Answer :
To understand what [tex]\( C(76.1) \)[/tex] represents, let's break down the concepts and steps involved in using the given function.
The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Here's what each part of the function means:
1. Input Temperature: The function takes a temperature, [tex]\( F \)[/tex], in degrees Fahrenheit. In this case, [tex]\( F = 76.1 \)[/tex].
2. Subtract 32: The Fahrenheit scale is adjusted by subtracting 32 because, on this scale, water freezes at 32 degrees.
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]: This fraction converts the adjusted Fahrenheit temperature to Celsius by scaling it to match the Celsius scale.
Given the specific input of 76.1 degrees Fahrenheit, you apply the formula step by step:
- First, subtract 32 from the Fahrenheit temperature: [tex]\( 76.1 - 32 = 44.1 \)[/tex].
- Next, multiply the result by [tex]\(\frac{5}{9}\)[/tex] to convert it to Celsius: [tex]\( \frac{5}{9} \times 44.1 \)[/tex].
When you complete this calculation, you determine that the temperature in degrees Celsius is approximately 24.5.
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. This matches the first option:
- 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 to degrees Celsius. Here's what each part of the function means:
1. Input Temperature: The function takes a temperature, [tex]\( F \)[/tex], in degrees Fahrenheit. In this case, [tex]\( F = 76.1 \)[/tex].
2. Subtract 32: The Fahrenheit scale is adjusted by subtracting 32 because, on this scale, water freezes at 32 degrees.
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]: This fraction converts the adjusted Fahrenheit temperature to Celsius by scaling it to match the Celsius scale.
Given the specific input of 76.1 degrees Fahrenheit, you apply the formula step by step:
- First, subtract 32 from the Fahrenheit temperature: [tex]\( 76.1 - 32 = 44.1 \)[/tex].
- Next, multiply the result by [tex]\(\frac{5}{9}\)[/tex] to convert it to Celsius: [tex]\( \frac{5}{9} \times 44.1 \)[/tex].
When you complete this calculation, you determine that the temperature in degrees Celsius is approximately 24.5.
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. This matches the first option:
- the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
