The image shows a multiple-choice question about converting temperatures between Celsius, Kelvin, and Fahrenheit. Let's break down the information presented in the question.

The problem states:

• The function $F(C) = \frac{9}{5}C + 32$ is used to convert temperatures from Celsius ($C$) to Fahrenheit ($F$).
• The function $C(K) = K - 273.15$ is used to convert temperatures from Kelvin ($K$) to Celsius ($C$).

The task is to find the correct function for converting temperatures from Kelvin ($K$) to Fahrenheit ($F$).

Solution:

To convert from Kelvin to Fahrenheit directly, you can follow these steps:

1. Convert from Kelvin to Celsius: $C(K) = K - 273.15$

2. Use the Celsius to Fahrenheit conversion formula: $F(C) = \frac{9}{5}C + 32$

3. Substitute the expression for $C(K)$ into the formula for Fahrenheit: $F(K) = \frac{9}{5}(K - 273.15) + 32$

Thus, the correct conversion formula from Kelvin to Fahrenheit is: $F(K) = \frac{9}{5}(K - 273.15) + 32$

Looking at the options provided in the image:

• Option D: $\frac{9}{5}(K - 273.15) + 32$ is the correct one.

Would you like further explanation on any part of this?

5 Related Questions:

1. How do you convert temperatures from Fahrenheit to Kelvin?
2. What is the difference between Celsius, Kelvin, and Fahrenheit in terms of scale?
3. How do you derive the formula for converting between different temperature units?
4. What are practical applications of temperature conversion in science and engineering?
5. How would the conversion formula change if the Fahrenheit to Celsius formula had a different scaling factor?

Tip:

Always remember to handle temperature units carefully in scientific calculations, as the scale differences can significantly impact your results.