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 a 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 = 1.32 times 10^5, R = 1.3 times 10^-2, and dR/dt = 1.0 times 10^-5. (Round your answer to 4 decimal places.) S = C(R^2 - r^2) dS/dt =

Answer 1

dS/dt ≈ 0.0343

Explanation:

We are given;

C = 1.32 x 10^(5)

R = 1.3 x 10^(-2)

dR/dt = 1.0 x 10^(-5)

The function is: S = C(R² - r²)

We want to find dS/dt when r is constant.

Thus, let's differentiate since we have dR/dt;

dS/dR = 2CR

So, dS = 2CR.dR

Let's accommodate dt. Thus, divide both sides by dt to obtain;

dS/dt = 2CR•dR/dt

Plugging in the relevant values to get;

dS/dt = 2(1.32 x 10^(5))x 1.3 x 10^(-2) x 1.0 x 10^(-5)

dS/dt = 3.432 x 10^(-2)

dS/dt ≈ 0.0343