Question

The equation above shows how temperature F,measured in degrees Fahrenheit,Relates to temperature C,measured in degrees Celsius.Based on the equation,Which of the follow must be true?

Answer 1

Check the complete question attached.

We have the equation
`C= (5)/(9) (F-31)` equation (1); solving for F we get:

`(9)/(5) C=F-31`

`F= (9)/(5) C+31`

`F= (9)/(5) (C+31)` equation (2)

I. To check this we are going to use equation (1) to see what hapen when temperature rises from 32 Fahrenheit to 33 Fahrenheit:
For 32 Fahrenheit:

`C= (5)/(9) (32-31)`

`C= (5)/(9) (1)`

`C= (5)/(9)`

For 33 Fahrenheit:

`C= (5)/(9) (33-31)`

`C= (5)/(9) (2)`

`C= (10)/(9)`
Now we are going to subtract the two temperatures in degrees Celsius:

`(10)/(9) - (5)/(9) = (5)/(9)` As you can see, the temperature increased
`(5)/(9)` degree Celsius.

We can conclude that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
`(5)/(9)` degree Celsius.

II. To check this one we are going to use equation (2) to see what happens when temperature raises from 1 degree Celsius to 2 degrees Celsius:
For 1 degree Celsius:

`F= (9)/(5) (C+31)`

`F= (9)/(5) (1+31)`

`F= (9)/(5) (32)`

`F=57.6`

For 2 degrees Celsius:

`F= (9)/(5) (C+31)`

`F= (9)/(5) (2+31)`

`F= (9)/(5) (33)`

`F=59.4`
Now we are going to subtract the two temperatures in Fahrenheit:

`59.4-57.6=1.8` As you can see, the temperature increased 1.8 Fahrenheit.

We can conclude that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 Fahrenheit.

III. Since a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
`(5)/(9)` degree Celsius, we can conclude that this one is false.

The correct answer is D) I and II only