Answer
(a) $s = f(d) = \sqrt{d^2+36}$
(b) $d = g(t) = 30t$
(c) $f \circ g = \sqrt{900t^2+36}$
This function represents the ship's distance from the lighthouse as a function of time.
Work Step by Step
(a) We can use the Pythagorean theorem to find the distance $s$ as a function of $d$:
$s = f(d) = \sqrt{d^2+(6)^2} = \sqrt{d^2+36}$
(b) We can use the ship's speed to find the distance $d$ as a function of time:
$d = g(t) = 30t$
(c) We can find $f\circ g$:
$f \circ g = \sqrt{(30t)^2+36} = \sqrt{900t^2+36}$
This function represents the ship's distance from the lighthouse as a function of time.
