if Z varies inversely as w, and Z = 10 when w= .5 find Z when w= 8

Let's form an equation with a constant A

Z \propto \frac{1}{w}

therefore Z = \frac{A}{w}

Where A is a constant

Now you can use your values for w and Z to find A, then you can use A and the new w to find the new Z using the same formula above.

Good luck!

I agree with capuchin and would like to applaud the use of \propto. We're getting some major LaTeX practice around here lately!