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4. If water is being drained from a swimming pool and V liters is the volume of the water at the time t minutes after the draining starts, where � = 250 1600 − 80� + � 2 , how fast is the water flowing out of the water pool 5 minutes after the draining starts?

Respuesta :

MrRoyal

Answer:

Water is leaving at 17500m^3 per minute

Step-by-step explanation:

Given

[tex]V(t)= 250(1600 - 80t + t^2)[/tex]

Required

The rate when time is 5 minutes

We have:

[tex]V(t)= 250(1600 - 80t + t^2)[/tex]

Open bracket

[tex]V(t)= 400000 - 20000t + 250t^2[/tex]

Differentiate

[tex]V'(t) = 0 - 20000 + 2*250t[/tex]

[tex]V'(t) = 0 - 20000 + 500t[/tex]

[tex]V'(t) = -20000 + 500t[/tex]

At 5 minutes, we have:

[tex]V'(5) = -20000 + 500*5[/tex]

[tex]V'(5) = -20000 + 2500[/tex]

[tex]V'(5) = -17500[/tex]

This means that water is leaving at 17500m^3 per minute

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