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2 March, 01:12

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 =

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  1. 2 March, 01:38
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    dS/dt ≈ 0.0343

    Step-by-step 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
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