AN86 Answers: Chapter 11 81. $3000 from Bank One, $1000 from Bank Two, $6000 from Bank Three 83. 8 Deltas, 5 Betas, 10 Sigmas 85. = = = = I I I I 1, 3, 8, 4 1 2 3 4 87. (a) 2 bananas, 4 oranges, 1 papaya (b) 3 bananas, 6 oranges, 3 papayas 89. First Supplement Second Supplement Third Supplement 50 mg 75 mg 0 mg 36 mg 76 mg 8 mg 22 mg 77 mg 16 mg 8 mg 78 mg 24 mg 94. { } − < < x x 1 6 , or ( ) −1, 6 95. y y 5 2 x 5 21 x 6 (1, 0) (23, 5) (0, 21) 0 9 26 1 2 2 1 2 , 2 1 2 2 3 5 , 1 2 7 8 3, 96. { } x x is any real number , or ( ) −∞∞, 97. 2.42 98. x y 8 27 3 12 99. ( ) ( ) − − − = y x 5 16 4 9 1 2 2 100. − π ⋅ i e 18 18 3; 36 i 5 3 101. $3007.44 102. π 2 103. ( ) + + x h x x h 2 2 2 11.3 Assess Your Understanding (page 792) 1. − ad bc 2. − − 5 3 3 4 3. F 4. F 5. F 6. a 7. 22 9. −2 11. 10 13. −26 15. ( ) = = x y 6, 2; 6, 2 17. ( ) = = x y 3, 2; 3, 2 19. ( ) = = − − x y 8, 4; 8, 4 21. ( ) = − = − x y 3, 5; 3, 5 23. Not applicable 25. ( ) = = x y 1 2 , 3 4 ; 1 2 , 3 4 27. ( ) = = x y 1 10 , 2 5 ; 1 10 , 2 5 29. ( ) = = x y 3 2 , 1; 3 2 , 1 31. ( ) = = x y 4 3 , 1 5 ; 4 3 , 1 5 33. ( ) = = = − − x y z 1, 3, 2; 1,3, 2 35. ( ) = − = = − x y z 2, 1 3 , 1; 2, 1 3 , 1 37. Not applicable 39. ( ) = = = x y z 0, 0, 0; 0, 0, 0 41. Not applicable 43. −4 45. 12 47. 8 49. 8 51. −5 53. 13 11 55. 0 or −9 57. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) − − − + − = − + − = − − − − = − + − − − − − = − − − − = − − − yyxxxyxyxy y yx x xyxy xy x x y x x y y yxxy xy x xy x x y y y y x y y x y y y y x x x x 0 1 2 1 2 1 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1 1 2 1 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 1 2 1 2 1 1 59. The triangle has an area of 5 square units. 61. 50.5 square units 63. ( ) ( ) − + + = x y 3 2 25 2 2 65. If = a 0, we have = + = by s cx dy t Thus, = y s b and = − = − x t dy c tb ds bc Using Cramer’s Rule, we get = − − = − = − − = x sd tb bc tb sd bc y sc bc s b If = b 0, we have = + = ax s cx dy t Since = ≠ D ad 0, then ≠ ≠ a d 0 and 0. Thus, = x s a and = − = − y t cx d ta cs ad Using Cramer’s Rule, we get = = = − x sd ad s a y ta cs ad If = c 0, we have + = = ax by s dy t Since = ≠ D ad 0, then ≠ a 0 and ≠ d 0. Thus, = y t d and = − = − x s by a sd bt ad Using Cramer’s Rule, we get = − = = x sd bt ad y at ad t d If = d 0, we have + = = ax by s cx t Since = − ≠ D bc 0, then ≠ b 0 and ≠ c 0. Thus, = x t c and = − = − y s ax b sc at bc Using Cramer’s Rule, we get = − − = = − − = − x tb bc t c y at sc bc sc at bc 67. ( ) ( ) ( ) = − − + − − − a a a ka ka ka a a a ka a a a a ka a a a a ka a a a a 11 12 13 21 22 23 31 32 33 21 12 33 32 13 22 11 33 31 13 23 11 32 31 12 ( ) ( ) ( ) [ ] = − − + − − − = k a a a a a a a a a a a a a a a k a a a a a a a a a 21 12 33 32 13 22 11 33 31 13 23 11 32 31 12 11 12 13 21 22 23 31 32 33 69. ( ) ( ) ( )( ) ( ) ( ) + + + = + − − + − + + − a ka a ka a ka a a a a a a a ka a a a a a ka a a a a a ka a a a a 11 21 12 22 13 23 21 22 23 31 32 33 11 21 22 33 32 23 12 22 21 33 31 23 13 23 21 32 31 22 = − + − − + − + + − + − a a a a a a ka a a kaaa aaa aaa ka a a ka a a a a a a a a ka a a ka a a 11 22 33 11 32 23 21 22 33 21 32 23 12 21 33 12 31 23 22 21 33 22 31 23 13 21 32 13 31 22 23 21 32 23 31 22 ( ) ( ) ( ) = − − + + − = − − − + − = aaa aaa aaa aaa aaa aaa a a a a a a a a a a a a a a a a a a a a a a a a 11 22 33 11 32 23 12 21 33 12 31 23 13 21 32 13 31 22 11 22 33 32 23 12 21 33 31 23 13 21 32 31 22 11 12 13 21 22 23 31 32 33
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