If a tank holds 3000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the volume \( V \) of water remaining in the tank after \( t \) minutes as:

\[ V = 3000 \left(1 - \frac{t}{40}\right)^2 \quad 0 \leq t \leq 40 \]

Find the rate at which the water is draining out of the tank after:

(a) 5 minutes
(b) 20 minutes
(c) 40 minutes

To find the rate at which water is draining out of the tank, we can use Torricelli's Law equation. We need to find the derivative of V with respect to t and substitute different values of t in the derivative equation.

Explanation:

To find the rate at which water is draining out of the tank after a certain amount of time, we can use Torricelli's Law. The volume of water remaining in the tank after t minutes can be calculated using the equation V = 3000(1 - t/40)2. (a) To find the rate at which water is draining out after 5 minutes, we need to find the derivative of V with respect to t and substitute t = 5 in the derivative equation. (b) To find the rate at which water is draining out after 20 minutes, we need to find the derivative of V with respect to t and substitute t = 20 in the derivative equation. (c) To find the rate at which water is draining out after 40 minutes, we need to find the derivative of V with respect to t and substitute t = 40 in the derivative equation.

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