Skip to content
Textbook Guides

Solution Manual for College Algebra, 11th Edition

Solution Manual for College Algebra, 11th Edition provides expert solutions to textbook questions, making complex problems easier to solve.

Preview 16 of 1093 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    S OLUTIONS M ANUAL T IM B RITT Jackson State Community College C OLLEGE A LGEBRA E LEVENTH E DITION Michael Sullivan Chicago State University

  2. Page 2
  3. Page 3
    Read page 3 as text

    Table of Contents Chapter R Review R.1 Real Numbers ........................................................................................................................... 1 R.2 Algebra Essentials .................................................................................................................... 5 R.3 Geometry Essentials ............................................................................................................... 11 R.4 Polynomials ............................................................................................................................ 16 R.5 Factoring Polynomials ............................................................................................................ 23 R.6 Synthetic Division .................................................................................................................. 28 R.7 Rational Expressions .............................................................................................................. 30 R.8 n th Roots; Rational Exponents ............................................................................................... 40 Chapter 1 Equations and Inequalities 1.1 Linear Equations ..................................................................................................................... 50 1.2 Quadratic Equations ................................................................................................................ 68 1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93 1.5 Solving Inequalities ............................................................................................................... 116 1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127 1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications 137 Chapter Review ............................................................................................................................ 145 Chapter Test ................................................................................................................................. 154 Chapter Projects ........................................................................................................................... 156 Chapter 2 Graphs 2.1 The Distance and Midpoint Formulas ................................................................................... 157 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170 2.3 Lines ...................................................................................................................................... 184 2.4 Circles ................................................................................................................................... 202 2.5 Variation................................................................................................................................ 216 Chapter Review ............................................................................................................................ 222 Chapter Test ................................................................................................................................. 228 Cumulative Review ...................................................................................................................... 230 Chapter Project ............................................................................................................................. 232 Chapter 3 Functions and Their Graphs 3.1 Functions ............................................................................................................................... 233 3.2 The Graph of a Function ....................................................................................................... 251 3.3 Properties of Functions.......................................................................................................... 260 3.4 Library of Functions; Piecewise-defined Functions .............................................................. 277 3.5 Graphing Techniques: Transformations ................................................................................ 289 3.6 Mathematical Models: Building Functions ........................................................................... 307 Chapter Review ............................................................................................................................ 315 Chapter Test ................................................................................................................................. 322 Cumulative Review ...................................................................................................................... 325 Chapter Projects ........................................................................................................................... 329

  4. Page 4
    Read page 4 as text

    Chapter 4 Linear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models ............................................................... 331 4.2 Building Linear Functions from Data ................................................................................... 342 4.3 Quadratic Functions and Their Properties ............................................................................. 348 4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371 4.5 Inequalities Involving Quadratic Functions .......................................................................... 379 Chapter Review ............................................................................................................................ 399 Chapter Test ................................................................................................................................. 407 Cumulative Review ...................................................................................................................... 409 Chapter Projects ........................................................................................................................... 412 Chapter 5 Polynomial and Rational Functions 5.1 Polynomial Functions............................................................................................................ 415 5.2 Graphing Polynomial Functions; Models.............................................................................. 425 5.3 Properties of Rational Functions ........................................................................................... 441 5.4 The Graph of a Rational Function ......................................................................................... 451 5.5 Polynomial and Rational Inequalities.................................................................................... 507 5.6 The Real Zeros of a Polynomial Function............................................................................. 528 5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559 Chapter Review ............................................................................................................................ 568 Chapter Test ................................................................................................................................. 583 Cumulative Review ...................................................................................................................... 587 Chapter Projects ........................................................................................................................... 592 Chapter 6 Exponential and Logarithmic Functions 6.1 Composite Functions ............................................................................................................. 594 6.2 One-to-One Functions; Inverse Functions ............................................................................ 612 6.3 Exponential Functions ........................................................................................................... 634 6.4 Logarithmic Functions .......................................................................................................... 655 6.5 Properties of Logarithms ....................................................................................................... 677 6.6 Logarithmic and Exponential Equations ............................................................................... 686 6.7 Financial Models ................................................................................................................... 706 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models .............................................................................................................. 714 6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 723 Chapter Review ............................................................................................................................ 729 Chapter Test ................................................................................................................................. 741 Cumulative Review ...................................................................................................................... 745 Chapter Projects ........................................................................................................................... 748

