The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

Given :

The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 3 cm/s.

When the length is 7 cm and the width is 4 cm .

To find :-

how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

A = lb

To find the rate :-

d(A)/dt = d(lb)/dt .

Differenciate :-

dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

dA/dt = 9*4 + 7*3

dA/dt = 36 + 21 cm²/s

dA/dt = 57 cm²/s

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step-by-step explanation:

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b. x- 48 =120

step-by-step explanation: