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Differential Calculus Solutions

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A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows in at the rate of 12 cu. ft. per min.

Solution:

$$Vol = A_{base} h$$

$$\frac{dVol}{dt} = (3)(10)\frac{dh}{dt}$$

$$12 = 30 \frac{dh}{dt}$$

$$\frac{dh}{dt} = 0.4 fpm$$

The surfaces rises at 0.4 feet per minute.