9 The curve \(C\) has parametric equations
$$x = 4 t + 2 t ^ { \frac { 3 } { 2 } } , \quad y = 4 t - 2 t ^ { \frac { 3 } { 2 } } , \quad \text { for } 0 \leqslant t \leqslant 4$$
Find the arc length of \(C\), giving your answer correct to 3 significant figures.
Find the mean value of \(y\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant 32\).
9 The curve $C$ has parametric equations
$$x = 4 t + 2 t ^ { \frac { 3 } { 2 } } , \quad y = 4 t - 2 t ^ { \frac { 3 } { 2 } } , \quad \text { for } 0 \leqslant t \leqslant 4$$
Find the arc length of $C$, giving your answer correct to 3 significant figures.
Find the mean value of $y$ with respect to $x$ over the interval $0 \leqslant x \leqslant 32$.
\hfill \mbox{\textit{CAIE FP1 2015 Q9}}