A-46 Answers to Selected Exercises [8.4] 9. v = 10; u = 126.9° 10. (a) 81, -39 (b) 8-6, 189 (c) -20 (d) 210 11. 41.8° [8.1] 12. 2.7 mi [8.4] 13. 8-346, 4519 [8.3] 14. 1.91 mi [8.1] 15. 14 m [8.3] 16. bearing: 357°; airspeed: 220 mph 17. 18.7° 18. 237 newtons [8.5] 19. 7 - 3i y x 0 7 – 3i 2 – 4i 5 + i –3 –4 1 5 7 20. (a) 31cos 90° + i sin 90°2 (b) 25 cis 63.43° (c) 21cos 240° + i sin 240°2 21. (a) 3 23 2 + 3 2 i (b) 3.06 + 2.57i (c) 3i [8.5, 8.6] 22. (a) 161cos 50° + i sin 50°2 (b) 223 + 2i (c) 423 + 4i [8.6] 23. 2 cis 67.5°, 2 cis 157.5°, 2 cis 247.5°, 2 cis 337.5° [8.7] 24. Answers may vary. (a) 15, 90°2, 15, -270°2 (b) A222, 225°B, A222, -135°B 25. (a) Q3 22 2 , - 322 2 R (b) 10, -42 1808 08 908 2708 3 r = 3 cos 3U 1808 08 908 2708 2 r = 1 – cos U 1 26. cardioid 27. three-leaved rose x y 0 6 6 x2 + y2 = 36 y x 0 –4 2 x – 2y = –4 28. (a) x - 2y = -4 (b) x2 + y2 = 36 y x 0 x = 2 cos 2t y = 2 sin 2t for t in [0, 2P] 2 x y x = 4t – 3 y = t2 for t in [–3, 4] 16 –16 (–15, 9) (13, 16) (–3, 0) 2 [8.8] 29. 30. Chapter 9 Systems and Matrices 9.1 Exercises 1. 4 3. -11 5. infinitely many 7. 51-4, 126 9. 5148, 826 11. 511, 326 13. 51-1, 326 15. 513, -426 17. 510, 226 19. 51-7, 526 21. 511, 326 23. 514, -226 25. 512, -226 27. 514, 626 29. 515, 226 31. ∅; inconsistent system 33. 51x , 4x - 926; infinitely many solutions 35. ∅; inconsistent system 37. E Ax, -7x + 6 2 B F ; infinitely many solutions 39. ∅; inconsistent system 41. x - 3y = -3 3x + 2y = 6 43. 510.820, -2.50826 45. 510.892, 0.45326 47. 511, 2, -126 49. 512, 0, 326 51. 511, 2, 326 53. 514, 1, 226 55. E A1 2 , 2 3 , -1B F 57. 51-3, 1, 626 59. EQ-z + 4 3 , 4z - 7 3 , zRF 61. EQ -5z + 69 5 , -z + 15, zRF 63. 51-9z + 47, 7z - 32, z26 65. ∅; inconsistent system 67. E A - z 9 , z 9 , zB F ; infinitely many solutions 69. 512, 226 71. E A1 5 , 1B F 73. 514, 6, 126 75. k ≠-6; k = -6 77. y = -3x - 5 79. y = 3 4 x 2 + 1 4 x - 1 2 81. y = 3x - 1 83. y = - 1 2 x 2 + x + 1 4 85. x 2 + y2 - 4x + 2y - 20 = 0 87. x2 + y2 + x - 7y = 0 89. x2 + y2 - 7 5 x + 27 5 y - 126 5 = 0 91. (a) a = 0.0128, b = 0.8441, c = 317; C = 0.0128x2 + 0.8441x + 317 (b) 2087 93. 2006 –2017 95. 12005.2, 1.262 97. year; population (in millions) 99. 23, 24 101. baseball: $230.64; football: $536.04 103. 120 gal of $9.00; 60 gal of $3.00; 120 gal of $4.50 105. 28 in.; 17 in.; 14 in. 107. $100,000 at 3%; $40,000 at 2.5%; $60,000 at 1.5% 109. 5140, 15, 3026 111. 11.92 lb of Arabian Mocha Sanani; 14.23 lb of Organic Shade Grown Mexico; 23.85 lb of Guatemala Antigua 113. (a) $16 (b) $11 (c) $6 114. (a) 8 (b) 4 (c) 0 115. See the answer to Exercise 117. 116. (a) 0 (b) 40 3 (c) 80 3 117. q 0 (8, 6) p = q p 2 8 16 6 10 p = 16 – q 3 4 5 4 118. price: $6; demand: 8 9.2 Exercises 1. 2 rows, 4 columns; 2 * 4 3. c -3 5 6 2 ` 2 7d 5. £ 3 2 0 -9 0 6 0 -8 1 3 5 1 4 § 7. c 1 0 4 -9d 9. £ 1 0 4 5 13 7 6 11 0§ 11. c 2 1 3 2 2 11 8d ; 2 * 3 13. £ 2 3 1 1 -4 1 1 2 1 3 3 -7 2§; 3 * 4
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