Answer
$149$ million kilometers.
Work Step by Step
The given function is
$\Rightarrow f(x)=0.2x^{\frac{3}{2}}$
$f(x)=365$.
Substitute into the given function.
$\Rightarrow 365=0.2x^{\frac{3}{2}}$
Divide both sides by $0.2$.
$\Rightarrow \frac{365}{0.2}=\frac{0.2x^{\frac{3}{2}}}{0.2}$
Simplify.
$\Rightarrow 1825=x^{\frac{3}{2}}$
$\Rightarrow (18250)^{\frac{2}{3}}=[x^{\frac{3}{2}}]^{\frac{2}{3}}$
Simplify.
$\Rightarrow 149.34=x$
$149$.
