Question

Write a function that models a combined variation situation with two independent variables. Let one of the variables have a direct variation with the dependent variable, and the other one have an inverse

Answer 1

We can approach this problem in the following way:
1) We construct a variation equation for each variation
2) We combine these two
First variation equation would be:
$y=k_1x$
This is a direct variation equation.
Second variation equation is:
$g= \frac{k_2}{z}$
This is a inverse variation equation.
We combine these two by multiplying them. This will give us our final function.
Let us call it f(x,z).
$f(x,z)=y(x)g(z)= \frac{k_1k_2x}{z}$
Since $k_1$ and $k_2$ are only constants we can just combine them and call their product k.
Our final function would be:
$f(x,z)=\frac{kx}{z}$