If a cylindrical tank holds 100,000 gallons of water, which can be drained from

Question

If a cylindrical tank holds 100,000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as V(t)=100,000(1-1/60t)^2
a) find the rate at which the water is flowing out of the tank as a function t. use the limit defination for the derivative.
b) fill out the following table, including the units in the third column header.
time t in minutes (0,10,20,30,40,50,60)
amount of water in tank V(t) in gallons
flow rate V'(t)in
c) summarize the table above discussing when the flow rate is greatest and when it is least.

Explanation / Answer

he water in the tank in a certain time =100000-v(t) =t^2/3600 - t/30 dv/dt = t/1800 - 1/30 at 20 = -1/45

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