+0

# If a tank holds 6000 gallons of water, which drains from the bottom

0
689
1

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
Sort:

#1
+90590
0

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

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details