A-55 Answers to Selected Exercises 35. ellipse x y 5 –2 + (y + 1)2 = 1 (3, –1) 0 (x – 3)2 4 31, 54; 3-2, 04; 11, -12, 15, -12 37. hyperbola (–3, –2) x 0 –3 –2 –4 y (y + 2)2 4 ( x + 3)2 9 – = 1 1-∞, ∞2; 1-∞, -44 ´30, ∞2; 1-3, -42, 1-3, 02; y = { 2 3 1x + 32 - 2 39. circle x y 0 (2, –3) x2 – 4x + y2 + 6y = –12 (x – 2)2 + (y + 3)2 = 1 31, 34; 3-4, -24 41. ellipse x y 0 (–2, 2) 5x2 + 20x + 2y2 – 8y = –18 (x + 2)2 2 ( y – 2)2 5 + = 1 C -2 - 22, -2 + 22 D ; C 2 - 25, 2 + 25 D ; A -2, 2 - 25 B , A -2, 2 + 25 B 47. x 2 12 + y2 16 = 1 49. y2 16 - x2 9 = 1 51. 1y - 222 = 12x 53. x 2 25 + y2 21 = 1 55. x2 9 - y2 16 = 1 57. 1x - 222 16 + y2 12 = 1 59. x 2 16 - y2 9 = 1 61. x2 6,111,883 + y2 432,135 = 1 43. –3 4 –4 x y 0 = – 1 – 16 y2 3 x 3-3, 04; 3-4, 44 45. y = – 1 + x2 x 1 –1 y 1-∞, ∞2; 1-∞, -14; function Chapter 10Test [10.1] 1. y = –x2 + 6x (3, 9) x 1 0 6 y 1-∞, ∞2; 1-∞, 94; 13, 92; x = 3 2. x = 4y2 + 8y (–4, –1) x 1 0 1 y 3-4, ∞2; 1-∞, ∞2; 1-4, -12; y = -1 [10.3] 11. x y 0 –1 2 – = 1 4 x2 4 y2 1-∞, -24 ´32, ∞2; 1-∞, ∞2; y = {x 12. 9x2 – 4y2 = 36 x 3 6 y –3 0 1-∞, -24 ´32, ∞2; 1-∞, ∞2; y = { 3 2 x 6. y x 0 (8, 5) 10 10 (x – 8)2 100 ( y – 5)2 49 + = 1 3-2, 184; 3-2, 124 7. y x 0 1 1 16x2 + 4y2 = 64 3-2, 24; 3-4, 44 3. A 1 32 , 0B ; x = - 1 32 4. 1y - 322 = - 1 5 1x - 22 5. (a) y = 3 500 x 2 (b) 41.7 ft [10.2] 8. y x 1 6 –6 0 y = – 1 – 36 x2 function 9. x 2 9 + y2 4 = 1 10. x 2 400 + y2 144 = 1; 10.4 ft 13. y 2 25 - x2 11 = 1 [10.4] 14. circle 15. hyperbola 16. ellipse 17. parabola 18. point 19. no graph [10.3] 20. y1 = 7 3 x2 25 - 1, y2 = -7 3 x2 25 - 1 Chapter 11 FurtherTopics in Algebra 11.1 Exercises 1. sequence 3. recursive 5. n an 1 7 2 12 3 17 4 22 5 27 7. 85 9. 3, -9, 27, -81, 243 11. 14, 18, 22, 26, 30 13. 6 5 , 7 6 , 8 7 , 9 8 , 10 9 15. 0, 1 9 , 2 27 , 1 27 , 4 243 17. -2, 4, -6, 8, -10 19. 1, 7 6 , 1, 5 6 , 19 27 21. 3, 4, 7, 12, 19 23. finite 25. finite 27. infinite 29. infinite 31. -2, 1, 4, 7 33. 1, 1, 2, 3 35. 2, 4, 12, 48 37. 35 39. 25 12 41. 288 43. 3 45. -18 47. 728 9 49. 28 51. 343 53. 30 55. 1490 57. -154 59. -2 + 1-12 + 0 + 1 + 2; 0 61. -1 + 1 + 3 + 5 + 7; 15 63. -10 - 4 + 0; -14 65. 0 + 1 2 + 2 3 + 3 4 ; 23 12 67. 124 + 111 + 100 + 91; 426 69. -3.5 + 0.5 + 4.5 + 8.5; 10 71. 0 + 4 + 16 + 36; 56 73. -1 - 1 3 - 1 5 - 1 7 ; - 176 105 75. 600 77. 1240 79. 90 81. 220 83. 304
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