Answer
$\text{approximately }54.2 \text{ miles per hour}$
Work Step by Step
Substituting $x=280$ in the given function, $
S(x)=\sqrt{10.5x}
,$ results to
\begin{array}{l}\require{cancel}
S(x)=\sqrt{10.5(280)}
\\
S(x)=\sqrt{196\cdot15}
\\
S(x)=\sqrt{(14)^2\cdot15}
\\
S(x)=14\sqrt{15}
\\
S(x)\approx54.2
.\end{array}
Hence, the speed of the car, $S(x),$ is $
\text{approximately }54.2 \text{ miles per hour}
.$
