Answer
a) $s(d) = \sqrt{d^2+1}$
b) $d(t)=350t$
c) $(s$ º $d)(t)=\sqrt {122500t^2+1}$
Work Step by Step
a) We'll use the Pythagorean theorem to find $s$: $c^2=a^2+b^2$, where $a$ is one of the legs, $b$ is the other leg, and $c$ is the hypotenuse:
$s^2=d^2+1^2$ square root both sides
$s= \sqrt{d^2+1}$ and that's our equation $s$ as a function of $d$
$s(d)= \sqrt{d^2+1}$
b) we'll use the formula $d=v \cdot t $, where $d$ is distance, $v$ is speed, and $t$ is time. We know that the speed is 350 miles per hour.
$d(t)=350t$ and that's our equation $d$ as a function of $t$
c) $(s$ º $d)(t)=s(d(t))=\sqrt{(350t)^2+1}=\sqrt{122500t^2+1}$
