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g A water tank has a square base with each side of length 5 meters. Water enters through a hose at a constant rate of 20 liters per minute. At the same time a valve in the bottom is opening, so that after t minutes, water leaves at a rate of t liters per minute. If the tank starts out filled to a depth of 5 meters, after how many minutes will the tank be empty

Respuesta :

Answer:

221 minutes

Step-by-step explanation:

It's a known fact that

1 m³ = 1000 L

W(t) = 2*2*5 m^3 + 20t - t²/2

W(t) = 20 + 20t - t²/2, on differentiating, we have

-0.5² + 20t + 20000 = 0, and

t = [40 +- √161600] / 2

= 20 + 20√101 for t > 0

so t = 221 minutes

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