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The area of a circular sun spot is growing at a rate of 1,400 km^2/s. . (a) How fast is the radius growing at the instant when it equals 8,000 km?. (b) How fast is the radius growing at the instant when the sun spot has an area of 640,000 km^2?

Verified Answer :

In solving a, we must get the formula needed then substitute
the given so we have

A=πr2

dA/dt=1,400 km2/s

then solve for dA/dt

1400 km2/s=2π(8000 km)dr/dt

drdt≈0.028 km/s

In solving b,
its just the same as solving the letter a, the only difference is that the
radius is not given so we get the formula for A, then substitute

640,000 k=πr2⟹r≈451.352 km

Then solve for
dAdt

1,400 km2/s=2π(451.352 km)drdt⟹drdt≈0.494 km/s

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