Answer
(a) See prove below.
(b) minimum $E\approx169$ kcal when $x\approx5.1$ miles
Work Step by Step
(a) For the right triangle $\Delta ABC$, use Pythagorean Theorem, we have $\bar {AC}=\sqrt {x^2+5^2}$, thus
the total energy required is given by $E(x)=14\times\bar {AC}+10\times\bar {CD}=14\sqrt {x^2+25}+10(12-x)$
(b) Graph the above function as shown in the figure. A minimum can be found as $E=168.99\approx169$ kcal
when $x=5.103\approx5.1$ miles
