A-29 Answers to Selected Exercises 43. 52.1026 45. 5-2.4876 47. 536 49. 5ln 36 51. 56.9596 53. 5e13/36 55. U 24 10 - 7 2 V 57. 536 59. E - 4 3 , 5F 61. E1, 10 3 F 63. 526 65. 5-36 67. I0 = I 10d / 10 69. 51.3156 71. (a) 10,000,000I0 (b) 158,500,000I0 (c) 15.85 times greater 73. 3.0% 75. $20,363.38 77. 17.3 yr 79. 2018 81. (a) $15,207 (b) $10,716 (c) $4491 (d) They are the same. Chapter 4 Test [4.1] 1. (a) 1-∞, ∞2; 1-∞, ∞2 (b) The graph is a stretched translation of y = 23 x, which passes the horizontal line test and is thus a one-to-one function. (c) ƒ-11x2 = x 3 + 7 2 (d) 1-∞, ∞2; 1-∞, ∞2 (e) x y f(x) = !2x – 7 3 f –1(x) = x3 + 7 2 10 –10 –10 10 0 The graphs are reflections of each other across the line y = x. [4.2, 4.3] 2. (a) B (b) A (c) C (d) D 3. E1 2F 4. (a) log4 8 = 3 2 (b) 82/3 = 4 [4.1–4.3] 5. y x 0 4 1 1 4 g(x) = log1/2 x f(x) = ( ) x 1 2 They are inverses. [4.3] 6. 2 log7 x + 1 4 log7 y - 3 log7 z [4.4] 7. 3.3780 8. 7.7782 9. 1.1674 [4.2] 10. 506 11. 546 [4.5] 12. 50.6316 13. 512.5486 14. 52.8116 [4.2] 15. 5{1256 [4.5] 16. E0, ln 3 2F [4.3] 17. E 3 4F [4.5] 18. 50, 66 19. 526 20. ∅ 21. E7 2F [4.4] 22. The expression log5 27 is the exponent to which 5 must be raised in order to obtain 27. To approximate it with a calculator, use the change-of-base theorem. log5 27 = log 27 log 5 ≈2.0478 [4.6] 23. 10 sec 24. (a) 42.8 yr (b) 42.7 yr 25. 39.2 yr 26. (a) 329.3 g (b) 13.9 days Chapter 5 Trigonometric Functions 5.1 Exercises 1. 1 360 3. 180° 5. 90° 7. 1 60 9. 55° 15′ 11. (a) 60° (b) 150° 13. (a) 45° (b) 135° 15. (a) 36° (b) 126° 17. (a) 89° (b) 179° 19. (a) 75° 40′ (b) 165° 40′ 21. (a) 69° 49′ 30″ (b) 159° 49′ 30″ 23. 70°; 110° 25. 30°; 60° 27. 40°; 140° 29. 107°; 73° 31. 69°; 21° 33. 150° 35. 7° 30′ 37. 130° 39. 83° 59′ 41. 179° 19′ 43. -23° 49′ 45. 38° 32′ 47. 60° 34′ 49. 17° 01′ 49″ 51. 30° 27′ 53. 35.5° 55. 112.25° 57. -60.2° 59. 20.91° 61. 91.598° 63. 274.316° 65. 39° 15′ 00″ 67. 126° 45′ 36″ 69. -18° 30′ 54″ 71. 31° 25′ 47″ 73. 89° 54′ 01″ 75. 178° 35′ 58″ 77. 392° 79. 386° 30′ 81. 320° 83. 234° 30′ 85. 1° 87. 359° 89. 179° 91. 130° 93. 240° 95. 120° In Exercises 97 and 99, answers may vary. 97. 450°, 810°; -270°, -630° 99. 360°, 720°; -360°, -720° 101. 30° + n # 360° 103. 135° + n # 360° 105. -90° + n # 360° 107. 0° + n # 360°, or n # 360° 109. 0° and 360° are coterminal angles. Angles other than those given are possible in Exercises 111–121. 111. 0 x y 75° 435°; –285°; quadrant I 113. 0 x y 174° 534°; –186°; quadrant II 115. 0 x y 300° 660°; –60°; quadrant IV 117. 0 x y –61° 299°; –421°; quadrant IV 119. 0 x y 90° 450°; –270°; no quadrant 121. 0 x y –90° 270°; –450°; no quadrant 123. 3 4 125. 1800° 127. 12.5 rotations per hr 129. 4 sec 5.2 Exercises 1. 322 3. - 22 2 5. possible 7. impossible 9. possible In Exercises 11–25 and 43–49, we give, in order, sine, cosine, tangent, cotangent, secant, and cosecant. 11. 0 x y (5, –12) –12 5 U - 12 13 ; 5 13 ; - 12 5 ; - 5 12 ; 13 5 ; - 13 12 13. 0 x y (3, 4) 4 3 U 4 5 ; 3 5 ; 4 3 ; 3 4 ; 5 3 ; 5 4
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