rates of change, derivatives how fast is the side of the square shrinking when the length, of the side is 2m and the area is deacreasing at 0.25 m^2/s?  

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embizze | High School Teacher | (Level 1) Educator Emeritus

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We are asked to find the rate at which the side of a square is decreasing at the time when the side length x=2m and where the area is decreasing at the rate of .25 square meters per second.

We have x=2 and `(dA)/(dt)=-.25` and we are asked to find `(dx)/(dt)` .

We know that `A=x^2` . Taking the derivative with respect to t we get:

`(dA)/(dt)=2x(dx)/(dt)` Substituting the known values we get:

`-.25=2(2)(dx)/(dt)` Solving for `(dx)/(dt)` we get:

`(dx)/(dt)=-1/16`

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The side of the square is changing at a rate of `-1/16` meters per second.

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