Answer :
To answer the question about what [tex]\( C(76.1) \)[/tex] represents, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] does. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Here's how it works:
1. Identify the Input: The input for the function is given as 76.1 degrees Fahrenheit. So, we need to find what [tex]\( C(76.1) \)[/tex] represents.
2. Apply the Function: Substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
3. Calculate the Difference:
- First, subtract 32 from 76.1:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
4. Apply the Conversion Factor:
- Multiply the result by [tex]\(\frac{5}{9}\)[/tex] to convert it to Celsius:
[tex]\[
C = \frac{5}{9} \times 44.1 \approx 24.5
\][/tex]
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius, which is approximately 24.5 degrees Celsius.
Given this explanation, the correct choice from the options provided is:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
Here's how it works:
1. Identify the Input: The input for the function is given as 76.1 degrees Fahrenheit. So, we need to find what [tex]\( C(76.1) \)[/tex] represents.
2. Apply the Function: Substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
3. Calculate the Difference:
- First, subtract 32 from 76.1:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
4. Apply the Conversion Factor:
- Multiply the result by [tex]\(\frac{5}{9}\)[/tex] to convert it to Celsius:
[tex]\[
C = \frac{5}{9} \times 44.1 \approx 24.5
\][/tex]
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius, which is approximately 24.5 degrees Celsius.
Given this explanation, the correct choice from the options provided is:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
