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The length x of a rectangle is decreasin...

The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When `x =10`cm and `y = 6`cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

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To solve the problem, we need to find the rates of change of the perimeter and the area of the rectangle given the rates of change of its length and width. ### Given: - The length \( x \) is decreasing at the rate of \( \frac{dx}{dt} = -3 \) cm/min (negative because it is decreasing). - The width \( y \) is increasing at the rate of \( \frac{dy}{dt} = 2 \) cm/min. - At the moment of interest, \( x = 10 \) cm and \( y = 6 \) cm. ### (a) Rate of change of the perimeter ...
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