Answer
(a) Respectively: $28.14 \space mi$ and $39.8 \space mi$
(b) 41.27 mi
(c) 235.56 mi
(d) 194.29 mi
Work Step by Step
(a) Substitute the values for $h$ into the function and use a calculator to find $D(h)$ in each case. Remember: $(r = 3960)$
$$D(0.1) = \sqrt {2r(0.1) + (0.1)^2}= 28.14$$
$$D(0.2) = \sqrt {2r(0.2) + (0.2)^2}= 39.8$$
(b) $1 \space mi = 5280 \space ft$
$h = 1135 \space ft \times \frac{1 \space mi}{5280 \space ft} = 0.215 \space mi$
$$D(0.215) = \sqrt {2r(0.215) + (0.215)^2}= 41.27$$
(c)
$$D(7) = \sqrt {2r(7) + (7)^2}= 235.56$$
(d)
$D(7) - D(0.215) = 235.56 - 41.27 = 194.29$
