Answer
$z=\dfrac{1}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use $
z=\dfrac{k}{w}
$ and solve for the value of $k$ with the given $
z
$ and $
w
$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $z$ varies inversely as $w,$ then $
z=\dfrac{k}{w}
.$ Substituting the given values, $
z=10
$ and $
w=\dfrac{1}{2}
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
10=\dfrac{k}{\dfrac{1}{2}}
\\\\
10=k\div\dfrac{1}{2}
\\\\
10=k\cdot2
\\\\
\dfrac{10}{2}=k
\\\\
k=5
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
z=\dfrac{k}{w}
\\\\
z=\dfrac{5}{w}
.\end{array}
If $w=10,$ then
\begin{array}{l}\require{cancel}
z=\dfrac{5}{w}
\\\\
z=\dfrac{5}{10}
\\\\
z=\dfrac{1}{2}
.\end{array}
