## Calculus: Early Transcendentals 8th Edition

(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.
(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.