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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?

Respuesta :

isaacoranseola

Answer:

57 cm^2/s

Step-by-step explanation:

The area of a rectangle is the length times the width of the rectangle

A =lw

Where l is the length while w is the width of the rectangle respectively

This equation can be found by taking the derivative of the previous equation

dA/dt = dl/dt.w + l.dw/dt

Given that the length = 7cm and the width = 4cm

The increasing rate for the length = 9cm/s while the increasing rate for the width is = 3cm/s

We can solve for the unknown variable by using the given numbers.

dA/dt = 9(4 )+ 7(3)

= 36 + 21

= 57 cm^2/s

VirαtKσhli

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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