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**Continuous Functions - Setting up word problems**

## Homework Statement

Each side of a square is expanding at 5 cm/sec. What is the rate of change when the length of the sides are 10 cm.

## Homework Equations

[tex] A = ab [/tex]

## The Attempt at a Solution

[tex] a = 5t, b = 5t [/tex]

and the area is described as [tex] A = ab [/tex]

so the rate of change in the area should be

[tex] \frac {dA}{dt} = a \frac {db}{dt} + b \frac {da}{dt} [/tex]

then [tex] \frac {da}{dt} = 5 [/tex] and [tex] \frac {db}{dt} = 5 [/tex]

so [tex] \frac {dA}{dt} = 5a + 5b [/tex]

then at [tex] t = 2 [/tex]

[tex] \frac {dA}{dt} = 5 *10 + 5 *10 = 50 + 50 = 100 cm^{2}/sec [/tex]

So the area of the square is changing at a rate of 100 sq cm/sec when the sides are at 10 cm

is this correct?

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