For an average​ person, the rate of change of weight W​ (in pounds) with respect to height h​ (in inches) is given approximately by the foll

Question

For an average​ person, the rate of change of weight W​ (in pounds) with respect to height h​ (in inches) is given approximately by the following formula.

dW/dh=0.0018h^2

Find​ W(h) if ​W(80​)equals=287.2 pounds. ​ Also, find the weight of a person who is 5​ feet, 8 inches tall.

W(h)=_______

A Person who is 5 feet, 8 inches tall weighs about _______ lbs

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Melody 2 weeks 2021-10-11T18:40:30+00:00 1 Answer 0

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    2021-10-11T18:41:38+00:00

    Answer:

    W(h)=0.0006h^3-20.

    A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.

    Step-by-step explanation:

    We know the rate of change of weight W​ (in pounds) with respect to height h​ (in inches)

    \frac{dW}{dh}=0.0018h^2

    This is a separable equation. A separable equation is a first-order differential equation in which the expression for \frac{dy}{dx} can be factored as a function of x times a function of y. In other words, it can be written in the form

    \frac{dy}{dx}=g(x)f(y)

    • To find W(h), we write the equation in terms of differentials and integrate both sides:

    \frac{dW}{dh}=0.0018h^2\\\\dW=(0.0018h^2)dh\\\\\int dW=\int (0.0018h^2)dh\\\\W=0.0006h^3+C

    To find the value of C, we use W(80​) = 287.2 lbs

    287.2=0.0006(80)^3+C\\0.0006\left(80\right)^3+C=287.2\\307.2+C=287.2\\307.2+C-307.2=287.2-307.2\\C=-20

    Thus,

    W(h)=0.0006h^3-20

    • To find the weight of a person who is 5​ feet, 8 inches tall you must:

    Convert the 5 feet into inches

    5 \:ft \:\frac{12 \:in}{1\:ft} = 60 \:in

    Add 60 in and 8 in, to find the total height of the person

    h = 68 in

    Substitute h = 68 in into W(h)=0.0006h^3-20 to find the weight:W(68)=0.0006(68)^3-20=168.7

    A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.

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