Answer :
To solve this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] does. This function is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
The question asks what [tex]\( C(76.1) \)[/tex] represents. Let's break it down step-by-step:
1. Identify the given function and the input:
- The function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- The input, [tex]\( F \)[/tex], is 76.1 degrees Fahrenheit.
2. Compute the output of the function [tex]\( C(F) \)[/tex] with the input 76.1:
- Substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\( C(76.1) = \frac{5}{9}(76.1 - 32) \)[/tex].
3. Perform the calculation:
- First, compute the inside of the parentheses: [tex]\( 76.1 - 32 = 44.1 \)[/tex].
- Next, apply the fraction [tex]\( \frac{5}{9} \)[/tex] to this value:
[tex]\( C(76.1) = \frac{5}{9} \times 44.1 \)[/tex].
4. Calculate the multiplication:
- The value of [tex]\( \frac{5}{9} \times 44.1 \)[/tex] is approximately 24.5.
So, [tex]\( C(76.1) \)[/tex] approximately equals 24.5 degrees Celsius.
Understanding what [tex]\( C(76.1) \)[/tex] represents:
- The input to the function was 76.1 degrees Fahrenheit.
- The output, 24.5, gives us the equivalent temperature in degrees Celsius.
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
So, the correct answer is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
The question asks what [tex]\( C(76.1) \)[/tex] represents. Let's break it down step-by-step:
1. Identify the given function and the input:
- The function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- The input, [tex]\( F \)[/tex], is 76.1 degrees Fahrenheit.
2. Compute the output of the function [tex]\( C(F) \)[/tex] with the input 76.1:
- Substitute [tex]\( F = 76.1 \)[/tex] into the function:
[tex]\( C(76.1) = \frac{5}{9}(76.1 - 32) \)[/tex].
3. Perform the calculation:
- First, compute the inside of the parentheses: [tex]\( 76.1 - 32 = 44.1 \)[/tex].
- Next, apply the fraction [tex]\( \frac{5}{9} \)[/tex] to this value:
[tex]\( C(76.1) = \frac{5}{9} \times 44.1 \)[/tex].
4. Calculate the multiplication:
- The value of [tex]\( \frac{5}{9} \times 44.1 \)[/tex] is approximately 24.5.
So, [tex]\( C(76.1) \)[/tex] approximately equals 24.5 degrees Celsius.
Understanding what [tex]\( C(76.1) \)[/tex] represents:
- The input to the function was 76.1 degrees Fahrenheit.
- The output, 24.5, gives us the equivalent temperature in degrees Celsius.
Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
So, the correct answer is:
The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
