Question
Convert \( 57^{\circ} \mathrm{F} \) to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. \begin{tabular}{l}\( C=\frac{5}{9}(F-32) \) \\ \\ \( \qquad=\frac{9}{5} C+32 \) \\ \( 57^{\circ} \mathrm{F}=\prod^{\circ} \mathrm{C} \) \\ \hline\end{tabular}
Ask by Gray Mullins. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 57^{\circ} \mathrm{F} \) is approximately \( 13.9^{\circ} \mathrm{C} \).
Solution
1. Start with the formula for converting Fahrenheit to Celsius:
\[
C = \frac{5}{9}(F - 32)
\]
2. Substitute \( F = 57 \) into the formula:
\[
C = \frac{5}{9}(57 - 32)
\]
3. Calculate the expression in the parentheses:
\[
57 - 32 = 25
\]
4. Multiply by \(\frac{5}{9}\):
\[
C = \frac{5}{9} \times 25 = \frac{125}{9}
\]
5. Convert \(\frac{125}{9}\) to a decimal:
\[
\frac{125}{9} \approx 13.8889
\]
6. Round to the nearest tenth:
\[
C \approx 13.9^{\circ} \mathrm{C}
\]
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Simplify this solution Extra Insights
To convert \( 57^{\circ} \mathrm{F} \) to degrees Celsius, we can use the formula \( C=\frac{5}{9}(F-32) \). First, substitute \( F = 57 \): \[ C = \frac{5}{9}(57 - 32) \] Now calculate \( 57 - 32 \): \[ 57 - 32 = 25 \] Next, substitute that back into the equation: \[ C = \frac{5}{9} \times 25 \] Now calculate \( \frac{5}{9} \times 25 \): \[ C = \frac{5 \times 25}{9} = \frac{125}{9} \approx 13.8889 \] Rounding to the nearest tenth, we get: \[ C \approx 13.9^{\circ} \mathrm{C} \] So, \( 57^{\circ} \mathrm{F} \) is approximately \( 13.9^{\circ} \mathrm{C} \).
