-12 ft- 0 2 46 8 10 12 3. 4 ft P(t) 46 53 57 60 62 63 3. The figure above shows an aboveground swimming pool in the shape of a cylinder with a radius of 12 feet and a height of 4 feet. The pool contains 1000 cubic feet of water at time t = 0. During the time interval 0

Algebra & Trigonometry with Analytic Geometry
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Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
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-12 ft-
2
4
6 | 8 | 10 12
t
3.
4 ft
P(t)| 0
46 | 53 | 57 60 | 62
63
3. The figure above shows an aboveground swimming pool in the shape of a cylinder with a radius of 12 feet and a
height of 4 feet. The pool contains 1000 cubic feet of water at time t = 0. During the time interval 0 < t < 12
hours, water is pumped into the pool at the rate P(t) cubic feet per hour. The table above gives values of P(t)
for selected values of t. During the same time interval, water is leaking from the pool at the rate R(t) cubic feet
per hour, where R(t) = 25e 0051. (Note: The volume V of a cylinder with radius r and height h is given by
V = ar²h.)
(a) Use a midpoint Riemann sum with three subintervals of equal length to approximate the total amount of
water that was pumped into the pool during the time interval 0 <t < 12 hours. Show the computations that
lead to your answer.
(b) Calculate the total amount of water that leaked out of the pool during the time interval 0 <t < 12 hours.
(c) Use the results from parts (a) and (b) to approximate the volume of water in the pool at time t = 12 hours.
Round your answer to the nearest cubic foot.
Transcribed Image Text:-12 ft- 2 4 6 | 8 | 10 12 t 3. 4 ft P(t)| 0 46 | 53 | 57 60 | 62 63 3. The figure above shows an aboveground swimming pool in the shape of a cylinder with a radius of 12 feet and a height of 4 feet. The pool contains 1000 cubic feet of water at time t = 0. During the time interval 0 < t < 12 hours, water is pumped into the pool at the rate P(t) cubic feet per hour. The table above gives values of P(t) for selected values of t. During the same time interval, water is leaking from the pool at the rate R(t) cubic feet per hour, where R(t) = 25e 0051. (Note: The volume V of a cylinder with radius r and height h is given by V = ar²h.) (a) Use a midpoint Riemann sum with three subintervals of equal length to approximate the total amount of water that was pumped into the pool during the time interval 0 <t < 12 hours. Show the computations that lead to your answer. (b) Calculate the total amount of water that leaked out of the pool during the time interval 0 <t < 12 hours. (c) Use the results from parts (a) and (b) to approximate the volume of water in the pool at time t = 12 hours. Round your answer to the nearest cubic foot.
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