The side length of a square is decreasing at a rate of 2 kilometers per hour.At a certain instant, the side length is 9 kilometers.What is the rate of change of the area of the square at that instant (in square kilometers per hour)?Choose 1 answer:(A) −324(B) −4(C) −36(D) −81
Q. The side length of a square is decreasing at a rate of 2 kilometers per hour.At a certain instant, the side length is 9 kilometers.What is the rate of change of the area of the square at that instant (in square kilometers per hour)?Choose 1 answer:(A) −324(B) −4(C) −36(D) −81
Square Area Formula: The area of a square is given by the formula A=s2, where s is the side length.
Side Length Rate: If the side length s is decreasing at a rate of 2 km/h, we can represent this as dtds=−2 km/h, where dtds is the rate of change of the side length with respect to time.
Rate of Area Change: To find the rate of change of the area dtdA, we use the chain rule: dtdA=2s⋅dtds.
Calculation: Substitute s=9 km and dtds=−2 km/h into the equation: dtdA=2×9×(−2)=−36 km2/h.
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