To determine the increase in temperature in degrees Fahrenheit given an increase of 2.10 kelvins, we need to understand the relationship between Kelvin and Fahrenheit temperatures.
The formula that converts a temperature from Kelvin to Fahrenheit is:
[tex]\[ F(x) = \frac{9}{5}(x - 273.15) + 32 \][/tex]
However, since we are only interested in the increase in temperature, we focus on how a change in temperature in Kelvin affects the change in Fahrenheit. The key part of the conversion formula for this purpose is:
[tex]\[ \Delta F = \frac{9}{5} \Delta K \][/tex]
Here, [tex]\(\Delta K\)[/tex] represents the change in temperature in Kelvin, and [tex]\(\Delta F\)[/tex] represents the change in temperature in Fahrenheit.
Given that the temperature increase in Kelvin ([tex]\(\Delta K\)[/tex]) is 2.10, we substitute this value into our simplified equation to determine the increase in Fahrenheit:
[tex]\[
\Delta F = \frac{9}{5} \times 2.10
\][/tex]
Now, we calculate this step-by-step:
1. Multiply 2.10 by 9:
[tex]\[
2.10 \times 9 = 18.9
\][/tex]
2. Divide the result by 5:
[tex]\[
\frac{18.9}{5} = 3.78
\][/tex]
Therefore, the temperature increase in degrees Fahrenheit corresponding to an increase of 2.10 kelvins is:
[tex]\[ \Delta F = 3.78^{\circ} \][/tex]
The correct answer is:
(A) [tex]\(3.78^{\circ}\)[/tex]
