High School

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

Answer :

Certainly! Let's break down the problem and understand what [tex]\( C(76.1) \)[/tex] represents when using the function provided.

1. Understanding the Function: The function given, [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Here, [tex]\( F \)[/tex] stands for the temperature in Fahrenheit.

2. Substituting the Value: We need to find [tex]\( C(76.1) \)[/tex]. This involves substituting 76.1 for [tex]\( F \)[/tex] in the function. So, we calculate:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

3. Performing the Calculation:
- First, subtract 32 from 76.1:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Next, multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
\frac{5}{9} \times 44.1 \approx 24.5
\][/tex]

4. Interpreting the Result: The result, approximately 24.5, represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

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