Section A.9 AN103 43. 21 { } 45. 2, 2 { } − 47. 6{ } 49. 3, 3 { } − 51. 4, 1 { } − 53. 1, 3 2 { } − 55. 4, 4 { } − 57. 2{ } 59. No real solution 61. 2, 2 { } − 63. 1, 3 { } − 65. 2, 1, 0, 1 { } − − 67. 0, 4 { } 69. 6, 2 { } − 71. 1 2 , 3 { } − 73. 3, 4 { } 75. 3 2{ } 77. 2 3 , 3 2 { } − 79. 3 4 , 2 { } − 81. 6 { } − 83. 2, 1, 1, 2 { } − − 85. 6, 5 { } − − 87. 3 2 , 2 { } − 89. 5, 0, 4 { } − 91. 1, 1 { } − 93. 2, 1 2 , 2 { } − 95. 5, 5 { } − 97. 1, 3 { } − 99. 3, 0 { } − 101. 16 103. 1 16 105. 1 9 107. 7, 3 { } − 109. 1 4 , 3 4 { } − 111. 1 7 6 , 1 7 6 { } − − − + 113. 2 2, 2 2 { } − + 115. 5 29 2 , 5 29 2 { } − + 117. 1, 3 2 { } 119. No real solution 121. 1 5 4 , 1 5 4 { } − − − + 123. 3 15 2 , 3 15 2 { } − − − + 125. No real solution 127. Repeated real solution 129. Two unequal real solutions 131. R R R R R 1 2 1 2 = + 133. R mv F 2 = 135. r S a S = − 137. b b ac a b b ac a b a b a 4 2 4 2 2 2 2 2 − + − + − − − = − = − 139. k 1 2 or 1 2 = − 141. The solutions of ax bx c 0 2 − + = are b b ac a 4 2 2 + − and b b ac a 4 2 2 − − . 143. b A.7 Assess Your Understanding (page A65) 1. T 2. 5 3. F 4. real; imaginary; imaginary unit 5. F 6. T 7. F 8. b 9. a 10. c 11. + i 8 5 13. − + i 7 6 15. − − i 6 11 17. − i 6 18 19. − i 18 21 21. − i 10 5 23. 26 25. + i 6 5 8 5 27. − i 1 2 29. − i 5 2 7 2 31. − + i 1 2 3 2 33. i2 35. −i 37. 1 39. −6 41. − i 10 43. − + i 2 2 45. 0 47. 0 49. i2 51. i5 53. i 2 3 55. i 10 2 57. i5 59. { } − i i 2, 2 61. { } −4, 4 63. { } − + i i 3 2 , 3 2 65. { } − + i i 3 , 3 67. { } − + i i 1 5 1 5 , 1 5 1 5 69. { } − + i i 1 5 2 5 , 1 5 2 5 71. { } − − − + i i 1 2 3 2 , 1 2 3 2 73. { } − − − + i i 4,2 23,2 23 75. { } − − i i 2, 2, 2, 2 77. { } − − i i i i 3, 2, 2, 3 79. Two complex solutions that are conjugates of each other 81. Two unequal real solutions 83. A repeated real solution 85. − i 2 3 87. 6 89. 25 91. + i 2 3 ohms 93. ( ) ( ) ( ) ( ) +=+ +− = −=+ −− = z z a bi a bi a z z a bi a bi bi 2 ; 2 95. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) +=+ ++ =+++ =+−+ =− +− =+ z w a bi c di a c b d i a c b d i a bi c di z w A.8 Assess Your Understanding (page A73) 1. mathematical modeling 2. interest 3. uniform motion 4. F 5. T 6. a 7. b 8. c 9. π = = = A r r A ; radius, area 2 11. = = = A s A s ; area, length of a side 2 13. = = = = F ma F m a ; force, mass, acceleration 15. = = = = W Fd W F d ; work, force, distance 17. = = = C x C x 150 ; total variable cost, number of dishwashers 19. Invest $1875 in bonds and $3125 in the CD 21. $4000 at 4% 23. Mix 75 lb of Earl Grey tea with 25 lb of Orange Pekoe tea. 25. Mix 156 lb of cashews with the almonds. 27. The speed of the current is 2.286 mi h. 29. The speed of the current is 5 mi h. 31. Karen walked at 3.75 ft sec. 33. A doubles tennis court is 78 feet long and 36 feet wide. 35. Working together, it takes 12 min. 37. (a) The dimensions are 10 ft by 5 ft. (b) The area is 50 sq ft. (c) The dimensions would be 7.5 ft by 7.5 ft. (d) The area would be 56.25 sq ft. 39. The defensive back catches up to the tight end at the tight end’s 45-yd line. 41. Add 2 3 gal of water. 43. Evaporate 10.67 oz of water. 45. 40 g of 12-karat gold should be mixed with 20 g of pure gold. 47. Mike passes Dan 1 3 mile from the start, 2 min from the time Mike started to run. 49. Start the auxiliary pump at 9:45 am. 51. The tub will fill in 1 hour. 53. Run: 12 miles; bicycle: 75 miles 55. Bolt would beat Burke by 18.25 m. 57. The dimensions should be 4 ft by 4 ft. 61. The average speed is 49.5 mi/h. 63. The solution mixture percent must be between the two percents of the components used to make the solution. A.9 Assess Your Understanding (page A84) 3. closed interval 4. Multiplication Properties 5. T 6. T 7. T 8. F 9. T 10. F 11. d 12. c 13. [ ] 0, 2 ; ≤ ≤ x 0 2 15. [ )∞ ≥ x 2, ; 2 17. [ ) ≤ < x 0, 3 ; 0 3 19. (a) < 6 8 (b) − < 2 0 (c) < 9 15 (d) − >− 6 10 21. (a) > 7 0 (b) − >− 1 8 (c) >− 12 9 (d) − < 8 6 23. (a) + < x2 4 5 (b) − <− x2 4 3 (c) + < x6 3 6 (d) − − >− x4 2 4 25. [ ] 0, 4 4 0 27. [ ) 4, 6 6 4 29. [ ) − ∞3, 3 31. ( ) −∞ −, 4 4 59. { } < x x 4 or ( ) −∞, 4 4 61. { } ≥ x x 2 or [ )∞ 2, 2 63. { } > x x 3 or ( )∞3, 3 65. { } ≥ x x 2 or [ )∞ 2, 2 33. ≤ ≤ x 2 5 5 2 35. − < ≤ x 4 3 4 3 ] 37. ≥ x 4 4 39. <− x 3 3 41. < 43. > 45. ≥ 47. < 49. ≤ 51. > 53. ≥ 55. < < x 0 1 1 5 57. < − < x 1 1 5 0 67. { } >− x x 7 or ( ) − ∞ 7, 7 69. { } ≤ x x 2 3 or (−∞ ⎤ ⎦ ⎥ , 2 3 2 3 71. { } <− x x 20 or ( ) −∞ −, 20 20 73. { } ≥ x x 4 3 or ) ⎡ ∞ ⎣ ⎢ 4 3 , 4 3
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