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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 55E

(a)

To determine

**To express:** The distance between the lighthouse and the ship as a function of *d*.

Expert Solution

The distance between the light house and the ship as of function *d* is,

**Given:**

The speed of the ship is 30 km/h.

The distance between the ship and shore is 6 km.

**Diagram:**

Draw a rough diagram to indicate the positions of the ship, lighthouse and shore as shown below in Figure 1.

Consider the right triangle from Figure 1.

In order to find the distance *s*, use Pythogorean theorem.

Therefore, the distance between the light house and the ship as a function *d* is,

(b)

To determine

**To express:** The function *d* as a function of *t* where t is the time elapsed since noon.

Expert Solution

The function *d* as a function of *t* is,

**Given:**

The speed of the ship is 30 km/h.

*d* is the distance in terms of kilometer and *t* is the time in hours.

Distance travelled is the product of speed and time.

Thus, the required function is,

(c)

To determine

**To find:** The composition function

Expert Solution

The composition function

From part(a),

The composition function is,

Then

Substitute

Therefore, the composition function is,