Section 10.7 AN81 25. y x2 1 0 2 + − = 27. x y y 16 7 48 64 0 2 2 + + − = 29. x y x 3 12 9 0 2 2 − + + = 31. x y y 4 3 16 64 0 2 2 + − − = 33. x y y 9 5 24 36 0 2 2 + − − = 35. x y x 3 4 12 36 0 2 2 + − − = 37. r 1 1 sinθ = + 39. r 12 5 4 cosθ = − 41. r 12 1 6 sinθ = − 43. Use d D P p r , cosθ ( ) = − in the derivation of equation (6). 45. Use d D P p r , sinθ ( ) = + in the derivation of equation (6). 47. Aphelion: 35 AU; perihelion: 0.587 AU 5 25 40 25 49. 0.0125 m 51. v GM r 2 e 0 0 = 52. 27.81 53. Amplitude 4; Period 10π = = 54. 3 , , 5 3 π π π { } 55. 26 56. r 24 ft π = 57. 19.83 years ≈ 58. Decreasing: 1, 0 ; [ ] − Increasing: 2, 1 [ ] − − and 0, [ )∞ 59. k 12 5 = 60. f x x 1 3 3 8 2 ( ) ( ) = − + + 61. 40 sq units 7. y x 6 12 x y3 1 0 − + = 9. y x 5 5 y x 2 = − 11. y x 10 10 y x 8 = − 13. y x 5 3 x y 3 1 2 ( ) = − 15. y x 5 5 y x 2 2 = + 17. y x 3 3 y x3 = 19. y x 5 5 x y 4 9 1 2 2 + = 21. y x 5 5 x y 4 9 1 2 2 + = 23. y x 2 2 (!2, 1) x y 1 2 2 − = 25. y x 1 1 back and forth twice x y 1 + = 43. y x 20 5 (0, 0) (1, 1) (4, 16) (24, 16) (21, 1) C1 y x 16 2.5 (1, 1) (21, 1) C2 y x 20 5 (1, 1) (4, 16) C3 y x 20 5 (1, 1) (4, 16) C4 45. 7 25 25 9 47. 4 26 26 6 27. x t t x t t y t t y t t or 1 4 4 1 ( ) ( ) ( ) ( ) = = + = − = 29. x t t x t t y t t y t t or 1 1 3 2 6 ( ) ( ) ( ) ( ) = = = + = + 31. x t t x t t y t t y t t or 3 3 ( ) ( ) ( ) ( ) = = = = 33. x t t x t t y t t t y t t t or , 0 , 0 3 2 3 2 ( ) ( ) ( ) ( ) = = = ≥ = ≥ 35. x t t y t t t 2, , 0 5 ( ) ( ) = + = ≤ ≤ 37. x t t y t t t 3cos , 2sin , 0 2π ( ) ( ) = = ≤ ≤ 39. x t t y t t t 2 cos , 3sin , 0 2 π π ( ) ( ) ( ) ( ) = = − ≤ ≤ 41. x t t y t t t 2 sin 2 , 3cos 2 , 0 1 π π ( ) ( ) ( ) ( ) = = ≤ ≤ 10.7 Assess Your Understanding (page 745) 2. plane curve; parameter 3. b 4. a 5. F 6. T 49. (a) x t 3 ( ) = (or any number except 0) y t t t 16 50 6 2 ( ) = − + + (b) 3.24 sec (c) 1.56 sec; 45.06 ft (d) 50 0 5 0 51. (a) Train: x t t y t , 1; 1 2 1 ( ) ( ) = = Bill: x t t y t 5 5 , 3 2 2 ( ) ( ) ( ) = − = (b) Bill won’t catch the train. (c) 5 0 Bill Train 100 0 t 5 8 53. (a) x t t y t t t 145cos20 16 145sin20 5 2 ( ) ( ) ( ) ( ) = ° = − + ° + (b) 3.20 sec (c) 435.65 ft (d) 1.55 sec; 43.43 ft (e) 170 0 2120 440
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