Let's start by understanding the given function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is a conversion formula used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
We are asked to find what [tex]\( C(76.1) \)[/tex] represents.
1. Identify the Function:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
Here, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit, and [tex]\( C(F) \)[/tex] represents the corresponding temperature in degrees Celsius.
2. Plug in the Temperature in Fahrenheit:
We are given a temperature of [tex]\( 76.1^{\circ}F \)[/tex].
So we substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\[
C(76.1) = \frac{5}{9} (76.1 - 32)
\][/tex]
3. Simplify the Expression Inside the Parentheses:
First, calculate the value inside the parentheses:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
4. Apply the Conversion Formula:
Next, multiply by the fraction [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]
5. Compute the Conversion Result:
Simplifying the multiplication, we get:
[tex]\[
C(76.1) \approx 24.5
\][/tex]
So, [tex]\( C(76.1) \approx 24.5 \)[/tex].
Now let's analyze the options to determine what [tex]\( C(76.1) \)[/tex] represents:
1. The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
2. The temperature of 76.1 degrees Celsius converted to degrees Fahrenheit.
3. The amount of time it takes for a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius.
4. The amount of time it takes for a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit.
Given that the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] converts temperatures directly from Fahrenheit to Celsius, the correct interpretation is:
1. 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.
