007A Sample Final 2, Problem 5

The velocity  $V$  of the blood flow of a skier is modeled by

$V=375(R^{2}-r^{2})$

where  $R$  is the radius of the blood vessel,  $r$  is the distance of the blood flow from the center of the vessel and is a constant. Suppose the skier's blood vessel has radius  $R=0.08$  mm and that cold weather is causing the vessel to contract at a rate of  ${\frac {dR}{dt}}=-0.01$  mm per minute. How fast is the velocity of the blood changing?

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