BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.1, Problem 71E
To determine

To find: the distance between the two numbers on the given number line.

Expert Solution

Answer to Problem 71E

The distance between the two numbers is 5 .

Explanation of Solution

Given information:

A number line is given as

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.1, Problem 71E , additional homework tip  1

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:

Consider the given number line.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.1, Problem 71E , additional homework tip  2

Two numbers on the number line is 2 and 3 .

Distance between the numbers can be calculated as shown below:

  d(a,b)=|ab|=|23|=|5|

Now, compare the distancewith |a| :

  |a|=|5|a=5

Now, by absolute value property:

  |a|=a0

Therefore, |5|=5

Hence, distance between the numbers is 5 units.

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