Question

The speed S of blood that is r centimeters from the center of an artery is given below, where C is a constant, R is the radius of the artery, and S is measured in centimeters per second. Suppose a drug is administered and the artery begins to dilate at a rate of dR/dt. At a constant distance r, find the rate at which S changes with respect to t for C = 1.54 105, R = 1.3 10-2, and dR/dt = 1.0 10-5.

S = C(R^2 − r^2)

dS/dt =______cm/s

Answer 1

dS/dt = C[ 2R*dR/dt] =1.76*10^5[2*1.2*10^-2*10^-5] = 0.04224 round to 0.042
note since r is a constant its derivative is zero.