Answer
$2310$ RPMs.
Work Step by Step
The equation modeling the speed of the boat is:
$$s(x)=0.00547x^3-0.225x^2+3.62x-11.\tag1$$
Substitute $s(x)=20$ in Eq. $(1)$:
$$\begin{align*}
20&=0.00547x^3-0.225x^2+3.62x-11\\
0&=0.00547x^3-0.225x^2+3.62x-31.\tag2
\end{align*}$$
Use a graphing calculator to approximate the real zeros of the function from Eq. $(2)$:
$$f(x)=0.00547x^3-0.225x^2+3.62x-31.$$
From the graph we notice that there is one real zero: $x\approx 23.1$.
So the tachometer reading is about $2310$ RPMs.
