Question

The formula F=9/5C+32 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 1

(a)
`\therefore C=\frac59(F-32)`

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

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

Explanation:

Given that,the formula is

`F=\frac95 C+32`......(1)

(a)

Given that,

`F=\frac95 C+32`

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

`\Rightarrow F-32=\frac95 C`

`\Rightarrow \frac95 C=F-32`

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

`\therefore C=\frac59(F-32)`

(b)

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

Putting F=212 in equation (2)

`\therefore C=\frac59(212-32)`

`\Rightarrow C=\frac59* 180`

`\Rightarrow C=5* 20`

`\Rightarrow C=100`

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)

`\therefore C=\frac59(80-32)`

`\Rightarrow C=\frac59* 48`

`\Rightarrow C\approx26.7`

The setting in Celsius scale is 26.7°C.