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The sides of a square increase in length at a rate of 2 m/s. At what rate is the area of the square changing when the sides are 10 m long?

User Elvie
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when the sides of the square are 10 m long, the area of square is changing at a rate of 40 m^2/s.

Let's denote the length of the sides of the square as "s" and the area as "A". The formula for the area of a square is A = s^2.

To find the rate at which the area is changing, we need to find dA/dt, the when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s. when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s.with respect to time.

Since the side bbs of the square are increasing at a rate of 2 m/s, we have ds/dt = 2 m/s.

Now, let's differentiate the area formula with respect to time:

dA/dt = d/dt (s^2)

Using the power rule for differentiation, we get:

dA/dt = 2s * ds/dt

Substituting the given values, we have:

dA/dt = 2 * 10 * 2

dA/dt = 40 m^2/s

Therefore, when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s.

User Erszcz
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