Answer
a) $1 ft$; $ 10.173 ft$; and $13 ft$
b) $ 9.667 ft$
Work Step by Step
a) Here, $H(t)=\sqrt {t+1}+5t^{1/3}$
Now, $H(0)=1 ft$; $T(4)=\sqrt 5+5 \sqrt [3] 4 \approx 10.173 ft$; and $T(8)=3+10=13 ft$
b) Consider the integral:
$\dfrac{1}{8}\int_{0}^{8} \sqrt {t+1}+5t^{1/3} dt=\dfrac{1}{8} (18+60-\dfrac{2}{3}-0)\approx 9.667 ft$
