To find the temperature in Kelvin, [tex]\( K \)[/tex], corresponding to a given temperature in Fahrenheit, [tex]\( F \)[/tex], using the formula [tex]\( F = \frac{9}{5}(K - 273) + 32 \)[/tex], we need to isolate [tex]\( K \)[/tex] in this equation.
Given:
[tex]\[ F = \frac{9}{5}(K - 273) + 32 \][/tex]
Let’s follow the steps to solve for [tex]\( K \)[/tex]:
1. Subtract 32 from both sides of the equation:
[tex]\[ F - 32 = \frac{9}{5}(K - 273) \][/tex]
2. Multiply both sides of the equation by [tex]\(\frac{5}{9}\)[/tex] to cancel out the [tex]\(\frac{9}{5}\)[/tex]:
[tex]\[ \frac{5}{9}(F - 32) = K - 273 \][/tex]
3. Add 273 to both sides of the equation to solve for [tex]\( K \)[/tex]:
[tex]\[ K = \frac{5}{9}(F - 32) + 273 \][/tex]
Therefore, the correct formula to convert temperature from Fahrenheit to Kelvin is:
[tex]\[ K = \frac{5}{9}(F - 32) + 273 \][/tex]
Now, let's match this with the given options:
A. [tex]\(\frac{9}{5}(F - 273) - 32\)[/tex]
B. [tex]\(\frac{5}{9}(F - 32) + 273\)[/tex]
C. [tex]\(\frac{9}{5}(F - 32) + 273\)[/tex]
D. [tex]\(\frac{5}{9}(F - 32) - 273\)[/tex]
The correct answer is:
B. [tex]\(\frac{5}{9}(F - 32) + 273\)[/tex]
