# To express: The horizontal distance (in miles) covered by a plane as a function of time t . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

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

#### Solutions

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 d(t)=350t.

### Explanation of Solution

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 t=0.

Result used:

Distance= Time × Speed

Calculation:

Let the horizontal distance be d.

Substitute t for time and 350 for speed in the distance formula, d(t)=350t.

Thus, the function is d(t)=350t where d(t) is measured in miles.

Therefore, the horizontal distance covered by the plane after t hours is d(t)=350t.

(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 s(d)=1+d2.

### Explanation of Solution

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.

s2=12+d2s2=12+d2s=12+d2

Thus, the function is s(d)=1+d2 where s(d) is measured in miles.

Therefore, the distance between the plane and radar station as a function of d is s(d)=1+d2.

(c)

To determine

### To find: The expression for (s∘d)(t).

Expert Solution

The value of (sd)(t)=1+122500t2.

### Explanation of Solution

The composite function (sd)(t) is defined as (sd)(t)=s(d(t)).

From part (a), the value of d(t)=350t.

Thus, (sd)(t)=s(350t)

Substitute 350t for d in s(d)=1+d2,

s(350t)=1+(350t2)=1+122500t2

Thus, the required composition function, (sd)(t)=1+122500t2.

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