Answer
a) $ 0.0035 $
b) $ 54.6875 \ \mathrm{ohms} $
Work Step by Step
a) We will plug in $ x=0.005 $ and $ R=140 $:
$$ \begin{align*}
\displaystyle R& = \frac{k}{x^2} \\\\
140& = \frac{k}{(0.005)^2} \\\\
k& =140(0.005)^2 \\\\
k& = 0.0035\\\\
\end{align*} $$
b) We'll use $ x=0.008 $ and $ k=0.0035 $ to find $ R $:
$$ \begin{align*}
\displaystyle R& = \frac{k}{x^2} \\\\
& = \frac{0.0035}{(0.008)^2} \\\\
& =54.6875 \\\\
\end{align*} $$
