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How fast is the area of the rectangle changing if one side is 10 cm long and it is...
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The dimensions of the rectangle, at the time t, are x and y cm.
We'll compute the area of the rectangle, at the time t:
A = x*y cm^2 (1)
We'll have to determine dA/dt if we want to know how fast the area of the rectangle is changing.
We'll differentiate (1) with respect to t:
dA/dt = [(dx/dt)*y + (dy/dt)*x] (2)
We know, from enunciation, that dx/dt = 2 and dy/dt = -3.
We'll replace the values into (2):
dA/dt = 2*8 + (-3)*10
dA/dt = 16 - 30
dA/dt = -14 cm^2/s
Since the value obtained for dA/dt is negative, it means that the area of the rectangle is decreasing at the rate of 14 cm^2/s.
Posted by giorgiana1976 on May 21, 2011 at 3:57 PM (Answer #1)
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