Dambit
contestada

C=
5
9
(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

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cryssatemp

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\ÂșF[/tex]:

[tex]C=(1\ÂșF-32)\frac{5}{9}=-17.22\ÂșC[/tex]

This means: [tex]1\ÂșF=-17.22\ÂșC[/tex]

Now we are going to increase 1 degree Farenheit. In other words, we are going to use [tex]2\ÂșF[/tex]:

[tex]C=(2\ÂșF-32)\frac{5}{9}=-16.66\ÂșC[/tex]

This means: [tex]2\ÂșF=-16.66\ÂșC[/tex]

Calculating the difference between [tex]-16.66\ÂșC[/tex]   and  [tex]-17.22\ÂșC[/tex]:

[tex]-16.66\ÂșC-(-17.22\ÂșC)=0,55\ÂșC[/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\ÂșC[/tex]:

[tex]F=(\frac{9}{5}1\ÂșC)+32[/tex]  

[tex]F=33.8\ÂșF[/tex]  

This means: [tex]1\ÂșC=33.8\ÂșF[/tex]  

Now we are going to increase 1 degree Celsius. In other words, we are going to use [tex]2\ÂșC[/tex]:

[tex]F=(\frac{9}{5}2\ÂșC)+32[/tex]  

[tex]F=35.67\ÂșF[/tex]  

This means: [tex]2\ÂșC=35.67\ÂșF[/tex]  

Calculating the difference between [tex]35.67\ÂșF[/tex]   and  [tex]33.8\ÂșF[/tex]:

[tex]35.67\ÂșF-33.8\ÂșF=1.8\ÂșF[/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\ÂșC[/tex]:

[tex]F=(\frac{9}{5}1\ÂșC)+32[/tex]  

[tex]F=33.8\ÂșF[/tex]  

This means: [tex]1\ÂșC=33.8\ÂșF[/tex]  

Now we are going to add [tex]\frac{5}{9}\ÂșF[/tex]:

[tex]33.8\ÂșF+\frac{5}{9}\ÂșF=34.35\ÂșF[/tex]

And use this value in the Celsius formula:

[tex]C=(34.35\ÂșF-32)\frac{5}{9}=1.30\ÂșC[/tex]

This means: [tex]1.30\ÂșC=34.35\ÂșF[/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.

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