# the distance between the two numbers 7 15 and − 1 21 . ### 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 74E

a)

To determine

## To find: the distance between the two numbers 715 and −121 .

Expert Solution

The distance between the two numbers is 15 .

### Explanation of Solution

Given information:

Two numbers are given as

715 and 121 .

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 715 and 121 .

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|715(121)|=|715+121|=|49+5105|=|54105|

Now, compare the distancewith |a| :

|a|=|54105|a=54105

Now, by absolute value property:

|a|=a0

Therefore, |54105|=54105

Hence, distance between the numbers is 54105 units.

b)

To determine

### To find: the distance between the two numbers −38 and −57 .

Expert Solution

The distance between the two numbers is 21 .

### Explanation of Solution

Given information:

Two numbers are given as

38 and 57

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 38 and 57

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|38(57)|=|38+57|=|21|

Now, compare the distance with |a| :

|a|=|21|a=21

Now, by absolute value property:

|a|=a0

Therefore, |21|=21

Hence, distance between the numbers is 21 units.

c)

To determine

### To find: the distance between the two numbers −2.6 and −1.8 .

Expert Solution

The distance between the two numbers is 44 .

### Explanation of Solution

Given information:

Two numbers are given as

2.6 and 1.8

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 2.6 and 1.8 .

Distance between the numbers can be calculated as shown below:

d(a,b)=|ab|=|2.6(1.8)|=|2.6+1.8|=|44|

Now, compare the distance with |a| :

|a|=|44|a=44

Now, by absolute value property:

|a|=a0

Therefore, |44|=44

Hence, distance between the numbers is 44 units.

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