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.
C = (5/9)(F-32)
change in C = (5/9) * change in F
so change in F = (9/5) or 1.8 * change in C
====================================
look at choice 1
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
(5/9) degree Celsius.
Is that true ?
YES
--------------------------------------------------------
Look at choice 2
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
YES
==============================
look at choice 3
A temperature increase of
(5/9) degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
NO
if change in F = 5/9 then change in C =(5/9)(5/9) = 25/81
In other words dC/dF = (5/9) = delta C / delta F
To determine which of the given statements must be true based on the equation, we need to analyze the equation itself:
C = (5/9)(F - 32)
From the equation, we can see that the coefficient (5/9) in front of the Fahrenheit term relates the temperature increase between Celsius and Fahrenheit. Let's analyze each statement:
Statement 1: A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of (5/9) degree Celsius.
To verify this statement, we can substitute F = 1 into the equation and calculate C:
C = (5/9)(1 - 32)
C = (5/9)(-31)
C = -155/9
So, a temperature increase of 1 degree Fahrenheit is equivalent to (-155/9) degree Celsius, not (5/9) degree Celsius. Therefore, Statement 1 is NOT true.
Statement 2: A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
To verify this statement, we can rearrange the equation to solve for F in terms of C:
C = (5/9)(F - 32)
9C = 5(F - 32)
9C = 5F - 160
5F = 9C + 160
F = (9C/5) + 32
Now we can calculate the temperature increase in Fahrenheit when there is a 1-degree Celsius increase:
F2 = (9(C + 1)/5) + 32
F2 = (9C/5) + 1.8 + 32 = (9C/5) + 33.8
Therefore, a temperature increase of 1 degree Celsius is equivalent to (9/5) + 33.8 degrees Fahrenheit, which is approximately 1.8 degrees Fahrenheit as stated in Statement 2. So, Statement 2 is true.
Statement 3: A temperature increase of (5/9) degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
To verify this statement, we can substitute F = (5/9) into the equation and calculate C:
C = (5/9)((5/9) - 32)
C = (5/9)(-286/9)
C = -1430/81
So, a temperature increase of (5/9) degree Fahrenheit is equivalent to (-1430/81) degree Celsius, not 1 degree Celsius. Therefore, Statement 3 is NOT true.
In conclusion, based on the equation, the only statement that must be true is Statement 2: A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.