College

On his first day of school, Kareem found the high temperature in degrees using the function [tex]C(F)=\frac{5}{9}(F-32)[/tex] to convert the temperature from degrees Fahrenheit. What does this 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
D. The amount of time it takes for a temperature of 76.1 degrees Celsius to [tex]b[/tex]

Answer :

To solve the problem and understand what [tex]$C(F)=\frac{5}{9}(F-32)$[/tex] represents, let's walk through the steps to convert a temperature from Fahrenheit to Celsius using this formula.

1. Understand the formula:
- [tex]\( C(F) \)[/tex] is the formula to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
- The formula is given as:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]

2. Identify the given temperature:
- We are given a temperature of 76.1 degrees Fahrenheit.

3. Apply the formula:
- Substitute 76.1 for [tex]\( F \)[/tex] in the formula:
[tex]\[
C = \frac{5}{9}(76.1 - 32)
\][/tex]

4. Calculate step-by-step:
- First, subtract 32 from 76.1:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Next, multiply 44.1 by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9} \times 44.1 \approx 24.5
\][/tex]

5. Interpret the result:
- The temperature of 76.1 degrees Fahrenheit converts to approximately 24.5 degrees Celsius.

Therefore, the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents the conversion of a temperature from degrees Fahrenheit to degrees Celsius. Given the result we calculated (24.5), this supports that we are converting the Fahrenheit temperature to Celsius.