  5. Page 5
    Read page 5 as text

    Chapter 7 Analytic Geometry 7.2 The Parabola.......................................................................................................................... 751 7.3 The Ellipse ............................................................................................................................ 765 7.4 The Hyperbola ....................................................................................................................... 782 Chapter Review ............................................................................................................................ 802 Chapter Test ................................................................................................................................. 806 Cumulative Review ...................................................................................................................... 809 Chapter Projects ........................................................................................................................... 811 Chapter 8 Systems of Equations and Inequalities 8.1 Systems of Linear Equations: Substitution and Elimination ................................................. 814 8.2 Systems of Linear Equations: Matrices ................................................................................. 837 8.3 Systems of Linear Equations: Determinants ......................................................................... 862 8.4 Matrix Algebra ...................................................................................................................... 876 8.5 Partial Fraction Decomposition ............................................................................................. 895 8.6 Systems of Nonlinear Equations ........................................................................................... 914 8.7 Systems of Inequalities.......................................................................................................... 942 8.8 Linear Programming ............................................................................................................. 957 Chapter Review ............................................................................................................................ 970 Chapter Test ................................................................................................................................. 985 Cumulative Review ...................................................................................................................... 994 Chapter Projects ........................................................................................................................... 997 Chapter 9 Sequences; Induction; the Binomial Theorem 9.1 Sequences ............................................................................................................................ 1000 9.2 Arithmetic Sequences.......................................................................................................... 1010 9.3 Geometric Sequences; Geometric Series ............................................................................ 1019 9.4 Mathematical Induction....................................................................................................... 1030 9.5 The Binomial Theorem ....................................................................................................... 1038 Chapter Review .......................................................................................................................... 1045 Chapter Test ............................................................................................................................... 1049 Cumulative Review .................................................................................................................... 1052 Chapter Projects ......................................................................................................................... 1055 Chapter 10 Counting and Probability 10.1 Counting ............................................................................................................................ 1057 10.2 Permutations and Combinations........................................................................................ 1060 10.3 Probability ......................................................................................................................... 1065 Chapter Review .......................................................................................................................... 1072 Chapter Test ............................................................................................................................... 1073 Cumulative Review .................................................................................................................... 1075 Chapter Projects ......................................................................................................................... 1078 Appendix Graphing Utilities Section 1 The Viewing Rectangle ............................................................................................. 1081 Section 2 Using a Graphing Utility to Graph Equations ........................................................... 1082 Section 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry ................. 1087 Section 5 Square Screens .......................................................................................................... 1089

  6. Page 6
    Read page 6 as text

    1 Chapter R Review Section R.1 1. rational 2. 4 5 6 3 4 30 3 31        3. Distributive 4. c 5. a 6. b 7. True 8. False; The Zero-Product Property states that if a product equals 0, then at least one of the factors must equal 0. 9. False; 6 is the Greatest Common Factor of 12 and 18. The Least Common Multiple is the smallest value that both numbers will divide evenly. The LCM for 12 and 18 is 36. 10. True 11.       1, 3, 4,5, 9 2, 4, 6, 7,8 1, 2,3, 4, 5, 6, 7,8, 9 A B     12.       1, 3, 4,5, 9 1, 3, 4, 6 1, 3, 4, 5, 6, 9 A C     13.       1, 3, 4,5, 9 2, 4, 6, 7,8 4 A B     14.       1, 3, 4,5, 9 1, 3, 4, 6 1, 3, 4 A C     15.               ( ) 1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6 1, 2,3, 4,5, 6, 7,8,9 1,3, 4, 6 1, 3, 4, 6 A B C         16.               ( ) 1, 3, 4,5, 9 2, 4, 6, 7,8 1,3, 4, 6 4 1, 3, 4, 6 1,3, 4, 6 A B C         17.   0, 2, 6, 7, 8 A  18.   0, 2, 5, 7, 8, 9 C  19.         1, 3, 4, 5, 9 2, 4, 6, 7, 8 4 0, 1, 2, 3, 5, 6, 7, 8, 9 A B      20.         2, 4, 6, 7, 8 1, 3, 4, 6 1, 2, 3, 4, 6, 7, 8 0, 5, 9 B C      21.       0, 2, 6, 7, 8 0, 1, 3, 5, 9 0, 1, 2, 3, 5, 6, 7, 8, 9 A B     22.       0, 1, 3, 5, 9 0, 2, 5, 7, 8, 9 0, 5, 9 B C     23. a.   2,5 b.   6, 2,5  c.   1 6, , 1.333... 1.3, 2,5 2     d.    e.   1 6, , 1.333... 1.3, , 2,5 2      24. a.   1 b.   0,1 c.   5 , 2.060606... 2.06,1.25, 0,1 3   d.   5

