Formulas...................................................................... 744Chapter Review ............................................................................................................................. 754Chapter Test................................................................................................................................... 778Cumulative Review........................................................................................................................ 782Chapter Projects............................................................................................................................. 787Chapter 8Applications of Trigonometric Functions8.1 Right Triangle Trigonometry; Applications ........................................................................... 7918.2 The Law of Sines.................................................................................................................... 8038.3 The Law of Cosines................................................................................................................ 8168.4 Area of a Triangle................................................................................................................... 8258.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................... 832Chapter Review ............................................................................................................................. 840Chapter Test................................................................................................................................... 852Cumulative Review........................................................................................................................ 855Chapter Projects............................................................................................................................. 861
Page 5 of 16
Solution Manual for Precalculus, 8th Edition - Page 5 preview imageChapter 9Polar Coordinates; Vectors9.1 Polar Coordinates.................................................................................................................... 8659.2 Polar Equations and Graphs.................................................................................................... 8729.3 The Complex Plane; DeMoivre’s Theorem............................................................................ 9009.4 Vectors.................................................................................................................................... 9109.5 The Dot Product...................................................................................................................... 9209.6 Vectors in Space ..................................................................................................................... 9249.7 The Cross Product................................................................................................................... 930Chapter Review ............................................................................................................................. 940Chapter Test................................................................................................................................... 958Cumulative Review........................................................................................................................ 962Chapter Projects............................................................................................................................. 964Chapter 10Analytic Geometry10.2 The Parabola ......................................................................................................................... 96810.3 The Ellipse ............................................................................................................................ 98210.4 The Hyperbola ...................................................................................................................... 99710.5 Rotation of Axes; General Form of a Conic ....................................................................... 101510.6 Polar Equations of Conics................................................................................................... 102710.7 Plane Curves and Parametric Equations ............................................................................. 1034Chapter Review ........................................................................................................................... 1045Chapter Test................................................................................................................................. 1063Cumulative Review...................................................................................................................... 1068Chapter Projects........................................................................................................................... 1070Chapter 11Systems of Equations and Inequalities11.1 Systems of Linear Equations: Substitution and Elimination............................................... 107411.2 Systems of Linear Equations: Matrices .............................................................................. 109311.3 Systems of Linear Equations: Determinants....................................................................... 111511.4 Matrix Algebra.................................................................................................................... 112711.5 Partial Fraction Decomposition .......................................................................................... 114411.6 Systems of Nonlinear Equations......................................................................................... 