Answer Key
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53 . a. N ( x ) =15 x b. i. N (20) = 15(20) = 300; therefore, the vehicle can travel 300 mi on a full tank of gas. Ii. N (15) =225; therefore, the vehicle can travel 225 mi on 3/4 of a tank of gas. c. Domain: 0≤ x ≤20; range: [0, 300] d. The driver had to stop at least once, given that it takes approximately 39 gal of gas to drive a total of 578 mi. 55 . a. A ( t ) = A ( r ( t )) = π · ⎛ ⎝ 6− 5 t 2 +1 ⎞ ⎠ 2 b. Exact: 121 π 4 ; approximately 95 cm 2 c. C ( t ) = C ⎛ ⎝ r ( t ) ⎞ ⎠ =2 π ⎛ ⎝ 6− 5 t 2 +1 ⎞ ⎠ d.
Exact: 11 π ; approximately 35 cm 57 . a. S ( x ) =8.5 x +750 b. $962.50, $1090, $1217.50 c. 77 skateboards
59 . a. −1 b. Decreasing 61 . a. 3/4 b. Increasing 63 . a. 4/3 b. Increasing 65 . a. 0 b. Horizontal 67 . y =−6 x +9 69 . y = 1 3 x +4 71 . y = 1 2 x 73 . y = 3 5 x −3 75 . a. ( m =2, b =−3) b.
77 . a. ( m =−6, b =0) b.
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