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On the sample problem it asks.... - If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. V = 6000(1 - t/50)^2 where 0<= t<= 50 Then it says - Find the rate at which water is draining from the tank after the following amount of time. after 5 min.

Guest Feb 20, 2017
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On the sample problem it asks.... - If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. V = 6000(1 - t/50)^2 where 0<= t<= 50 Then it says - Find the rate at which water is draining from the tank after the following amount of time. after 5 min.

 

\(V = 6000(1 -\frac{ t}{50})^2\\ \frac{dV}{dt}=12000(1-\frac{t}{50})^1*\frac{-1}{50}\\ \frac{dV}{dt}=-240(1-\frac{t}{50})\\ When \;\;t=5\\ \frac{dV}{dt}=-240(1-\frac{5}{50})\\ \frac{dV}{dt}=-240(1-\frac{1}{10})\\ \frac{dV}{dt}=-240*0.9\\ \frac{dV}{dt}=-216 \)

 

So after 5 minutes the water is draining at an instantaneous rate of   216 gallons/minute

Melody  Feb 20, 2017

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