Right answer: I and II only
If we already have the formula to find how temperature measured in degrees Fahrenheit, relates to a temperature in degres Celsius:
[tex]C=(F-32)\frac{5}{9}[/tex] (1)
We can know the formula to find how temperature measured in degrees Celsius, relates to a temperature in degres Fahrenheit, only by isolating F:
[tex]F=(\frac{9}{5}C)+32[/tex] (2)
Having both formulas, let’s begin:
I) If we want to prove that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius:
Beginning with [tex]1\ºF[/tex]:
[tex]C=(1\ºF-32)\frac{5}{9}=-17.22\ºC[/tex]
This means: [tex]1\ºF=-17.22\ºC[/tex]
Now we are going to increase 1 degree Farenheit. In other words, we are going to use [tex]2\ºF[/tex]:
[tex]C=(2\ºF-32)\frac{5}{9}=-16.66\ºC[/tex]
This means: [tex]2\ºF=-16.66\ºC[/tex]
Calculating the difference between [tex]-16.66\ºC[/tex] and [tex]-17.22\ºC[/tex]:
[tex]-16.66\ºC-(-17.22\ºC)=0,55\ºC[/tex]>>>>This is equal to 5/9 degree Celsius, hence is correct
II) If we want to prove that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit:
Beginning with [tex]1\ºC[/tex]:
[tex]F=(\frac{9}{5}1\ºC)+32[/tex]
[tex]F=33.8\ºF[/tex]
This means: [tex]1\ºC=33.8\ºF[/tex]
Now we are going to increase 1 degree Celsius. In other words, we are going to use [tex]2\ºC[/tex]:
[tex]F=(\frac{9}{5}2\ºC)+32[/tex]
[tex]F=35.67\ºF[/tex]
This means: [tex]2\ºC=35.67\ºF[/tex]
Calculating the difference between [tex]35.67\ºF[/tex] and [tex]33.8\ºF[/tex]:
[tex]35.67\ºF-33.8\ºF=1.8\ºF[/tex]>>>>This is a proof of the statement, hence is also correct.
III) If we want to prove that a temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius:
Beginning with [tex]1\ºC[/tex]:
[tex]F=(\frac{9}{5}1\ºC)+32[/tex]
[tex]F=33.8\ºF[/tex]
This means: [tex]1\ºC=33.8\ºF[/tex]
Now we are going to add [tex]\frac{5}{9}\ºF[/tex]:
[tex]33.8\ºF+\frac{5}{9}\ºF=34.35\ºF[/tex]
And use this value in the Celsius formula:
[tex]C=(34.35\ºF-32)\frac{5}{9}=1.30\ºC[/tex]
This means: [tex]1.30\ºC=34.35\ºF[/tex]
In other words: An increase in 5/9 degree Fahrenheit is equivalent to a temperature increase of 1.30 degree Celsius, not 1 degree Celsius.
Therefore this statement is incorrect.
