Matlab commands (with some prior working)

Question

I am not too sure how to input the next two questions into Matlab. Would anyone know how to do this?

Consider individuals for whom the Mosteller formula and the du Bois & du Bois formulae are both accurate.

Equation 1: Mosteller: sqrt hw/3600

Equation 2: du Bois and du Bois: 0:007184 h^0.725 w^0.425

1. Use the two formulae to get a formula for w as a function of h. Use Matlab to plot w for h between 0 and 200 cm.

2. Use the two formulae to get an expression for surface area as a function of h. Use Matlab to plot the surface area for h between 0 and 200 cm.

I'm not too sharp with Matlab just yet!

Answer 1

Here is some help for the first item. I am assuming that you are given

$$ A = \sqrt{ { hw \over \delta } } = \alpha h^{\beta} w^{\gamma} $$

and that you want to solve for $w$ in terms of $h$. Square both sides and rearrange to get $w$ by itself:

$$ hw = \delta \alpha^2 h^{2\beta} w^{2\gamma} \\ \Rightarrow w=\left( \delta \alpha^2 h^{2\beta-1} \right)^{ 1 \over {1-2\gamma}} $$

To plot this in matlab, try something like the following:

h = 0:1:200;
w = ( delta * alpha^2 * h.^(2*beta-1) ).^(1/(1-2*gamma));
plot( h, w );