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 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 the problem of converting [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit to degrees Celsius using the function provided, follow these steps:

1. Understand the Conversion Function:
The function to convert degrees Fahrenheit (F) to degrees Celsius (C) provided is:
[tex]\[
C(F) = \frac{5}{9} \times (F - 32)
\][/tex]
Here, [tex]\( C \)[/tex] represents the temperature in degrees Celsius and [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.

2. Substitute the Given Value:
You are given a temperature of [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit. Substitute [tex]\( F = 76.1 \)[/tex] into the conversion formula:
[tex]\[
C(76.1) = \frac{5}{9} \times (76.1 - 32)
\][/tex]

3. Calculate the Difference:
Perform the subtraction inside the parentheses first:
[tex]\[
76.1 - 32 = 44.1
\][/tex]

4. Apply the Conversion Factor:
Multiply the result by [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]

5. Perform the Multiplication:
Multiplying [tex]\( \frac{5}{9} \)[/tex] by [tex]\( 44.1 \)[/tex]:
[tex]\[
\frac{5}{9} \times 44.1 = 24.499999999999996
\][/tex]

Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^{\circ} \)[/tex] Fahrenheit converted to degrees Celsius, which is approximately [tex]\( 24.5^{\circ} \)[/tex].

Thus, the correct interpretation of [tex]\( C(76.1) \)[/tex] is:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.