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A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length at a rate of 3 cm/s. At what rate is the area of the rectangle increasing after 23 s?

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3 votes

Answer:

453 cm²/s

Explanation:

You want the rate of change in area of a rectangle initially 6 cm by 7 cm after 23 s when the side lengths are each increasing at 3 cm/s.

Rate of change

The area is given by ...

A = LW

Then the rate of change of area is ...

A' = L'W +LW'

Values

The length and width after 23 seconds are ...

L = 6 +3·23 = 75 . . . . cm

W = 7 +3·23 = 76 . . . cm

So, the rate of change of area is ...

L' = W' = 3 cm/s

A' = (3 cm/s)(76 cm) +(75 cm)(3 cm/s) = (151)(3) cm²/s = 453 cm²/s

The area of the rectangle is increasing at 453 cm²/s after 23 s.

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A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length-example-1
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