115711.7 Systems of Inequalities ....................................................................................................... 118411.8 Linear Programming ........................................................................................................... 1198Chapter Review ........................................................................................................................... 1209Chapter Test................................................................................................................................. 1235Cumulative Review...................................................................................................................... 1244Chapter Projects........................................................................................................................... 1248Chapter 12Sequences; Induction; the Binomial Theorem12.1 Sequences ........................................................................................................................... 125012.2 Arithmetic Sequences ......................................................................................................... 125912.3 Geometric Sequences; Geometric Series ............................................................................ 126512.4 Mathematical Induction ...................................................................................................... 127512.5 The Binomial Theorem....................................................................................................... 1282Chapter Review ........................................................................................................................... 1287Chapter Test................................................................................................................................. 1294Cumulative Review...................................................................................................................... 1297Chapter Projects........................................................................................................................... 1300
Page 6 of 16
Solution Manual for Precalculus, 8th Edition - Page 6 preview imageChapter 13Counting and Probability13.1 Counting ............................................................................................................................. 130313.2 Permutations and Combinations ......................................................................................... 130413.3 Probability ........................................................................................................................... 1308Chapter Review ........................................................................................................................... 1313Chapter Test................................................................................................................................. 1315Cumulative Review...................................................................................................................... 1317Chapter Projects........................................................................................................................... 1320Chapter 14A Preview of Calculus: The Limit, Derivative, and Integral of a Function14.1 Finding Limits Using Tables and Graphs ........................................................................... 132214.2 Algebra Techniques for Finding Limits.............................................................................. 132714.3 One-sided Limits; Continuous Functions ........................................................................... 133114.4 The Tangent Problem; The Derivative................................................................................ 133914.5 The Area Problem; The Integral ......................................................................................... 1348Chapter Review ........................................................................................................................... 1362Chapter Test................................................................................................................................. 1374Chapter Projects........................................................................................................................... 1378Appendix AReviewA.1 Algebra Essentials................................................................................................................ 1383A.2 Geometry Essentials............................................................................................................. 1388A.3 Polynomials ......................................................................................................................... 1393A.4 Synthetic Division................................................................................................................ 1402A.5 Rational Expressions............................................................................................................ 1404A.6 Solving Equations ................................................................................................................ 1409A.7 Complex Numbers; Quadratic Equations in the Complex Number System ........................ 1423A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ..... 1428A.9 Interval Notation; Solving Inequalities ................................................................................ 1436A.10nth Roots; Rational Exponents............................................................................................ 1447Appendix BGraphing UtilitiesB.1 The Viewing Rectangle........................................................................................................ 1456B.2 Using a Graphing Utility to Graph Equations...................................................................... 1457B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ............................ 1461B.5 Square Screens ..................................................................................................................... 1463
