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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

 May 8, 2019
edited by Guest  May 8, 2019
 #1
avatar+106533 
+2

C  =  (5/9)(F - 32)

 

 

(1) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.

 

(2)A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

 

(3) A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

 

 

The slope of this linear equation  is  5/9

 

This means that  for every increase in Celsius of 5 degrees, Fahrenheit increases by 9 degrees  ⇒ (A)

 

Dividihg both quantities in A by 5......for every 1 degree increase in Celsius, Fahrenheit increases by (9/5) = 1.8 degrees

So (2)  is true

 

Next....divide both quantities in  (A) by 9    and we have that for every 5/9 of a degree change in Celsius, Fahrenheit changes by  1 degree

So ( 1) is also true

 

So... "D" is correct

 

cool cool cool

 May 8, 2019
edited by CPhill  May 9, 2019
 #2
avatar+8842 
+3

Here is another way to figure out the answer:

 

C  =  \(\frac59\)(F - 32)  =  \(\frac59\)F  -  \(\frac{160}9\)

 

When  F = 0 ,   C  =  \(\frac59\)(0)  -  \(\frac{160}9\)  =  - \(\frac{160}9\)

 

When  F = 1 ,   C  =  \(\frac59\)(1)  -  \(\frac{160}9\)  =  \(\frac59\) - \(\frac{160}9\)     Notice this value of  C  is  \(\frac59\)  more than it was when  F  was  0 .

 

When  F = 2 ,   C  =  \(\frac59\)(2)  -  \(\frac{160}9\)  =  \(\frac59\) + \(\frac59\) - \(\frac{160}9\)     Notice this value of  C  is  \(\frac59\)  more than the previous.

 

So a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.

 

C  =  \(\frac59\)(F - 32)

 

\(\frac95\)C  =  F - 32

 

\(\frac95\)C + 32  =  F

 

When  C = 0 ,   F  =  \(\frac95\)(0) + 32  =  32

 

When  C = 1 ,   F  =  \(\frac95\)(1) + 32  =  \(\frac95\) + 32       Notice this value of  F  is  \(\frac95\)  more than the previous.

 

When  C = 2 ,   F  =  \(\frac95\)(2) + 32  =  \(\frac95\) + \(\frac95\) + 32    Notice this value of  F  is  \(\frac95\)  more than the previous.

 

So a temperature increase of  1  degree Celsius is equivalent to a temperature increase of 9/5 degrees Fahrenheit. (And  9/5 = 1.8). In other words, a temperature increase of 9/5 degrees (not 5/9 degrees) Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

 May 9, 2019
edited by hectictar  May 9, 2019

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