  7. Page 7
    Read page 7 as text

    Chapter R: Review 2 e.   5 , 2.060606... 2.06,1.25, 0,1, 5 3   25. a.   1 b.   0,1 c.   1 1 1 0,1, , , 2 3 4 d. None e.   1 1 1 0,1, , , 2 3 4 26. a. None b.   1  c.   1.3, 1.2, 1.1, 1     d. None e.   1.3, 1.2, 1.1, 1     27. a. None b. None c. None d.   1 2, , 2 1, 2     e.   1 2, , 2 1, 2     28. a. None b. None c.   1 10.3 2  d.   2, 2    e.   1 2, 2, 10.3 2     29. a. 18.953 b. 18.952 30. a. 25.861 b. 25.861 31. a. 28.653 b. 28.653 32. a. 99.052 b. 99.052 33. a. 0.063 b. 0.062 34. a. 0.054 b. 0.053 35. a. 9.999 b. 9.998 36. a. 1.001 b. 1.000 37. a. 0.429 b. 0.428 38. a. 0.556 b. 0.555 39. a. 34.733 b. 34.733 40. a. 16.200 b. 16.200 41. 3 2 5   42. 5 2 10   43. 2 3 4 x    44. 3 2 2 y    45. 3 1 2 y   46. 2 4 6 x   47. 2 6 x   48. 2 6 y   49. 6 2 x  50. 2 6 x  51. 9 4 2 5 2 7      52. 6 4 3 2 3 5      53. 6 4 3 6 12 6        54. 8 4 2 8 8 0      55. 18 5 2 18 10 8      56. 100 10 2 100 20 80      57. 1 12 1 13 4 3 3 3     58. 1 4 1 3 2 2 2 2    

  8. Page 8
    Read page 8 as text

    Section R.1: Real Numbers 3 59.     6 3 5 2 3 2 6 15 2 1 6 17 11                      60.         2 8 3 4 2 3 2 8 3 6 3 2 8 18 3 2 10 3 20 3 23                                61.     4 9 5 6 7 3 4 14 42 3 56 42 3 14 3 17                62.     1 4 3 2 2 1 12 2 2 1 12 11             63.         10 6 2 2 8 3 2 10 6 4 5 2 10 2 5 2 10 7 2 10 14 4                           64.       2 5 4 6 3 4 2 20 6 1 18 6 18 6 12                            65.     1 1 5 3 2 1 2 2    66.     1 1 5 4 9 3 3 3    67. 4 8 12 6 5 3 2     68. 2 4 2 1 5 3 2       69. 3 10 3 2 5 3 5 21 5 3 7        2 5   5 3  2 7 7   70. 5 3 5 3 5 9 10 3 3 5 2        3  3 3 5   1 6 2   71. 6 10 2 3 5 2 2 3 25 27 5 5 3 9           5  2 5  5 3   4 45 9   72. 21 100 3 7 4 25 3 25 3 25 3        7 4 25    25 3  28  73. 3 2 15 8 23 4 5 20 20     74. 4 1 8 3 11 3 2 6 6     75. 7 4 49 32 81 8 7 56 56     76. 8 15 16 135 151 9 2 18 18     77. 5 1 10 3 13 18 12 36 36     78. 2 8 6 40 46 15 9 45 45     79. 5 8 25 64 39 13 24 15 120 120 40        80. 3 2 9 4 5 14 21 42 42     81. 3 2 9 8 1 20 15 60 60     82. 6 3 12 15 3 35 14 70 70      83. 5 18 5 27 5 9 3 5 9 18 11 9 2 11 11 27                      3 9  15 22 2 11    84. 5 21 5 35 5 7 5 5 7 21 2 7 3 2 2 35                      5 7  25 6 3 2   

