# the distance between the two numbers 2 and 17 .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 73E

a)

To determine

## To find: the distance between the two numbers 2 and 17 .

Expert Solution

The distance between the two numbers is 15 .

### Explanation of Solution

Given information:

Two numbers are given as

2 and 17

Formula used:

Distance between two numbers a and b is given by

d(a,b)=|ab|=|ba|=d(b,a)

Absolute value property:

For any real number a,

|a|=a0|a|=|a|=a

Calculation:

Two numbers is 2 and 17 .

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|217|=|15|

Now, compare the distance with |a| :

|a|=|15|a=15

Now, by absolute value property:

|a|=a0

Therefore, |15|=15

Hence, distance between the numbers is 15 units.

b)

To determine

### To find: the distance between the two numbers −3 and 21 .

Expert Solution

The distance between the two numbers is 24 .

### Explanation of Solution

Given information:

Two numbers are given as

3 and 21

Formula used:

Distance between two numbers a and b is given by

d(a,b)=|ab|=|ba|=d(b,a)

Absolute value property:

For any real number a,

|a|=a0|a|=|a|=a

Calculation:

Two numbers is 3 and 21 .

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|321|=|24|

Now, compare the distance with |a| :

|a|=|24|a=24

Now, by absolute value property:

|a|=a0

Therefore, |24|=24

Hence, distance between the numbers is 24 units.

c)

To determine

### To find: the distance between the two numbers 118 and −310 .

Expert Solution

The distance between the two numbers is 6740 .

### Explanation of Solution

Given information:

Two numbers are given as

118 and 310

Formula used:

Distance between two numbers a and b is given by

d(a,b)=|ab|=|ba|=d(b,a)

Absolute value property:

For any real number a,

|a|=a0|a|=|a|=a

Calculation:

Two numbers is 118 and 310 .

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|118(310)|=|118+310|=|55+1240|=|6740|

Now, compare the distance with |a| :

|a|=|6740|a=6740

Now, by absolute value property:

|a|=a0

Therefore, |6740|=6740

Hence, distance between the numbers is 6740 units.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!