Page 7 of 16
Solution Manual for Precalculus, 8th Edition - Page 7 preview image1Chapter 1GraphsSection 1.11.02.()5388− −==3.2234255+==4.22211601213600372161+=+==Since the sum of the squares of two of the sidesof the triangle equals the square of the third side,the triangle is a right triangle.5.12bh6.true7.x-coordinate;y-coordinate8.quadrants9.midpoint10.False; the distance between two points is nevernegative.11.False; points that lie in Quadrant IV will have apositivex-coordinate and a negativey-coordinate.The point()1, 4−lies in Quadrant II.12.True;1212,22xxyyM++=13.(a)Quadrant II(b)x-axis(c)Quadrant III(d)Quadrant I(e)y-axis(f)Quadrant IV14.(a)Quadrant I(b)Quadrant III(c)Quadrant II(d)Quadrant I(e)y-axis(f)x-axis15.The points will be on a vertical line that is twounits to the right of they-axis.
Page 8 of 16
Solution Manual for Precalculus, 8th Edition - Page 8 preview imageChapter 1:Graphs216.The points will be on a horizontal line that isthree units above thex-axis.17.221222(,)(20)(10)21415d P P=−+−=+=+=18.221222(,)( 20)(10)( 2)1415d P P=−−+−=−+=+=19.221222(,)( 21)(21)( 3)19110d P P=−−+−=−+=+=20.()221222(,)2( 1)(21)319110d P P=− −+−=+=+=21.()()( )221222(,)(53)4428464682 17d P P=−+− −=+=+==22.()()()( )221222(,)214034916255d P P=− −+−=+=+==23.()221222(,)6( 3)(02)9(2)81485d P P=− −+−=+ −=+=24.()()221222(,)422( 3)2542529d P P=−+− −=+=+=25.()221222(,)(64)4( 3)2744953d P P=−+− −=+=+=26.()()221222(,)6(4)2( 3)1051002512555d P P=− −+− −=+=+==27.22122222(,)(0)(0)()()d P Pababab=−+−=−+ −=+28.221222222(,)(0)(0)()()22d P Paaaaaaaa=−+−=−+ −=+==29.( 2,5),(1,3),( 1, 0)ABC= −== −()()()222222222222(,)1( 2)(35)3( 2)9413(,)11(03)( 2)( 3)4913(,)1( 2)(05)1( 5)12526d A Bd B Cd A C=− −+−=+ −=+==− −+−=−+ −=+==− − −+−=+ −=+=Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()()()222222(,)(,)(,)1313261313262626d A Bd B Cd A C+=+=+==The area of a triangle is12Abh=⋅. In thisproblem,
Page 9 of 16
Solution Manual for Precalculus, 8th Edition - Page 9 preview imageSection 1.1:The Distance and Midpoint Formulas3[] []1(,)(,)2111313132213 square units2Ad A Bd B C=⋅⋅=⋅=⋅⋅=30.( 2, 5),(12, 3),(10,11)ABC= −==−()()()222222222222(,)12( 2)(35)14( 2)1964200102(,)1012( 113)( 2)( 14)4196200102(,)10( 2)( 115)12(16)14425640020d A Bd B Cd A C=− −+−=+ −=+===−+ −−=−+ −=+===− −+ −−=+ −=+==Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()()()222222(,)(,)(,)10210220200200400400400d A Bd B Cd A C+=+=+==The area of a triangle is12Abh=. In thisproblem,[] []1(,)(,)21 102 10221 100 22100 square unitsAd A Bd B C=⋅⋅=⋅⋅=⋅⋅=31.(5,3),(6, 0),(5,5)ABC=−==()()()222222222222(,)6(5)(03)11(3)1219130(,)56(50)(1)512526(,)5(5)(53)1021004104226d A Bd B Cd A C=− −+−=+ −=+==−+−=−+=+==− −+−=+=+==Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()()()222222(,)(,)(,)1042613010426130130130d A Cd B Cd A B+=+=+==The area of a triangle is12Abh=. In this
Page 10 of 16
Solution Manual for Precalculus, 8th Edition - Page 10 preview imageChapter 1:Graphs4problem,[] []1(,)(,)211042621 2262621 2 26226 square unitsAd A Cd B C=⋅⋅=⋅⋅=⋅⋅=⋅⋅=32.( 6, 3),(3,5),( 1, 5)ABC= −=−= −()()()222222222222(,)3( 6)( 53)9( 8)8164145(,)13(5( 5))( 4)1016100116229(,)1(6)(53)5225429d A Bd B Cd A C=− −+ −−=+ −=+==− −+− −=−+=+===− − −+−=+=+=Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()()()222222(,)(,)(,)29229145294 2914529116145145145d A Cd B Cd A B+=+=+⋅=+==The area of a triangle is12Abh=. In thisproblem,[] []1(,)(,)2129 22921 2 29229 square unitsAd A Cd B C=⋅⋅=⋅⋅=⋅⋅=33.(4,3),(0,3),(4, 2)ABC=−=−=()()()()222222222222(,)(04)3( 3)(4)0160164(,)402( 3)45162541(,)(44)2( 3)05025255d A Bd B Cd A C=−+ −− −=−+=+===−+− −=+=+==−+− −=+=+==Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()222222(,)(,)(,)45411625414141d A Bd A Cd B C+=+=+==The area of a triangle is12Abh=. In this
Page 11 of 16
Solution Manual for Precalculus, 8th Edition - Page 11 preview imageSection 1.1:The Distance and Midpoint Formulas5problem,[] []1(,)(,)21 4 5210 square unitsAd A Bd A C=⋅⋅=⋅⋅=34.(4,3),(4, 1),(2, 1)ABC=−==()()()()222222222222(,)(44)1( 3)04016164(,)2411( 2)04042(,)(24)1( 3)( 2)44162025d A Bd B Cd A C=−+− −=+=+===−+−=−+=+===−+− −=−+=+==Verifying that∆ABC is a right triangle by thePythagorean Theorem:[][][]()222222(,)(,)(,)4225164202020d A Bd B Cd A C+=+=+==The area of a triangle is12Abh=. In this problem,[] []1(,)(,)21 4 224 square unitsAd A Bd B C=⋅⋅=⋅⋅=35.The coordinates of the midpoint are:1212( ,),224435 ,2280,22(4, 0)xxyyx y++=−++===36.The coordinates of the midpoint are:()1212( ,),222204,2204,220, 2xxyyx y++=−++===37.The coordinates of the midpoint are:1212( ,),223620,2232,223 ,12xxyyx y++=−++===38.The coordinates of the midpoint are:1212( ,),222432,2261,2213,2xxyyx y++=+−+=−==−
Page 12 of 16
