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 1.10, Problem 70E

(a)

To determine

To find: The values of temperature in Celsius and Fahrenheit.

Expert Solution

Answer to Problem 70E

The complete table of different values of F for corresponding values of C is shown below.

C F
30° 22°
20° 4°
10° 14°
0° 32°
10° 50°
20° 68°
30° 86°

Explanation of Solution

Given:

The equation that determines the relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given,

F=95C+32 (1)

Calculation:

Convert the 30°C temperature into Fahrenheit by using equation (1),

Substitute 30 for C in equation (1) to find the value of F,

F=95(30)+32=2705+32=54+32=22

The value of F is 22F .

Convert the 20°C temperature into Fahrenheit by using equation (1),

Substitute 20 for C in equation (1) to find the value of F,

F=95(20)+32=1805+32=36+32=4

The value of F is 4°F .

Convert the 10°C temperature into Fahrenheit by using equation (1),

Substitute 10 for C in equation (1) to find the value of F,

F=95(10)+32=905+32=18+32=14

The value of F is 14°F .

Convert the 0C temperature into Fahrenheit by using equation (1),

Substitute 0 for C in equation (1) to find the value of F,

F=95(0)+32=0+32=32

The value of F is 32°F .

Convert the 50°F temperature into Celsius by using equation (1),

Substitute 50 for F in equation (1) to find the value of C,

50=95C+3295C=5032C=1859=10

The value of C is 10°C .

Convert the 68°F temperature into Celsius by using equation (1),

Substitute 68 for F in equation (1) to find the value of C,

68=95C+3295C=6832C=3659=20

The value of C is 20°C .

Convert the 86°F temperature into Celsius by using equation (1),

Substitute 86 for F in equation (1) to find the value of C,

86=95C+3295C=8632C=5459=30

The value of C is 30°C .

Form a table of different values of F for corresponding values of C ,

C F
30° 22°
20° 4°
10° 14°
0° 32°
10° 50°
20° 68°
30° 86°

Thus, the above table shows different values of F for corresponding values of C .

(b)

To determine

To find: The temperature at which both temperature scales Fahrenheit and Celsius agree.

Expert Solution

Answer to Problem 70E

The temperature at which both temperature scales Fahrenheit and Celsius agree, is 40° .

Explanation of Solution

Given:

The equation that determines the relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given,

F=95C+32 .

Calculation:

Let, a is the temperature at which both temperature scales agree.

Substitute a for F and C in equation (1) and find the value of a,

a=95a+32a95a=3245a=32a=3254

Above equation gives the value of a is,

a=1604=40

Thus, The temperature at which both temperature scales Fahrenheit and Celsius agree, is 40° .

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