Question

Can I help with this problem. If z varies inversely as w^2 and z = 10 when w = 2. Find z when w = 6

Answer 1

First, we need the find the value of the constant k:

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

Then, we use the given values to find k. Therefore:

z = 10 when w = 2

$10=\frac{k}{2^2}$

And solve for k:

$\begin{gathered} 10=\frac{k}{4} \\ 10\cdot4=4\cdot\frac{k}{4} \\ k=40 \end{gathered}$

Now, when w = 6, z will be:

$z=\frac{k}{w^2}=\frac{40}{6^2}=\frac{40}{36}=\frac{10}{9}$

Answer:

$z=\frac{10}{9}$