Question 118621
A square sheet of Aluminum is placed in the hot sun. It begins to expand very slowly so that its diagonal is increasing at the rate of 1 milimeter per minute. At the moment that the diagonal is 100 milimeters, at what rate is the area increasing?
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Let each side of the square sheet be x.
Let the diagonal be D.
Then D = (sqrt2)x
Then dD/dt = (sqrt2)dx/dt
Since dD/dt = 1ml/min
So, 1ml/min = (sqrt2)dx/dt
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Area = x^2
But x = D/sqrt2
So, x^2 = D^2/2
Therefore Area = (1/2)D^2
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dA/dt = (1/2)(2D)dD/dt
dA/dt = D(dD/dt)
dA/dt = 100 ml (sqrt2(ml/min))
dA/dt = 100sqrt2(ml^2/min)
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Cheers,
Stan H.