A-22 Answers to Selected Exercises 73. (a) x - 3 x + 4 60 (b) x - 3 x + 4 … 0 (c) x - 3 x + 4 70 (d) x - 3 x + 4 Ú 0 75. x 73 77. x 7150 Summary Exercises on Solving Equations and Inequalities 1. (a) 1-1, 12 ´11, ∞2 (b) 1-∞, -14 ´516 2. (a) 1-∞, -12 ´1-1, 12 ´11, ∞2 (b) ∅ 3. (a) 506 (b) 1-3, 02 ´13, ∞2 4. (a) 51, 36 (b) 31, 22 ´12, 34 5. E4 3F 6. 5206 7. E -1 { 213 2 F 8. E - 1 4 { 27 4 i F 9. 53, 76 10. 526 11. 52, 36 12. 506 13. E { 1 8F 14. 5136 15. E9 2 , 14 3 , 16 3 , 11 2 F 16. 525, 646 17. E { 25, {i27F 18. 51, 76 19. E1 2 , - 3 4F 20. E - 11 5 , 3 5F 21. 1-∞, 52 22. A 6 13 , ∞B 23. 1-∞, -74 24. C - 4 3 , ∞B 25. 1-4, 12 26. C -1, 1 2D 27. A -∞, - 13 3 D ´31, ∞2 28. A -1, 5 2B 29. A -2, 4 3B 30. 1-∞, -32 ´A - 5 2 , ∞B 31. 1-∞, -44 ´C 5 3, ∞B 32. C -9, 7 2D 33. 516 34. 1-2, 02 ´12, ∞2 35. 1-∞, -42 ´A - 1 2, 1B ´15, ∞2 36. C -1, 2 3D ´C 3 2, 3D 37. A -∞, 2 5B ´A 2 5, ∞B 38. 1-∞, -14 ´34, ∞2 39. 5-1, 26 40. 5-36´31, ∞2 41. 5-4, 0, 36 42. A - 23, - 1 2B ´A 1 2, 23B 43. 1-∞, 02 ´C 3 2 , 3B ´35, ∞2 44. 1-2, -12 ´12, ∞2 3.7 Exercises 1. increases; decreases 3. 60 5. h = k t 7. -30 9. 60 11. 3 2 13. 12 5 15. 18 125 17. C 19. A 21. The circumference of a circle varies directly as (or is proportional to) its radius. 23. The speed varies directly as (or is proportional to) the distance traveled and inversely as the time. 25. The volume of a cone varies jointly as the square of its radius and its height. 27. 69.08 in. 29. 850 ohms 31. 12 km 33. 16 in. 35. 90 revolutions per minute 37. 0.0444 ohm 39. $875 41. 800 lb 43. 8 9 metric ton 45. 66p 17 sec 47. 21 49. 365.24 51. 92; undernourished 53. y is half as large as before. 55. y is one-third as large as before. 57. p is 1 32 as large as before. Chapter 3 Review Exercises 1. x y 1 1 (–4, –5) f(x) = 3(x + 4)2 – 5 0 vertex: 1-4, -52; axis: x = -4; x-intercepts: Q-12 { 215 3 , 0R ; y-intercept: 10, 432; domain: 1-∞, ∞2; range: 3-5, ∞2; increasing on 1-4, ∞2; decreasing on 1-∞, -42 [3.2] 3. no; 38 4. yes [3.3] 5. ƒ1x2 = x4 - 7x3 + 10x2 + 26x - 60 [3.4] 6. x y 10 2 –2 0 f(x) = x(x – 2)3(x + 2)2 7. x y 100 50 –100 –50 3 –3 0 f(x) = 2x4 – 9x3 – 5x2 + 57x – 45 f(x) = (x – 3)2(2x + 5)(x – 1) 8. x y 20 –3 3 –80 0 f(x) = –4x5 + 16x4 + 13x3 – 76x2 – 3x + 18 f(x) = –(x + 2)(2x + 1)(2x – 1)(x – 3)2 [3.5] 9. x y –5 –2 5 f(x) = x2 + 7x + 10 3x + 1 0 10. x 0 2 y 1 –1 f(x) = x2 + 2x + 1 x – 1 y = x + 3 3.6 Exercises 1. below 3. 50, 1, 26 5. 10, 12 ´12, ∞2 7. 526 9. 11, 22 ´13, ∞2 11. (a) 1-∞, -24 ´ 35, ∞2 (b) 1-∞, -22 ´ 15, ∞2 (c) 3-2, 54 (d) 1-2, 52 13. A -∞, -22B ´ 13, ∞2 15. 546 17. 3-6, 54 19. 1-∞, -12 ´ 12, ∞2 21. C 1 2 , 5D 23. (a) 1-∞, 04 ´ 31, 24 (b) 1-∞, 02 ´ 11, 22 (c) 30, 14 ´ 32, ∞2 (d) 10, 12 ´ 12, ∞2 25. A -∞, 1 2B ´ A 9 5 , 4B 27. C - 3 2 , 1 3D ´ 34, ∞2 29. 33, 44 31. 13, 42 ´ 14, 52 33. 3-4, -34 ´ C 1 2 , ∞B 35. 506´ 31, ∞2 37. 1-∞, 34 39. 516´ C 3 2 , ∞B 41. 1-2, -12 ´ 10, 42 43. ∅ 45. C -22, 1D ´ C 22, ∞B 47. 1-∞, ∞2 49. (a) 1-∞, 14 ´ 12, ∞2 (b) 1-∞, 12 ´ 12, ∞2 (c) 31, 22 (d) 11, 22 51. 30, 32 53. 1-∞, 12 ´ 14, ∞2 55. C - 3 2 , 5B 57. 12, 64 59. 1-∞, 22 ´ 14, ∞2 61. 3-1, 44 63. 1-2, 32 65. 3-2, 02 ´ 12, ∞2 67. 11, 42 ´ 17, ∞2 69. 1-∞, -34 ´ 1-2, 22 Answers will vary in Exercises 71 and 73. 71. (a) x2 + 4x - 5 60 (b) x2 + 4x - 5 … 0 (c) x2 + 4x - 5 70 (d) x2 + 4x - 5 Ú 0
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