Question

ship is traveling at 20 mi/h parallel to a straight shoreline. The ship is 5 mi from shore. It passes a lighthouse at noon. (a) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon; that is, find f so that s = f(d) . (b) Express d as a function of t, the time elapsed since noon; that is, find g so that d = g(t ) . (c) Find f ⁰ g. What does this function represent?

Answer 1

Answer:

It represents the distance between the lighthouse and the ship as a function of the time elapsed since noon.

Step-by-step explanation:

(a) To find the distance between the lighthouse and the ship as a function of , the distance the ship has traveled since noon you must:

Observe the below figure.

From the Pythagorean theorem,

(b) The relation between distance, speed, and time is, . Therefore, we have

.

We know that the ship is moving at a speed of 20 km/h.

is the distance as a function of time.

So, the distance traveled by the ship since noon time is

(c) Given two functions and , the composite function is defined by ------