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Answer :
To determine what [tex]\( C(76.1) \)[/tex] represents, let's look at the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert a temperature from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).
In this problem, Kareem is trying to convert a temperature of 76.1 degrees Fahrenheit into degrees Celsius.
Here's a breakdown of the steps involved:
1. Identify the given Fahrenheit temperature: 76.1 degrees Fahrenheit.
2. Use the conversion formula for Fahrenheit to Celsius:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
Substitute 76.1 for [tex]\( F \)[/tex] in the formula:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
3. Perform the arithmetic operation:
- Calculate [tex]\( 76.1 - 32 \)[/tex]:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Now, substitute 44.1 back into the formula:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]
- Calculate [tex]\( \frac{5}{9} \times 44.1 \)[/tex]:
[tex]\[
\frac{5}{9} \times 44.1 \approx 24.5
\][/tex]
Thus, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to approximately 24.5 degrees Celsius. Therefore, the correct interpretation is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
In this problem, Kareem is trying to convert a temperature of 76.1 degrees Fahrenheit into degrees Celsius.
Here's a breakdown of the steps involved:
1. Identify the given Fahrenheit temperature: 76.1 degrees Fahrenheit.
2. Use the conversion formula for Fahrenheit to Celsius:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
Substitute 76.1 for [tex]\( F \)[/tex] in the formula:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
3. Perform the arithmetic operation:
- Calculate [tex]\( 76.1 - 32 \)[/tex]:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Now, substitute 44.1 back into the formula:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]
- Calculate [tex]\( \frac{5}{9} \times 44.1 \)[/tex]:
[tex]\[
\frac{5}{9} \times 44.1 \approx 24.5
\][/tex]
Thus, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to approximately 24.5 degrees Celsius. Therefore, the correct interpretation is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
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