Answer
(a) $d = 350t$
(b) $s= \sqrt{1+d^2}$
(c) $s= \sqrt{1+122500t^2}$
Work Step by Step
(a) Since speed is distance over time, we know that:
$350 = \frac{d}{t}$
Which can be rearranged to:
$d = 350t$
(b) The 1 mile between the plane and the radar station at $t=0$ and distance $d$ are two sides that form a triangle, where $s$ is the hypotenuse. Thus, using the Pythagorean theorem:
$s^2=1^2 + d^2$
$s = \sqrt{1 + d^2}$
(c) $s$ can be expressed as a function of $t$ by inputting the equation in (a) into the equation in (s), as follows:
$s = \sqrt{1 + (350t)^2}$
$s= \sqrt{1+122500t^2}$
