Answer
\begin{align}
V_{ave} \approx 247219
\end{align}
Work Step by Step
$\text{The function of the value of yacht is given by}$
\begin{align}
V(t) = 275 000\times \sqrt {\frac{20}{t+20}}
\end{align}
$\text{The average value in the first 10 years will be}$
\begin{align}
& V_{ave} = \frac{275000}{10} \int_0^{10} \sqrt {\frac{20}{t+20}} \ dt = 27500 \int_0^{10} \frac{2 \sqrt 5}{\sqrt {t+20}} \ dt
\end{align}
$\text{Apply u = $\sqrt {t+20}$ $\Rrightarrow$ 2du = $\frac{1}{\sqrt {t+20}}$ dt:}$
\begin{align}
V_{ave} = 55000 \sqrt 5 \int_{\sqrt 20}^{\sqrt 30} 2du = 110000 \sqrt 5 \times (\sqrt 30 - \sqrt 20) \approx 247219
\end{align}
