Question

If a varies inversely as W^2, and z=20 when w=2, find z when w=3

Answer 1

Given:

z varies inversely as w²

so, we can write the following formula:

$z\propto\frac{1}{w^2}\rightarrow z=\frac{k}{w^2}$

Where (k) is the constant of proportionality

We will find the value of (k) using the given data:

when z = 20, w = 2

so,

$\begin{gathered} 20=\frac{k}{2^2} \\ \\ k=20\cdot2^2=20\cdot4=80 \end{gathered}$

So, the equation will be as follows:

$z=\frac{80}{w^2}$

We will find the value of (z) when w = 3

so, substitute with w = 3

$\begin{gathered} z=\frac{80}{3^2} \\ \\ z=\frac{80}{9} \end{gathered}$

So, the answer will be z = 80/9