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Answer :
Sure! Let's solve this step-by-step.
a) To derive the formula for converting degrees Fahrenheit (°F) to degrees Celsius (°C), we'll start with the original formula:
[tex]\[
{}^{\circ} F = \frac{9}{5} \times {}^{\circ} C + 32
\][/tex]
We need to solve for °C, so we'll rearrange the equation to make °C the subject of the formula.
1. Subtract 32 from both sides:
[tex]\[
{}^{\circ} F - 32 = \frac{9}{5} \times {}^{\circ} C
\][/tex]
2. Multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to isolate °C:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times ({}^{\circ} F - 32)
\][/tex]
This is the formula to convert degrees Fahrenheit to degrees Celsius.
b) Now, let's use this derived formula to convert [tex]\(25^{\circ} F\)[/tex] to degrees Celsius.
1. Plug [tex]\(25^{\circ} F\)[/tex] into the formula:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times (25 - 32)
\][/tex]
2. Calculate the subtraction inside the parentheses:
[tex]\[
25 - 32 = -7
\][/tex]
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times -7 \approx -3.89
\][/tex]
Therefore, [tex]\(25^{\circ} F\)[/tex] is approximately [tex]\(-3.89^{\circ} C\)[/tex].
a) To derive the formula for converting degrees Fahrenheit (°F) to degrees Celsius (°C), we'll start with the original formula:
[tex]\[
{}^{\circ} F = \frac{9}{5} \times {}^{\circ} C + 32
\][/tex]
We need to solve for °C, so we'll rearrange the equation to make °C the subject of the formula.
1. Subtract 32 from both sides:
[tex]\[
{}^{\circ} F - 32 = \frac{9}{5} \times {}^{\circ} C
\][/tex]
2. Multiply both sides by [tex]\( \frac{5}{9} \)[/tex] to isolate °C:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times ({}^{\circ} F - 32)
\][/tex]
This is the formula to convert degrees Fahrenheit to degrees Celsius.
b) Now, let's use this derived formula to convert [tex]\(25^{\circ} F\)[/tex] to degrees Celsius.
1. Plug [tex]\(25^{\circ} F\)[/tex] into the formula:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times (25 - 32)
\][/tex]
2. Calculate the subtraction inside the parentheses:
[tex]\[
25 - 32 = -7
\][/tex]
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
{}^{\circ} C = \frac{5}{9} \times -7 \approx -3.89
\][/tex]
Therefore, [tex]\(25^{\circ} F\)[/tex] is approximately [tex]\(-3.89^{\circ} C\)[/tex].
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