  9. Page 9
    Read page 9 as text

    Chapter R: Review 4 85. 1 4 17 4 17 21 1 3 7 21 21 21 21       86. 2 4 1 2 2 2 2 2 2 2 2 3 5 6 3 5 3 2 3 5 3 2 3 15 2 5 2 10 2 10 2 12 3 5 15 15 15 15 15 4 3 4 3 4 5 3 5 3 5                              87. 3 3 2 3 3 6 3 6 2 3 2 4 8 1 4 8 4 8 4 2 8 12 3 12 3 15 8 8 8 8                88. 5 1 3 5 1 3 5 1 3 5 1 3 6 2 1 6 2 3 2 2 3 2 2 5 1 5 1 4 2 2 2 2 2                    89.   6 4 6 24 x x    90.   4 2 1 8 4 x x    91.   2 4 4 x x x x    92.   2 4 3 4 12 x x x x    93. 3 1 3 1 2 3 2 2 2 2 4 2 4 2 2 2 2 2 3 2 3 1 2 2 2 2 x x x x x                      94. 2 1 2 1 3 2 3 3 3 3 3 6 3 6 3 3 2 3 2 3 1 2 3 3 2 2 x x x x x                      95.    2 2 2 4 4 2 8 6 8 x x x x x x x          96.    2 2 5 1 5 5 6 5 x x x x x x x          97.    2 2 9 2 7 2 7 18 63 2 11 63          x x x x x x x 98.    2 2 3 1 5 3 15 5 3 14 5          x x x x x x x 99.    2 2 8 2 2 8 16 10 16 x x x x x x x          100.    2 2 4 2 2 4 8 6 8 x x x x x x x          101. 2 2 2 3 ( 5 ) 3 60 3 15 3 60 15 60 4           x x k x x x xk x x xk x k 102. 2 2 2 2 2 2 2 2 2 2 2 2 2 ( )( 3 ) 4 12 3 3 4 12 (3 ) 3 4 12 (3 ) 3 4 12 (2 ) 3 4 12 2 4 2                               x k x k x x x kx kx k x x x x k k k x x x x k k k x x x x k k x x k k 103.     2 3 2 3 2 3 5 5 x x x x x x x            104. 2 3 4 2 12 14      since multiplication comes before addition in the order of operations for real numbers.   2 3 4 5 4 20      since operations inside parentheses come before multiplication in the order of operations for real numbers. 105.     2 3 4 2 12 24           2 3 2 4 6 8 48      106. 4 3 7 1 2 5 7     , but 4 3 4 5 3 2 20 6 26 13 2.6 2 5 10 10 10 5           107. Subtraction is not commutative; for example: 2 3 1 1 3 2       .

  10. Page 10
    Read page 10 as text

    Section R.2: Algebra Essentials 5 108. Subtraction is not associative; for example:     5 2 1 2 4 5 2 1        . 109. Division is not commutative; for example: 2 3 3 2  . 110. Division is not associative; for example:   12 2 2 6 2 3      , but   12 2 2 12 1 12      . 111. The Symmetric Property implies that if 2 = x, then x = 2. 112. From the principle of substitution, if 5 x  , then       2 2 2 5 5 25 25 5 30 x x x x x x x           113. There are no real numbers that are both rational and irrational, since an irrational number, by definition, is a number that cannot be expressed as the ratio of two integers; that is, not a rational number Every real number is either a rational number or an irrational number, since the decimal form of a real number either involves an infinitely repeating pattern of digits or an infinite, non- repeating string of digits. 114. The sum of an irrational number and a rational number must be irrational. Otherwise, the irrational number would then be the difference of two rational numbers, and therefore would have to be rational. 115. Answers will vary. 116. Since 1 day = 24 hours, we compute 12997 541.5416 24  . Now we only need to consider the decimal part of the answer in terms of a 24 hour day. That is,    0.5416 24 13  hours. So it must be 13 hours later than 12 noon, which makes the time 1 AM CST. 117. Answers will vary. Section R.2 1. variable 2. origin 3. strict 4. base; exponent (or power) 5. 3 1.2345678 10  6. d 7. a 8. b 9. True 10. False; the absolute value of a real number is nonnegative. 0 0  which is not a positive number. 11. False; a number in scientific notation is expressed as the product of a number , x , 1 10 x   or 10 1 x     , and a power of 10. 12. True 13.   5 2    3 4 14. 1 3 3 2     2 3 15. 1 0 2  16. 5 6  17. 1 2    18. 5 3 2    19. 3.14   20. 2 1.41 

