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 73E

a)

To determine

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

Expert Solution

Answer to Problem 73E

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

Answer to Problem 73E

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

Answer to Problem 73E

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.

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