If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w circle r) (x)?
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The balloon has a volume dependent on its radius
:
Differentiating with respect to time gives
If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of
The surface area of the balloon is
and differentiating gives
so that at the moment the radius is 3 m, its area is increasing at a rate of