  11. Page 11
    Read page 11 as text

    Chapter R: Review 6 21. 1 0.5 2  22. 1 0.33 3  23. 2 0.67 3  24. 1 0.25 4  25. 0 x  26. 0 z  27. 2 x  28. 5 y   29. 1 x  30. 2 x  31. Graph on the number line: 2 x     32. Graph on the number line: 4 x    33. Graph on the number line: 1 x     34. Graph on the number line: 7 x    35. ( , ) (0,1) 1 0 1 1 d C D d      36. ( , ) (0, 3) 3 0 3 3 d C A d         37. ( , ) (1,3) 3 1 2 2 d D E d      38. ( , ) (0,3) 3 0 3 3 d C E d      39. ( , ) ( 3,3) 3 ( 3) 6 6 d A E d        40. ( , ) (1, 1) 1 1 2 2 d D B d         41. 2 2 2 3 2 6 4 x y          42. 3 3( 2) 3 6 3 3 x y          43. 5 2 5( 2)(3) 2 30 2 28 xy          44. 2 2( 2) ( 2)(3) 4 6 2 x xy            45. 2( 2) 4 2 4 2 3 5 5 x x y          46. 2 3 1 1 2 3 5 5 x y x y            47. 3( 2) 2(3) 6 6 3 2 0 0 2 2 3 5 5 x y y            48. 2( 2) 3 4 3 2 3 7 3 3 3 x y          49. 3 ( 2) 1 1 x y       50. 3 ( 2) 5 5 x y       51. 3 2 3 2 5 x y        52. 3 2 3 2 1 x y        53. 3 3 1 3 3 x x    54. 2 2 1 2 2 y y        55. 4 5 4(3) 5( 2) 12 10 22 22 x y         56. 3 2 3(3) 2( 2) 9 4 5 5 x y         57. 4 5 4(3) 5( 2) 12 10 12 10 2 2 x y           

  12. Page 12
    Read page 12 as text

    Section R.2: Algebra Essentials 7 58. 3 2 3 3 2 2 3 3 2 2 9 4 13 x y            59. 2 1 x x  Part (c) must be excluded. The value 0 x  must be excluded from the domain because it causes division by 0. 60. 2 1 x x  Part (c) must be excluded. The value 0 x  must be excluded from the domain because it causes division by 0. 61. 2 ( 3)( 3) 9 x x x x x     Part (a) , 3 x  , must be excluded because it causes the denominator to be 0. 62. 2 9 x x  None of the given values are excluded. The domain is all real numbers. 63. 2 2 1 x x  None of the given values are excluded. The domain is all real numbers. 64. 3 3 2 ( 1)( 1) 1 x x x x x     Parts (b) and (d) must be excluded. The values 1, and 1 x x    must be excluded from the domain because they cause division by 0. 65. 2 2 3 5 10 5 10 ( 1)( 1) x x x x x x x x x         Parts (b), (c), and (d) must be excluded. The values 0, 1, and 1 x x x     must be excluded from the domain because they cause division by 0. 66. 2 2 3 2 9 1 9 1 ( 1) x x x x x x x x          Part (c) must be excluded. The value 0 x  must be excluded from the domain because it causes division by 0. 67. 4 5 x  5 x  must be exluded because it makes the denominator equal 0.   Domain 5 x x   68. 6 4 x   4 x   must be excluded sine it makes the denominator equal 0.   Domain 4 x x    69. 4 x x  4 x   must be excluded sine it makes the denominator equal 0.   Domain 4 x x    70. 2 6 x x   6 x  must be excluded sine it makes the denominator equal 0.   Domain 6 x x   71. 5 5 5 ( 32) (32 32) (0) 0 C 9 9 9 C F        72. 5 5 5 ( 32) (212 32) (180) 100 C 9 9 9 C F        73. 5 5 5 ( 32) (77 32) (45) 25 C 9 9 9 C F        74. 5 5 ( 32) ( 4 32) 9 9 5 ( 36) 9 20 C C F           75. 2 ( 9) ( 9)( 9) 81      76. 2 2 4 (4) 16      77. 2 2 1 1 4 16 4   

