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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 56E

(a)

To determine

**To express:** The horizontal distance (in miles) covered by a plane as a function of time *t*.

Expert Solution

The function that represents the horizontal distance in terms of time *t* is

**Given:**

The plane is flying at a speed of 350 mi/h and at an altitude of one mile.

The plane passes the radar station at time

**Result used:**

**Calculation:**

Let the horizontal distance be *d*.

Substitute *t* for time and 350 for speed in the distance formula,

Thus, the function is *d*(*t*) is measured in miles.

Therefore, the horizontal distance covered by the plane after *t* hours is

(b)

To determine

**To express:** The distance (*s*) between the plane and radar station in terms of *d*.

Expert Solution

The function that represents the distance between the plane and radar station in terms of the distance *d* is

Let the horizontal distance be *d* in mi/hr.

It is given that the altitude is 1 mile.

Use the Pythagoras formula and obtain the value of *s* as follows.

Thus, the function is *s*(*d*) is measured in miles.

Therefore, the distance between the plane and radar station as a function of *d* is

(c)

To determine

**To find:** The expression for

Expert Solution

The value of

The composite function

From part (a), the value of

Thus,

Substitute *d* in

Thus, the required composition function,