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
is it D
To determine which of the options must be true based on the given equation:
C = 5/9(F-32)
We can analyze the equation step by step:
1) To convert Fahrenheit to Celsius, we subtract 32 from the Fahrenheit temperature.
2) Then, we multiply the result by 5/9 to obtain the Celsius temperature.
Now let's analyze each option:
Option A: A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
To verify this, we need to determine the difference in Celsius temperature when the Fahrenheit temperature increases by 1 degree:
C2 = 5/9(F2-32)
For a temperature increase of 1 degree Fahrenheit:
C2 = 5/9((F+1)-32)
C2 = 5/9(F-31)
Comparing this to the original equation, we see that the Celsius temperature increases by 5/9 degree Celsius, indicating that option A is true.
Option B: A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
To verify this, we need to determine the difference in Fahrenheit temperature when the Celsius temperature increases by 1 degree:
C2 = C+1
F2 = (9/5*C2)+32
Now, let's compare the Fahrenheit temperatures:
F2 = (9/5*(C+1))+32
F2 = (9/5*C)+(9/5)+32
F2 = (9/5*C)+57/5
From the original equation, we know that F = (9/5*C)+32. Comparing this to F2, we find that the difference in Fahrenheit temperature is not 1.8 degrees Fahrenheit but rather 57/5 degrees Fahrenheit, indicating that option B is false.
Option C: A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
To verify this, we need to determine the difference in Celsius temperature when the Fahrenheit temperature increases by 5/9 degree Fahrenheit:
C2 = 5/9(F+5/9-32)
C2 = 5/9(F-14/9)
Comparing this to the original equation, we see that the Celsius temperature increases by 5/9 degree Celsius, indicating that option C is true.
Based on our analysis, we can conclude that options A and C are true, while option B is false. Therefore, the correct answer is:
D) I and III only.