Answer :
To find out what [tex]\( C(76.1) \)[/tex] represents, we need to understand the function given: [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
### Step-by-Step Solution
1. Identify the given temperature in Fahrenheit:
[tex]\[ F = 76.1^{\circ} \][/tex]
2. Use the conversion function [tex]\( C(F) \)[/tex] to convert the temperature:
[tex]\[ C(76.1) = \frac{5}{9} (76.1 - 32) \][/tex]
3. Calculate the difference:
[tex]\[ 76.1 - 32 = 44.1 \][/tex]
4. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C(76.1) = \frac{5}{9} \times 44.1 \][/tex]
5. Perform the multiplication:
[tex]\[ C(76.1) = 24.499999999999996 \][/tex]
After performing these steps, we see that:
[tex]\[ C(76.1) = 24.499999999999996 \][/tex]
This result tells us that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. Therefore, the correct interpretation of [tex]\( C(76.1) \)[/tex] is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
### Step-by-Step Solution
1. Identify the given temperature in Fahrenheit:
[tex]\[ F = 76.1^{\circ} \][/tex]
2. Use the conversion function [tex]\( C(F) \)[/tex] to convert the temperature:
[tex]\[ C(76.1) = \frac{5}{9} (76.1 - 32) \][/tex]
3. Calculate the difference:
[tex]\[ 76.1 - 32 = 44.1 \][/tex]
4. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C(76.1) = \frac{5}{9} \times 44.1 \][/tex]
5. Perform the multiplication:
[tex]\[ C(76.1) = 24.499999999999996 \][/tex]
After performing these steps, we see that:
[tex]\[ C(76.1) = 24.499999999999996 \][/tex]
This result tells us that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. Therefore, the correct interpretation of [tex]\( C(76.1) \)[/tex] is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.