๐ถ=5/9(๐นโ32)
The equation above shows how temperature ๐น, measured in degrees Fahrenheit, relates to a temperature ๐ถ, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. 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
The correct answer is D) I and II only.
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
This is true according to the equation ๐ถ=5/9(๐นโ32). When ๐น increases by 1 degree, ๐ถ increases by 5/9 degrees.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
To verify this, we can rearrange the equation to solve for ๐น in terms of ๐ถ:
๐ถ=5/9(๐นโ32)
9/5๐ถ=๐นโ32
9/5๐ถ+32=๐น
When ๐ถ increases by 1 degree, ๐น increases by 9/5(1)=1.8 degrees.
III. A temperature increase of 5/9-degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
This statement is not necessarily true. When ๐น increases by 5/9 degree, ๐ถ increases by 5/9 degrees, not necessarily 1 degree.