Answer
a) $T$ = $\int_0^M{\frac{dx}{\sqrt {15f(x_{i})}}}$
b) $\approx$ $3.347$
Work Step by Step
a)
$s$ = $\sqrt {15f(x_{i})}$
we assume the speed s is constant over al small interval $Δx$ then the time to cover that interval at that speed is
$t_{i}$ = $\frac{distance}{speed}$ = $\frac{Δx}{\sqrt {15f(x_{i})}}$
$T$ = $\int_0^M{\frac{dx}{\sqrt {15f(x_{i})}}}$
b)
$x_{10}$ = $\frac{1}{3}·(100)[\frac{1}{\sqrt {15(13000)}}+\frac{4}{\sqrt {15(11500)}}+...+\frac{1}{\sqrt {15(2000)}}]$ $\approx$ $3.347$
