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 determine what [tex]\( C(76.1) \)[/tex] represents, we need to understand the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

1. Identify the temperature given: In this problem, the temperature given is [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit.

2. Understand what [tex]\( C(76.1) \)[/tex] means: By applying the temperature [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit into the function [tex]\( C(F) \)[/tex], we are converting this specific temperature value into degrees Celsius.

3. Calculate the result: The function to convert is:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
Plug in [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

4. Interpret the calculation result: Based on the function and calculation, [tex]\( C(76.1) \)[/tex] represents the temperature in degrees Celsius corresponding to [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit.

Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. To be more specific based on calculation results, the Celsius temperature equivalent of [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit is approximately [tex]\( 24.5^{\circ} \)[/tex] Celsius.