Answer :
To convert a temperature from degrees Fahrenheit to degrees Celsius, we need to find the inverse of the given formula for converting Celsius to Fahrenheit:
The original formula is:
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
To find the inverse function, which will convert from Fahrenheit to Celsius, follow these steps:
1. Start with the given formula:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
2. Isolate the term with [tex]\( C \)[/tex] (subtract 32 from both sides):
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
3. Solve for [tex]\( C \)[/tex] (multiply both sides by [tex]\(\frac{5}{9}\)[/tex]):
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
This formula, [tex]\( C = \frac{5}{9} (F - 32) \)[/tex], is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Therefore, the formula for converting from degrees Fahrenheit to degrees Celsius is:
[tex]\[ C(F) = 0.5556 \times F - 17.7778 \][/tex]
These numerical values correspond to the coefficients you use in the conversion. When you calculate using [tex]\(\frac{5}{9}\)[/tex], it approximately equals 0.5556, and [tex]\(-32 \times \frac{5}{9}\)[/tex] approximately equals -17.7778.
The original formula is:
[tex]\[ F(C) = \frac{9}{5} C + 32 \][/tex]
To find the inverse function, which will convert from Fahrenheit to Celsius, follow these steps:
1. Start with the given formula:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
2. Isolate the term with [tex]\( C \)[/tex] (subtract 32 from both sides):
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
3. Solve for [tex]\( C \)[/tex] (multiply both sides by [tex]\(\frac{5}{9}\)[/tex]):
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
This formula, [tex]\( C = \frac{5}{9} (F - 32) \)[/tex], is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Therefore, the formula for converting from degrees Fahrenheit to degrees Celsius is:
[tex]\[ C(F) = 0.5556 \times F - 17.7778 \][/tex]
These numerical values correspond to the coefficients you use in the conversion. When you calculate using [tex]\(\frac{5}{9}\)[/tex], it approximately equals 0.5556, and [tex]\(-32 \times \frac{5}{9}\)[/tex] approximately equals -17.7778.
