Asked by Anonymous
The radius of a sector of a circle is increasing at a rate of 3 cm/sec while the area is decreasing at a rate of 1 cm2/sec. At what rate is the angle of the sector changing when the area is 20 cm2 and the radius os 5cm?
Answers
Answered by
Steve
Huh? How is this even possible? Anyway, just use the product rule to get
a = 1/2 r^2 θ
da/dt = 1/2 * 2rθ dr/dt + 1/2 r^2 dθ/dt
So, now all you ave to do is find θ when a=20 and r=5
Then plug that in to solve for dθ/dt
a = 1/2 r^2 θ
da/dt = 1/2 * 2rθ dr/dt + 1/2 r^2 dθ/dt
So, now all you ave to do is find θ when a=20 and r=5
Then plug that in to solve for dθ/dt
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