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

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) This is a separable equation. A separable equation is a first-order differential equation in which the expression for can be factored as a function of x times a function of y. In other words, it can be written in the form • To find W(h), we write the equation in terms of differentials and integrate both sides: To find the value of C, we use W(80​) = 287.2 lbs Thus, • To find the weight of a person who is 5​ feet, 8 inches tall you must:

Convert the 5 feet into inches Add 60 in and 8 in, to find the total height of the person

h = 68 in

Substitute h = 68 in into to find the weight: A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.