582
Chapter 5 | Integration
252. [T] The number of hamburgers sold at a restaurant throughout the day is given in the following table, with the accompanying graph plotting the best cubic fit to the data, b ( t ) =0.12 t 3 −2.13 t 3 +12.13 t +3.91, with t =0 corresponding to 9 a.m. and t =12 corresponding to 9 p.m. Compute the average value of b ( t ) to estimate the average number of hamburgers sold per hour. Hours Past Midnight No. of Burgers Sold
Time (sec)
Acceleration (mph/sec)
1
11.2
2
10.6
3
8.1
9
3
4
5.4
12
28
5
0
15
20
249. [T] The accompanying graph plots the best quadratic fit, a ( t ) =−0.70 t 2 +1.44 t +10.44, to the data from the preceding table. Compute the average value of a ( t ) to estimate the average acceleration between t =0 and t =5.
18
30
21
45
250. [T] Using your acceleration equation from the previous exercise, find the corresponding velocity equation. Assuming the final velocity is 0 mph, find the velocity at time t =0. 251. [T] Using your velocity equation from the previous exercise, find the corresponding distance equation, assuming your initial distance is 0 mi. How far did you travel while you accelerated your car? ( Hint: You will need to convert time units.)
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