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Answer :
To understand what [tex]\( C(76.1) \)[/tex] represents, let's break down the provided function and its purpose.
The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C). This is a standard formula for temperature conversion.
Now, let's look at the problem:
1. Identify what is given: The temperature in degrees Fahrenheit is 76.1°F.
2. Understand the question: We are asked what [tex]\( C(76.1) \)[/tex] represents when input into the function.
3. Substitute the given Fahrenheit temperature into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
4. Calculate the Celsius temperature:
- Subtract 32 from 76.1: [tex]\( 76.1 - 32 = 44.1 \)[/tex]
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]:
- First, calculate [tex]\( \frac{5}{9} \approx 0.5556 \)[/tex].
- Then, multiply [tex]\( 44.1 \times 0.5556 \)[/tex], which gives approximately 24.5.
5. Interpret the result:
The calculated temperature, around 24.5°C, tells us that [tex]\( C(76.1) \)[/tex] represents the conversion of 76.1 degrees Fahrenheit into degrees Celsius.
Therefore, the correct answer is that [tex]\( C(76.1) \)[/tex] represents "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius."
The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C). This is a standard formula for temperature conversion.
Now, let's look at the problem:
1. Identify what is given: The temperature in degrees Fahrenheit is 76.1°F.
2. Understand the question: We are asked what [tex]\( C(76.1) \)[/tex] represents when input into the function.
3. Substitute the given Fahrenheit temperature into the function:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
4. Calculate the Celsius temperature:
- Subtract 32 from 76.1: [tex]\( 76.1 - 32 = 44.1 \)[/tex]
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]:
- First, calculate [tex]\( \frac{5}{9} \approx 0.5556 \)[/tex].
- Then, multiply [tex]\( 44.1 \times 0.5556 \)[/tex], which gives approximately 24.5.
5. Interpret the result:
The calculated temperature, around 24.5°C, tells us that [tex]\( C(76.1) \)[/tex] represents the conversion of 76.1 degrees Fahrenheit into degrees Celsius.
Therefore, the correct answer is that [tex]\( C(76.1) \)[/tex] represents "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius."
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