To solve this problem and convert a temperature difference from degrees Celsius to degrees Fahrenheit, we use the conversion formula for temperature differences. The formula to convert a temperature difference from Celsius to Fahrenheit is based on the relationship between the two scales:
[tex]\[ \Delta T_F = \Delta T_C \times \frac{9}{5} \][/tex]
Let's go through this step-by-step:
1. Identify the given temperature difference in Celsius:
[tex]\[
\Delta T_C = 40^\circ \text{C}
\][/tex]
2. Use the conversion factor for temperature differences:
- The conversion factor from Celsius to Fahrenheit is [tex]\(\frac{9}{5}\)[/tex].
3. Apply the conversion factor:
[tex]\[
\Delta T_F = 40^\circ \text{C} \times \frac{9}{5}
\][/tex]
4. Calculate the result:
[tex]\[
\Delta T_F = 40 \times 1.8 = 72^\circ \text{F}
\][/tex]
Therefore, a temperature difference of [tex]\(40^\circ \text{C}\)[/tex] is equivalent to a temperature difference of [tex]\(72^\circ \text{F}\)[/tex].
Looking at the given options:
(1) [tex]\(45^\circ \text{F}\)[/tex]
(2) [tex]\(72^\circ \text{F}\)[/tex]
(3) [tex]\(32^\circ \text{F}\)[/tex]
(4) [tex]\(25^\circ \text{F}\)[/tex]
The correct answer is:
(2) [tex]\(72^\circ \text{F}\)[/tex]