Solution Manual for Precalculus, 8th Edition - Page 12 preview imageChapter 1:Graphs639.The coordinates of the midpoint are:1212( ,),224631,22210 ,22(5,1)xxyyx y++=+−+=−==−40.The coordinates of the midpoint are:1212( ,),224232,2221,2211,2xxyyx y++=−+−+=−−==−−41.The coordinates of the midpoint are:1212( ,),2200,22,22xxyyx yabab++=++==42.The coordinates of the midpoint are:1212( ,),2200,22,22xxyyx yaaaa++=++==43.The x coordinate would be235+=and the ycoordinate would be523−=. Thus the newpoint would be()5,3.44.The new x coordinate would be123− −= −andthe new y coordinate would be6410+=. Thusthe new point would be()3,10−45.a.If we use a right triangle to solve theproblem, we know the hypotenuse is 13 units inlength. One of the legs of the triangle will be2+3=5. Thus the other leg will be:222225132516914412bbbb+=+===Thus the coordinates will have an y value of11213− −= −and11211− +=. So the pointsare()3,11and()3,13−.b.Consider points of the form()3,ythat are adistance of 13 units from the point()2,1−−.()()()()( )()2221212222223( 2)1512512226dxxyyyyyyyy=−+−=− −+ − −=+ − −=+++=++()()()22222213226132261692260214301113yyyyyyyyyy=++=++=++=+−=−+11011yy−==or13013yy+== −Thus, the points()3,11and()3,13−are adistance of 13 units from the point()2,1−−.46.a.If we use a right triangle to solve theproblem, we know the hypotenuse is 17 units inlength. One of the legs of the triangle will be2+6=8. Thus the other leg will be:222228176428922515bbbb+=+===Thus the coordinates will have an x value of11514−= −and11516+=. So the points are()14,6−−and()16,6−.
Page 13 of 16
Solution Manual for Precalculus, 8th Edition - Page 13 preview imageSection 1.1:The Distance and Midpoint Formulas7b.Consider points of the form(),6x−that area distance of 17 units from the point()1, 2.()()()()()( )2221212222221262182164265dxxyyxxxxxxx=−+−=−+− −=−++=−++=−+()()()22222217265172652892650222401416xxxxxxxxxx=−+=−+=−+=−−=+−14014xx+== −or16016xx−==Thus, the points()14,6−−and()16,6−are adistance of 13 units from the point()1, 2.47.Points on thex-axis have ay-coordinate of 0. Thus,we consider points of the form(), 0xthat are adistance of 6 units from the point()4,3−.()()()()()22212122222243016831689825dxxyyxxxxxxx=−+−=−+ −−=−++ −=−++=−+()222222268256825368250811( 8)( 8)4(1)( 11)2(1)864448108228634332xxxxxxxxx=−+=−+=−+=−−− −±−−−=±+±==±==±433x=+or433x=−Thus, the points()433,0+and()433, 0−areon thex-axis and a distance of 6 units from thepoint()4,3−.48.Points on they-axis have anx-coordinate of 0.Thus, we consider points of the form()0,ythatare a distance of 6 units from the point()4,3−.()()()()2221212222224034961696625dxxyyyyyyyyy=−+−=−+ −−=+++=+++=++()222222266256625366250611( 6)(6)4(1)( 11)2(1)63644680226453252xxxxxxxxx=++=++=++=+−−±−−=−±+−±==−±== −±625x= −+or625x= −−Thus, the points()0,625−+and()0,625−−
Page 14 of 16
Solution Manual for Precalculus, 8th Edition - Page 14 preview imageChapter 1:Graphs8are on they-axis and a distance of 6 units from thepoint()4,3−.49.()1212,,22xxyyMx y++==.()111,( 3, 6)Pxy== −and( ,)( 1, 4)x y=−, so122222312231xxxxxx+=−+−=−= −+=and122222642862yyyyyy+=+==+=Thus,2(1, 2)P=.50.()1212,,22xxyyMx y++==.()222,(7,2)Pxy==−and( ,)(5,4)x y=−, so1211127521073xxxxxx+=+==+=and121112( 2)428( 2)6yyyyyy+=+ −−=−=+ −−=Thus,1(3,6)P=−.51.The midpoint of AB is:()0600,223, 0D++==The midpoint of AC is:()0404,222, 2E++==The midpoint of BC is:()6404,225, 2F++==()2222(,)04(34)(4)(1)16117d C D=−+−=−+ −=+=()2222(,)26(20)(4)21642025d B E=−+−=−+=+==2222(,)(20)(50)2542529d A F=−+−=+=+=52.Let12(0, 0),(0, 4),( ,)PPPx y===()()()221222122222222222,(00)(40)164,(0)(0)416,(0)(4)(4)4(4)16dPPdPPxyxyxydPPxyxyxy=−+−===−+−=+=→+==−+−=+−=→+−=Therefore,()222248168162yyyyyyy=−=−+==which gives2222161223xxx+=== ±Two triangles are possible. The third vertex is()()23, 2or23, 2−.53.Let()10, 0P=,()20,Ps=,()3, 0Ps=, and()4,Ps s=.yx(0,)s(0, 0)( , 0)s( ,)s sThe points1Pand4Pare endpoints of onediagonal and the points2Pand3Pare the
Page 15 of 16
Solution Manual for Precalculus, 8th Edition - Page 15 preview imageSection 1.1:The Distance and Midpoint Formulas9endpoints of the other diagonal.1,400,,2222ssssM++==2,300,,2222ssssM++==The midpoints of the diagonals are the same.Therefore, the diagonals of a square intersect attheir midpoints.54.Let()10, 0P=,()2, 0Pa=, and33,22aaP=. To show that these verticesform an equilateral triangle, we need to showthat the distance between any pair of points is thesame constant value.()()()()()22122121222,000dP Pxxyyaaa=−+−=−+−==()()()22232121222222,302234444dPPxxyyaaaaaaaa=−+−=−+−=+===()()()22132121222222,3002234444dP Pxxyyaaaaaaa=−+−=−+−=+===Since all three distances have the same constantvalue, the triangle is an equilateral triangle.Now find the midpoints:1 22 31 3456000,, 02223330,22,4422300322,,2244P PP PP PaaPMaaaaaPMaaaaPM++===++===++===()2245222233,0424344316162aaadPPaaaaa=−+−=+=+=()224622223,0424344316162aaadPPaaaaa=−+−=−+=+=()2256222333,44440242aaaadPPaaa=−+−=+==Since the sides are the same length, the triangleis equilateral.55.221222(,)(42)(11)(6)0366d P P=−−+−=−+==()222322(,)4(4)( 31)0(4)164d PP=−− −+ −−=+ −==221322(,)(42)( 31)(6)(4)3616522 13d P P=−−+ −−=−+ −=+==Since[][][]222122313(,)(,)(,)d P Pd PPd P P+=,the triangle is a right triangle.
Page 16 of 16
Solution Manual for Precalculus, 8th Edition - Page 16 preview imageChapter 1:Graphs1056.()221222(,)6( 1)(24)7(2)49453d P P=− −+−=+ −=+=()222322(,)46( 52)(2)(7)44953d PP=−+ −−=−+ −=+=()221322(,)4( 1)( 54)5(9)2581106d P P=− −+ −−=+ −=+=Since[][][]222122313(,)(,)(,)d P Pd PPd P P+=,the triangle is a right triangle.Since()()1223,,dPPdPP=, the triangle isisosceles.Therefore, the triangle is an isosceles righttriangle.57.()()221222(,)0(2)7( 1)28464682 17d P P=− −+− −=+=+==()222322(,)30(27)3(5)92534d PP=−+−=+ −=+=()()221322(,)3( 2)2( 1)5325934d P P=− −+− −=+=+=Since2313(,)(,)d PPd P P=, the triangle isisosceles.Since[][][]222132312(,)(,)(,)d P Pd PPd P P+=,the triangle is also a right triangle.Therefore, the triangle is an isosceles righttriangle.58.()()221222(,)4702( 11)(2)121412555d P P=−−+−=−+ −=+==()222322(,)4(4)(60)86643610010d PP=− −+−=+=+==()()221322(,)4762( 3)4916255d P P=−+−=−+=+==Since[][][]222132312(,)(,)(,)d P Pd PPd P P+=,the triangle is a right triangle.59.Using the Pythagorean Theorem:222229090810081001620016200902127.28 feetdddd+=+====≈90909090d60.Using the Pythagorean Theorem:222226060360036007200720060284.85 feetdddd+=+=→===≈60606060d61.a.First: (90, 0), Second: (90, 90),Third: (0, 90)
Preview Mode

