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A stone is dropped into a lake creating a circular ripple that travels outward at a speed of 70 cms Find the rate at which the area within the circle is increasing after 7 seconds?
Wiki User
∙ 13y ago
The area of a circle is A=πR2 , as a function of time (in seconds) it is A(t)=π(Rt)2
Find the derivative of the area with respect to the radius
dA/dR=A'(t)=2πRt
So the rate the area is increasing at 7s is given by
A'(7)=2π(70X7)=980π cm/s2 or 3078.76 cm/s2
Wiki User
∙ 13y ago
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