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

If we already have the formula to find how temperature measured in degrees Fahrenheit, relates to a temperature in degres Celsius:

   (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:

   (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 :

This means:

Now we are going to increase 1 degree Farenheit. In other words, we are going to use :

This means:

Calculating the difference between   and  :

>>>>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 :

This means:  

Now we are going to increase 1 degree Celsius. In other words, we are going to use :

This means:  

Calculating the difference between   and  :

>>>>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 :

This means:  

Now we are going to add :

And use this value in the Celsius formula:

This means:

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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