  13. Page 13
    Read page 13 as text

    Chapter R: Review 8 78. 2 2 1 1 4 16 4       79. 6 4 6 4 2 2 1 1 3 3 3 3 9 3          80. 2 3 2 3 1 4 4 4 4 4        81.      1 3 1 3 3 4 4 4 64        82.      3 1 3 1 3 2 2 2 8        83. 2 100 10 10   84. 2 36 6 6   85.   2 4 4 4     86.   2 3 3 3     87.     2 2 4 2 4 8 9 9 81   x x x 88.   1 2 2 2 1 1 4 4 4 x x x       89.       4 2 2 2 2 1 2 1 4 2 2 x x y x y x y y        90.     3 3 3 1 1 3 3 3 3 y x y x y x y x        91. 2 5 2 3 5 4 1 1 3 4       x y y x y x y x x y 92. 2 2 1 1 2 3 1 2 3 1 x y x y x y x y x y          93. 2 5 3 5 3 3 3 7 2 7 2 3 1 5 7 3 2 2 2 1 2 2 ( 4) ( ) 16 ( 3) 27 16 27 16 27 16 27               y x z y x z x y z x y z x y z x y z x z y 94. 2 1 2 1 1 3 4 4 2 4 1 1 1 6 2 1 6 2 4 ( ) 4 2 8 4 8 1 2 1 2 x y z x y z x y x y x y z x y z x y z                  95. 2 2 2 3 3 2 6 6 1 3 2 2 2 3 2 3 3 9 2 3 2 2 4                           y x x x x y y x y y 96.     3 3 3 2 2 2 2 2 2 3 3 2 6 3 6 3 2 5 5 6 6 6 5 6 216 125 5 y x x y x y x x y y                           97.     1 2 2 2 2 4 1 x xy y       98.     1 3 1 3 3 3 2 2 y x y x         99.     2 2 2 2 2 1 4 1 5 x y        100.     2 2 2 2 2 1 4 1 4 x y      101.         2 2 2 2 1 2 4 xy       102.         2 2 2 2 1 1 1 x y       103. 2 2 2 x x    104.   2 2 x x   105.     2 2 2 2 2 1 4 1 5 x y        106. 2 2 2 1 2 1 3 x y x y          107. 1 1 2 2 y x   

  14. Page 14
    Read page 14 as text

    Section R.2: Algebra Essentials 9 108.   2 1 1 x y    109. If 2, x  3 2 3 2 2 3 5 4 2 2 3 2 5 2 4 16 12 10 4 10 x x x                If 1, x  3 2 3 2 2 3 5 4 2 1 3 1 5 1 4 2 3 5 4 0 x x x                110. If 1, x  3 2 3 2 4 3 2 4 1 3 1 1 2 4 3 1 2 8 x x x               If 2, x  3 2 3 2 4 3 2 4 2 3 2 2 2 32 12 2 2 44 x x x               111. 4 4 4 4 (666) 666 3 81 222 (222)          112.   3 3 3 3 3 3 3 3 1 (0.1) (20) 2 10 10 1 2 10 10 2 8               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. 2 454.2 4.542 10   122. 1 32.14 3.214 10   123. 2 0.013 1.3 10    124. 3 0.00421 4.21 10    125. 4 32,155 3.2155 10   126. 4 21, 210 2.121 10   127. 4 0.000423 4.23 10    128. 2 0.0514 5.14 10    129. 4 6.15 10 61,500   130. 3 9.7 10 9700   131. 3 1.214 10 0.001214    132. 4 9.88 10 0.000988    133. 8 1.1 10 110, 000, 000   134. 2 4.112 10 411.2   135. 2 8.1 10 0.081    136. 1 6.453 10 0.6453    137. A lw  138.   2 P l w   139. C d   140. 1 2 A bh  141. 2 3 4 A x  142. 3 P x  143. 3 4 3 V r  

