A ship is moving at a speed of 20 km/h parallel to a straight shoreline. The ship is 5 km from shore and 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.
B) Express d as a function of t, the time elapsed since noon;that is, fing g, so that d = g(t).
C) Find f o g. What does this functionrepresent?

(a) .

(b) The distance traveled by the ship since noon time is .

(c) . 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

We have

So,

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

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.