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# MATH BOIII

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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

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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

May 8, 2019
edited by CPhill  May 9, 2019
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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