BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

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

Answer to Problem 55E

The distance between the light house and the ship as of function d is, s=d2+36 .

Explanation of Solution

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.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.3, Problem 55E

Consider the right triangle from Figure 1.

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

s2=d2+62s=d2+36s=f(d)=d2+36

Therefore, the distance between the light house and the ship as a function d is, s=d2+36 .

(b)

To determine

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

Expert Solution

Answer to Problem 55E

The function d as a function of t is, d=30t .

Explanation of Solution

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, d=30t .

(c)

To determine

To find: The composition function fg and explain.

Expert Solution

Answer to Problem 55E

The composition function fg=625t2+1 and this function represents the distance between the light house and the ship since noon.

Explanation of Solution

From part(a), s=f(d)=d2+36 and from part b, g(t)=d=30t .

The composition function is, fg=f(g(t)) .

Then f(g(t))=g(t)2+36

Substitute g(t) and find the value of the composition function.

f(30t)=(30t)2+36=900t2+36=36×25t2+36=625t2+1

Therefore, the composition function is, fg=625t2+1 and it represents the distance between the light house and the ship in terms of the elapsed time since noon.

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