High School

The formula [tex]F = \frac{9}{5}C + 32[/tex] converts temperatures from Celsius (C) to Fahrenheit (F).

A. Solve the formula for C.

B. The boiling point of water is 212 degrees F. What is the temperature in Celsius?

C. If a house thermostat is set at 80 degrees F, what is the setting in Celsius? Round your answer to the nearest tenth.

Answer :

Answer:

(a) [tex]\therefore C=\frac59(F-32)[/tex]

(b)The boiling point of water in Celsius scale is 100°C.

(c)The setting in Celsius scale is 26.7°C.

Step-by-step explanation:

Given that,the formula is

[tex]F=\frac95 C+32[/tex]......(1)

(a)

Given that,

[tex]F=\frac95 C+32[/tex]

[tex]\Rightarrow F-32=\frac95 C+32-32[/tex] [ subtracting 32 from both sides]

[tex]\Rightarrow F-32=\frac95 C[/tex]

[tex]\Rightarrow \frac95 C=F-32[/tex]

[tex]\Rightarrow C=\frac59(F-32)[/tex] ......(2) [Multiplying [tex]\frac59[/tex] ]

[tex]\therefore C=\frac59(F-32)[/tex]

(b)

Given that, the boiling point of water is 212°F.

Putting F=212 in equation (2)

[tex]\therefore C=\frac59(212-32)[/tex]

[tex]\Rightarrow C=\frac59\times 180[/tex]

[tex]\Rightarrow C=5\times 20[/tex]

[tex]\Rightarrow C=100[/tex]

The boiling point of water is 100°C.

(c)

Given that, a house thermostat is set at 80 degree.

Putting F=80 in equation (2)

[tex]\therefore C=\frac59(80-32)[/tex]

[tex]\Rightarrow C=\frac59\times 48[/tex]

[tex]\Rightarrow C\approx26.7[/tex]

The setting in Celsius scale is 26.7°C.

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