  15. Page 15
    Read page 15 as text

    Chapter R: Review 10 144. 2 4 S r   145. 3 V x  146. 2 6 S x  147. a. If 1000, x  4000 2 4000 2(1000) 4000 2000 $6000 C x        The cost of producing 1000 watches is $6000. b. If 2000, x  4000 2 4000 2(2000) 4000 4000 $8000 C x        The cost of producing 2000 watches is $8000. 148. 210 80 120 25 60 32 5 $98        His balance at the end of the month was $98. 149. We want the difference between x and 4 to be at least 6 units. Since we don’t care whether the value for x is larger or smaller than 4, we take the absolute value of the difference. We want the inequality to be non-strict since we are dealing with an ‘at least’ situation. Thus, we have 4 6 x   150. We want the difference between x and 2 to be more than 5 units. Since we don’t care whether the value for x is larger or smaller than 2, we take the absolute value of the difference. We want the inequality to be strict since we are dealing with a ‘more than’ situation. Thus, we have 2 5 x   151. a. 110 108 110 2 2 5 x        108 volts is acceptable. b. 110 104 110 6 6 5 x        104 volts is not acceptable. 152. a. 220 214 220 6 6 8 x        214 volts is acceptable. b. 220 209 220 11 11 8 x        209 volts is not acceptable. 153. a. 3 2.999 3 0.001 0.001 0.01 x        A radius of 2.999 centimeters is acceptable. b. 3 2.89 3 0.11 0.11 0.01 x         A radius of 2.89 centimeters is not acceptable. 154. a. 98.6 97 98.6 1.6 1.6 1.5 x        97˚F is unhealthy. b. 98.6 100 98.6 1.4 1.4 1.5 x       100˚F is not unhealthy. 155. The distance from Earth to the Moon is about 8 4 10 400, 000, 000   meters. 156. The height of Mt. Everest is about 3 8848 8.848 10   meters. 157. The wavelength of visible light is about 7 5 10 0.0000005    meters. 158. The diameter of an atom is about 10 1 10 0.0000000001    meters. 159. The diameter is about 2 0.0403 4.03 10    inches. 160. The tiniest motor is less than 5 0.00004 4 10    millimeters tall.

  16. Page 16
    Read page 16 as text

    Section R.3: Geometry Essentials 11 161.       5 1 1 2 2 1.86 10 6 10 2.4 10 3.65 10 186, 000 60 60 24 365          10 12 586.5696 10 5.865696 10     There are about 12 5.9 10  miles in one light- year. 162. 7 2 5 93, 000, 000 9.3 10 5 10 186, 000 1.86 10 500 seconds 8 min. 20 sec.        It takes about 8 minutes 20 seconds for a beam of light to reach Earth from the Sun. 163. 1 0.333333 ... 0.333 3   1 3 is larger by approximately 0.0003333 ... 164. 2 3 0.666666 ... 0.666   2 3 is larger by approximately 0.000666 ... 165.    6 13 19 20 5.24 10 6.5 10 34.06 10 3.406 10       166. 4 4 6 10 10 5 1.62 10 1.62 10 0.36 10 4.5 4.5 10 10 3.6 10             167. No. For any positive number a , the value 2 a is smaller and therefore closer to 0. 168. We are given that 2 1 10 x   . This implies that 1 10 x   . Since 10 3.162 x   and 3.142 x    , the number could be 3.15 or 3.16 (which are between 1 and 10 as required). The number could also be 3.14 since numbers such as 3.146 which lie between  and 10 would equal 3.14 when truncated to two decimal places. 169. Answers will vary. 170. Answers will vary. 5 < 8 is a true statement because 5 is further to the left than 8 on a real number line. Section R.3 1. right; hypotenuse 2. 1 2 A bh  3. 2 C r   4. similar 5. c 6. b 7. True. 8. True. 2 2 2 6 8 36 64 100 10      9. False; the surface area of a sphere of radius r is given by 2 4 V r   . 10. True. The lengths of the corresponding sides are equal. 11. True. Two corresponding angles are equal. 12. False. The sides are not proportional. 13. 2 2 2 2 2 5, 12, 5 12 25 144 169 13 a b c a b c            14. 2 2 2 2 2 6, 8, 6 8 36 64 100 10 a b c a b c            15. 2 2 2 2 2 10, 24, 10 24 100 576 676 26 a b c a b c            16. 2 2 2 2 2 4, 3, 4 3 16 9 25 5 a b c a b c           

1077 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Mathematics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.