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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.6, Problem 66E

(a)

To determine

The function *s* that shows the distance between the plane and the radar station as a function of the horizontal distance *d*.

Expert Solution

The value of the function *s* is

**Given:**

The speed of flying airplane is

The airplane is flying at an altitude of 1 mile.

The plane passes directly above the radar station at time

**Formula used:** Pythagoras Theorem for right angle triangle.

**Calculation:**

From the given information the airplane is flying at a speed of

Figure (1)

Since the function *s* that shows the distance between the plane and the radar station as a function of the horizontal distance *d*, therefore use the Pythagoras Theorem to find the function *s*.

Thus, the value of the function *s* is

(b)

To determine

The function *d* that shows the distance at time *t*.

Expert Solution

The value of the function *d* is

**Given:**

The speed of flying airplane is

**Calculation:**

Since the function *d* is the function that shows the distance at time *t*, therefore the function *d* is written as the product of speed of airplane and time *t* and the speed of airplane is

Thus, the value of the function *d* is

(c)

To determine

The function *s* as a function of *t* by composition of functions.

Expert Solution

The function *s* as a function of *t* is expressed as

**Given:**

From part (a), the value of function *s* is given below,

From part (b), the value of function *d* is given below,

**Calculation:**

The composite function

From equation (2), substitute

Substitute
*d* in equation (1), to find the value of

Substitute

The composite function
*s* as the function of time *t.*

Thus, the function *s* as a function of *t* is expressed as