This document has 1468 pages. Sign in to access the full document!

Study Now!

X-Copilot AI
Unlimited Access
Secure Payment
Instant Access
24/7 Support
Document Chat

Document Details

Subject
Mathematics
Textbook
Precalculus by Michael Sullivan

Related Documents

View all
Exam Guides

Test Bank For Precalculus, 11th Edition

4.5
00
Textbook Guides

Precalculus Enhanced with Graphing Utilities 4th Edition Solution Manual

4.4
00
Textbook Guides

Solution Manual for Precalculus, 11th Edition

4.5
00
Textbook Guides

Solution Manual for Precalculus Enhanced with Graphing Utilities, MyLab Math, 8th Edition

4.5
00
Textbook Guides

Solution Manual for Precalculus Enhanced with Graphing Utilities, 8th Edition

4.4
00
Textbook Guides

Solution Manual for Precalculus , 10th Edition

4.1
00
Exam Guides

Test Bank for Precalculus , 10th Edition

4.6
00
Exam Guides

Test Bank for Precalculus Enhanced with Graphing Utilities, 6th Edition

4.6
•70
Exam Guides

Test Bank for Precalculus Enhanced with Graphing Utilities , 7th Edition

4.3
•109
Quick Guides

Precalculus - Polynomial and Rational Functions