Section 3.5 AN17 87. (a) ≈ 625 16 39.1 ft (b) ≈ 7025 32 219.5 ft (c) About 170 ft (d) 240 0 0 200 (f) When the height is 100 ft, the projectile is about 135.7 ft from the cliff. 89. $500; $1,000,000 91. (a) 70,000 players (b) $2500 93. (a) 187 or 188 watches; $7031.20 (b) ( ) = − + − P x x x 0.2 43 1750 2 (c) 107 or 108 watches; $561.20 95. (a) 171 ft (b) 49 mph 97. = x a 2 99. 10 101. ( ) 2, 2 103. f is increasing on ( [ ) −∞ − ⎤ ⎦ ⎥ ∞ , 1 3 , 5, . f is decreasing on 1 3 , 5 ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥ 107. y x 5 5 y x2 1 y x2 4x 1 y x2 4x 1 111. 0, 1, or 2 113. Symmetric with respect to the x-axis, the y-axis, and the origin 114. x x { 4} ≤ or ( ] −∞, 4 115. Center ( ) − 5, 2 ; radius = 3 116. = − y x 117. = − + y x 5 7 7 118. Domain: { } 1, 2, 3, 4, 5 ; Range: { } − − − − − 7, 6, 5, 4, 3 ; Function 119. 0 120. x 121. ( ) + + x x x 28 40 3 5 2 2 3 122. + + x c 5 3.4 Assess Your Understanding (page 176) 3. (a) ( ) = − + R p p p 6 600 2 (b) p p 0 100 { } ≤ ≤ (c) $50 (d) $15,000 (e) 300 (f) R p (50, 15,000) 0 16,000 20,000 8000 4000 12,000 0 50 100 (g) Between $30 and $70 5. (a) ( ) = − + R p p p 5 100 2 (b) p p 0 20 { } ≤ ≤ (c) $10 (d) $500 (e) 50 (f) R p (10, 500) 0 400 500 600 200 100 300 0 6 12 20 (g) Between $8 and $12 7. (a) ( ) = − + A w w w 200 2 (b) A is largest when = w 100 yd. (c) 10,000 yd2 9. 2,000,000 m2 11. 18.75 m 13. (a) 3 in. (b) Between 2 in. and 4 in. 15. π ≈ 750 238.73 m by 375 m 17. (a) 0 80 32 20 (b) = − + + y x x 0.008 0.746 13.469 2 (c) 45.5 miles per hour (d) 19. (a) 250 50 15 23 (b) = − y x 24.520 311.104 (c) 301.89 million 21. (a) 640 440 20 70 (b) = − + y x x 0.067 2.696 500.971 2 (c) 672 milliseconds 23. 38 3 25. 248 3 28. 13 29. x y 6 7 2 2 ( ) + + = 30. { } − − − + 4 31 5 , 4 31 5 31. x-intercept: 28; y-intercept 20 32. { } − 8 3 , 22 3 33. − + x x4 7; 2 remainder 6 34. x x x x 4, 0, 4 { } ≠ − ≠ ≠ 35. ( ) = − + − y x 2 9 3 4 2 36. ( )( ) − + − − x h x 3 1 1 37. ( ) ( ) ( ) + − − x x x 1 7 9 31 4 3 3.5 Assess Your Understanding (page 182) 3. (a) x x x 2 or 2 ; , 2 2, { } ( ) ( ) <− > −∞− ∪ ∞ (b) x x 2 2 ; 2, 2 { } [ ] − ≤ ≤ − 5. (a) x x 2 1 ; 2, 1 { } [ ] − ≤ ≤ − (b) x x x 2 or 1 ; , 2 1, { } ( ) ( ) <− > −∞ − ∪ ∞ 7. x x 2 5 ; 2, 5 { } ( ) − < < − 9. x x x 0 or 4 ; , 0 4, { } ( ) ( ) < > −∞ ∪ ∞ 11. x x 3 3 ; 3, 3 { } ( ) − < < − 13. x x x 4 or 3 ; , 4 3, { } ( ) ( ) <− > −∞ − ∪ ∞ 15. x x 1 2 3 ; 1 2 , 3 { } ( ) − < < − 17. No real solution 19. No real solution 21. { } ( ) ( ) <− > −∞ − ∪ ∞ x x x 2 3 or 3 2 ; , 2 3 3 2 , 23. (a) { } −1, 1 (b) { } −1 (c) { } −1, 4 (d) x x x 1 or 1 ; , 1 1, { } ( ) ( ) <− > −∞ − ∪ ∞ (e) x x 1 ; , 1 { } ( ] ≤− −∞ − (f) x x x 1 or 4 ; , 1 4, { } ( ) ( ) <− > −∞ − ∪ ∞ (g) { } ( ] [ ) ≤− ≥ −∞ − ∪ ∞ x x x 2 or 2 ; , 2 2, 25. (a) { } −1, 1 (b) { } − 1 4 (c) { } −4, 0 (d) x x 1 1 ; 1, 1 { } ( ) − < < − (e) x x 1 4 ; , 1 4 { } ( ≤− −∞ − ⎤ ⎦ ⎥ (f) x x 4 0 ; 4, 0 { } ( ) − < < − (g) { }0 27. (a) { } −2, 2 (b) { } −2, 2 (c) { } −2, 2 (d) x x x 2 or 2 ; , 2 2, { } ( ) ( ) <− > −∞ − ∪ ∞ (e) x x x 2 or 2 ; , 2 2, { } ( ] [ ) ≤− ≥ −∞ − ∪ ∞ (f) { } ( ) ( ) <− > −∞ − ∪ ∞ x x x 2 or 2 ; , 2 2, (g) x x x 5 or 5 ; , 5 5, { } ( ] [ ) ≤− ≥ −∞ − ∪ ∞ 29. (a) { } −1, 2 (b) { } −2, 1 (c) 0{ } (d) x x x 1 or 2 ; , 1 2, { } ( ) ( ) <− > −∞ − ∪ ∞ (e) x x 2 1 ; 2, 1 { } [ ] − ≤ ≤ − (f) x x 0 ; , 0 { } ( ) < −∞ (g) { } ≤ − ≥ + −∞ ⎛ − ⎝ ⎜⎜⎜ ⎤ ⎦ ⎥ ⎥ ∪ + ∞ ⎡ ⎣ ⎢ ⎢ ⎞ ⎠ ⎟⎟ ⎟ x x x 1 13 2 or 1 13 2 ; , 1 13 2 1 13 2 , 31. x x x 4 or 4 ; , 4 4, { } ( ] [ ) ≤− ≥ −∞ − ∪ ∞ 33. (a) 5 s (b) The ball is more than 96 ft above the ground for time t between 2 and 3 s, < < t 2 3. 35. (a) $0, $1000 (b) The revenue is more than $800,000 for prices between $276.39 and $723.61, < < p $276.39 $723.61. 37. (a) c c 0.112 81.907; 0.112,81.907 { } ( ) < < (b) It is possible to hit a target 75 km away if = c 0.651 or = c 1.536. 44. x x 5 { } ≤ 45. Odd
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