College

On his first day of school, Kareem found the high temperature to be [tex]$76.1^{\circ}$[/tex] Fahrenheit. 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 understand what [tex]\( C(76.1) \)[/tex] represents, let's break down the function Kareem plans to use for converting temperatures from degrees Fahrenheit to degrees Celsius. The function given is:

[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

This function takes a Fahrenheit temperature [tex]\( F \)[/tex] and converts it to Celsius. Kareem wants to find [tex]\( C(76.1) \)[/tex], meaning he wants to convert a Fahrenheit temperature of 76.1 degrees into Celsius.

### Step-by-step Conversion

1. Identify the Fahrenheit Temperature: We have [tex]\( F = 76.1 \)[/tex].

2. Subtract 32 from the Fahrenheit Temperature: This is the first step in the conversion formula to adjust for the Fahrenheit scale start.
[tex]\[
F - 32 = 76.1 - 32 = 44.1
\][/tex]

3. Multiply the Result by [tex]\(\frac{5}{9}\)[/tex]: This step scales the adjusted temperature from the Fahrenheit degree to the Celsius degree.
[tex]\[
C = \frac{5}{9} \times 44.1
\][/tex]

The result of this calculation is approximately 24.5 degrees Celsius. Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to Celsius. This matches with the first option:

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

So, the correct answer is that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.