A graphing calculator is required for the following problem. Gasoline is pumped into a cylindrical tank with a radius of 16 feet and a height of 6 feet. The tank has 750 cubic feet of gasoline at time t=0 hours. The rate at which gasoline is pumped into the tank is given by the function R, where R(t) = 1,000e 20 cubic feet per hour for 0 st ≤ 10. During the same time interval, gasoline is drained out from the tank at a rate of D(t) = -0.02t³ +2.4t² +0.16t cubic feet per hour. (Note: The volume V of a cylinder with radius r and height h is given by V=²h.) a) Determine the volume of gasoline pumped into the tank over the entire 10-hour interval. b) Describe all open intervals of t for which the volume of gasoline in the tank is increasing. Justify your answer. c) What is the maximum volume of gasoline in the tank over the interval 0 st≤ 10? Justify your answer.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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FRQ 2
A graphing calculator is required for the following problem.
Gasoline is pumped into a cylindrical tank with a radius of 16 feet and a height of 6 feet. The tank has 750
cubic feet of gasoline at time t = 0 hours. The rate at which gasoline is pumped into the tank is given by
12
the function R, where R(t) = 1,000e 20 cubic feet per hour for 0 sts 10. During the same time interval,
gasoline is drained out from the tank at a rate of D(t) = -0.02r° + 2.4t + 0.16t cubic feet per hour. (Note:
The volume V of a cylinder with radiusr and height h is given by V = ar'h.)
a) Determine the volume of gasoline pumped into the tank over the entire 10-hour interval.
b) Describe all open intervals of t for which the volume of gasoline in the tank is increasing. Justify
your answer.
c) What is the maximum volume of gasoline in the tank over the interval 0 sts 10? Justify your
answer.
d) How fast is the gasoline level in the tank rising at time t = 4 hours? Justify your answer.
Transcribed Image Text:FRQ 2 A graphing calculator is required for the following problem. Gasoline is pumped into a cylindrical tank with a radius of 16 feet and a height of 6 feet. The tank has 750 cubic feet of gasoline at time t = 0 hours. The rate at which gasoline is pumped into the tank is given by 12 the function R, where R(t) = 1,000e 20 cubic feet per hour for 0 sts 10. During the same time interval, gasoline is drained out from the tank at a rate of D(t) = -0.02r° + 2.4t + 0.16t cubic feet per hour. (Note: The volume V of a cylinder with radiusr and height h is given by V = ar'h.) a) Determine the volume of gasoline pumped into the tank over the entire 10-hour interval. b) Describe all open intervals of t for which the volume of gasoline in the tank is increasing. Justify your answer. c) What is the maximum volume of gasoline in the tank over the interval 0 sts 10? Justify your answer. d) How fast is the gasoline level in the tank rising at time t = 4 hours? Justify your answer.
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