College

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be [tex]$76.1^{\circ}$[/tex]. He plans to use the function [tex]$C(F)=\frac{5}{9}(F-32)$[/tex] to convert this temperature from degrees Fahrenheit to degrees Celsius. What does [tex]$C(76.1)$[/tex] represent?

A. The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

B. The temperature of 76.1 degrees Celsius converted to degrees Fahrenheit.

C. The amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius.

D. The amount of time it takes a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit.

Answer :

To solve this problem, we want to understand what [tex]$C(76.1)$[/tex] represents using the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

1. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

2. Identify the Input:
- The input given is [tex]\( F = 76.1 \)[/tex] degrees Fahrenheit.

3. Compute [tex]\( C(76.1) \)[/tex]:
- Substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

4. Calculate:
- Simplify within the parentheses:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Apply the fraction:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]
- This calculation gives approximately [tex]\( 24.5 \)[/tex] degrees Celsius.

5. Conclusion:
- Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

The correct choice from the given options is: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.