Respuesta :
Answer:
[tex]W(h)=0.0006h^3-20[/tex].
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)
[tex]\frac{dW}{dh}=0.0018h^2[/tex]
This is a separable equation. A separable equation is a first-order differential equation in which the expression for [tex]\frac{dy}{dx}[/tex] can be factored as a function of x times a function of y. In other words, it can be written in the form
[tex]\frac{dy}{dx}=g(x)f(y)[/tex]
- To find W(h), we write the equation in terms of differentials and integrate both sides:
[tex]\frac{dW}{dh}=0.0018h^2\\\\dW=(0.0018h^2)dh\\\\\int dW=\int (0.0018h^2)dh\\\\W=0.0006h^3+C[/tex]
To find the value of C, we use W(80) = 287.2 lbs
[tex]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[/tex]
Thus,
[tex]W(h)=0.0006h^3-20[/tex]
- To find the weight of a person who is 5 feet, 8 inches tall you must:
Convert the 5 feet into inches
[tex]5 \:ft \:\frac{12 \:in}{1\:ft} = 60 \:in[/tex]
Add 60 in and 8 in, to find the total height of the person
h = 68 in
Substitute h = 68 in into [tex]W(h)=0.0006h^3-20[/tex] to find the weight:[tex]W(68)=0.0006(68)^3-20=168.7[/tex]
A Person who is 5 feet, 8 inches tall weighs about 168.7 lbs.
