Answer :
Sure! Let's go through a detailed, step-by-step process to understand what [tex]\( C(76.1) \)[/tex] represents when using the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
### Step-by-Step Solution
1. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius.
- In this function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] gives the temperature in degrees Celsius.
2. Identify the Given Temperature:
- The high temperature on Kareem's first day of school was [tex]\( 76.1^\circ \)[/tex] Fahrenheit.
3. Apply the Function:
- We need to find [tex]\( C(76.1) \)[/tex]. This means we substitute [tex]\( 76.1 \)[/tex] for [tex]\( F \)[/tex] in the function.
- Substitute [tex]\( 76.1 \)[/tex] into the equation:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
4. Interpret the Result:
- After performing the calculation, you get a result of approximately [tex]\( 24.5 \)[/tex].
- Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ \)[/tex] Fahrenheit converted to degrees Celsius, which is approximately [tex]\( 24.5^\circ \)[/tex] Celsius.
Thus, the correct interpretation of what [tex]\( C(76.1) \)[/tex] represents is "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius."
### Step-by-Step Solution
1. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius.
- In this function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] gives the temperature in degrees Celsius.
2. Identify the Given Temperature:
- The high temperature on Kareem's first day of school was [tex]\( 76.1^\circ \)[/tex] Fahrenheit.
3. Apply the Function:
- We need to find [tex]\( C(76.1) \)[/tex]. This means we substitute [tex]\( 76.1 \)[/tex] for [tex]\( F \)[/tex] in the function.
- Substitute [tex]\( 76.1 \)[/tex] into the equation:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
4. Interpret the Result:
- After performing the calculation, you get a result of approximately [tex]\( 24.5 \)[/tex].
- Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ \)[/tex] Fahrenheit converted to degrees Celsius, which is approximately [tex]\( 24.5^\circ \)[/tex] Celsius.
Thus, the correct interpretation of what [tex]\( C(76.1) \)[/tex] represents is "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius."
