Answer :
To solve the problem, we use the conversion formulas between Celsius and Fahrenheit:
1. To convert from Celsius ([tex]$C$[/tex]) to Fahrenheit ([tex]$F$[/tex]), we use
[tex]$$F = \frac{9}{5}C + 32.$$[/tex]
2. To convert from Fahrenheit ([tex]$F$[/tex]) to Celsius ([tex]$C$[/tex]), we use
[tex]$$C = \frac{5}{9}(F - 32).$$[/tex]
We are given some entries in a table and need to fill in the missing values. Let’s work through each part step by step.
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Step 1. Convert Celsius to Fahrenheit:
a) For [tex]$C = 0$[/tex]
Substitute [tex]$C = 0$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(0) + 32 = 0 + 32 = 32. $$[/tex]
Thus, when [tex]$C = 0$[/tex], [tex]$F = 32$[/tex].
b) For [tex]$C = 100$[/tex]
Substitute [tex]$C = 100$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(100) + 32 = 180 + 32 = 212. $$[/tex]
Thus, when [tex]$C = 100$[/tex], [tex]$F = 212$[/tex].
c) For [tex]$C = 25$[/tex]
Substitute [tex]$C = 25$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(25) + 32 = 45 + 32 = 77. $$[/tex]
Thus, when [tex]$C = 25$[/tex], [tex]$F = 77$[/tex].
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Step 2. Convert Fahrenheit to Celsius:
a) For [tex]$F = 104$[/tex]
Substitute [tex]$F = 104$[/tex] into the inverse formula:
[tex]$$ C = \frac{5}{9}(104 - 32) = \frac{5}{9}(72) = 40. $$[/tex]
Thus, when [tex]$F = 104$[/tex], [tex]$C = 40$[/tex].
b) For [tex]$F = 50$[/tex]
Substitute [tex]$F = 50$[/tex] into the formula:
[tex]$$ C = \frac{5}{9}(50 - 32) = \frac{5}{9}(18) = 10. $$[/tex]
Thus, when [tex]$F = 50$[/tex], [tex]$C = 10$[/tex].
c) For [tex]$F = 62.6$[/tex]
Substitute [tex]$F = 62.6$[/tex] into the formula:
[tex]$$ C = \frac{5}{9}(62.6 - 32) = \frac{5}{9}(30.6) \approx 17. $$[/tex]
Thus, when [tex]$F = 62.6$[/tex], [tex]$C \approx 17$[/tex].
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Finally, the completed table with the calculated values is as follows:
[tex]$$
\begin{array}{|c|c|c|c|c|c|c|}
\hline
C & 0 & 100 & 25 & \textbf{(for }F=104\textbf{)} & \textbf{(for }F=50\textbf{)} & \textbf{(for }F=62.6\textbf{)} \\ \hline
F & 32 & 212 & 77 & 104 & 50 & 62.6 \\ \hline
C \text{ (converted)} & - & - & - & 40 & 10 & 17 \\ \hline
\end{array}
$$[/tex]
Thus, the answers are:
- For [tex]$C=0$[/tex], [tex]$F=32$[/tex].
- For [tex]$C=100$[/tex], [tex]$F=212$[/tex].
- For [tex]$C=25$[/tex], [tex]$F=77$[/tex].
- For [tex]$F=104$[/tex], [tex]$C=40$[/tex].
- For [tex]$F=50$[/tex], [tex]$C=10$[/tex].
- For [tex]$F=62.6$[/tex], [tex]$C \approx 17$[/tex].
This completes the step-by-step conversion process.
1. To convert from Celsius ([tex]$C$[/tex]) to Fahrenheit ([tex]$F$[/tex]), we use
[tex]$$F = \frac{9}{5}C + 32.$$[/tex]
2. To convert from Fahrenheit ([tex]$F$[/tex]) to Celsius ([tex]$C$[/tex]), we use
[tex]$$C = \frac{5}{9}(F - 32).$$[/tex]
We are given some entries in a table and need to fill in the missing values. Let’s work through each part step by step.
──────────────────────────────
Step 1. Convert Celsius to Fahrenheit:
a) For [tex]$C = 0$[/tex]
Substitute [tex]$C = 0$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(0) + 32 = 0 + 32 = 32. $$[/tex]
Thus, when [tex]$C = 0$[/tex], [tex]$F = 32$[/tex].
b) For [tex]$C = 100$[/tex]
Substitute [tex]$C = 100$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(100) + 32 = 180 + 32 = 212. $$[/tex]
Thus, when [tex]$C = 100$[/tex], [tex]$F = 212$[/tex].
c) For [tex]$C = 25$[/tex]
Substitute [tex]$C = 25$[/tex] into the formula:
[tex]$$ F = \frac{9}{5}(25) + 32 = 45 + 32 = 77. $$[/tex]
Thus, when [tex]$C = 25$[/tex], [tex]$F = 77$[/tex].
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Step 2. Convert Fahrenheit to Celsius:
a) For [tex]$F = 104$[/tex]
Substitute [tex]$F = 104$[/tex] into the inverse formula:
[tex]$$ C = \frac{5}{9}(104 - 32) = \frac{5}{9}(72) = 40. $$[/tex]
Thus, when [tex]$F = 104$[/tex], [tex]$C = 40$[/tex].
b) For [tex]$F = 50$[/tex]
Substitute [tex]$F = 50$[/tex] into the formula:
[tex]$$ C = \frac{5}{9}(50 - 32) = \frac{5}{9}(18) = 10. $$[/tex]
Thus, when [tex]$F = 50$[/tex], [tex]$C = 10$[/tex].
c) For [tex]$F = 62.6$[/tex]
Substitute [tex]$F = 62.6$[/tex] into the formula:
[tex]$$ C = \frac{5}{9}(62.6 - 32) = \frac{5}{9}(30.6) \approx 17. $$[/tex]
Thus, when [tex]$F = 62.6$[/tex], [tex]$C \approx 17$[/tex].
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Finally, the completed table with the calculated values is as follows:
[tex]$$
\begin{array}{|c|c|c|c|c|c|c|}
\hline
C & 0 & 100 & 25 & \textbf{(for }F=104\textbf{)} & \textbf{(for }F=50\textbf{)} & \textbf{(for }F=62.6\textbf{)} \\ \hline
F & 32 & 212 & 77 & 104 & 50 & 62.6 \\ \hline
C \text{ (converted)} & - & - & - & 40 & 10 & 17 \\ \hline
\end{array}
$$[/tex]
Thus, the answers are:
- For [tex]$C=0$[/tex], [tex]$F=32$[/tex].
- For [tex]$C=100$[/tex], [tex]$F=212$[/tex].
- For [tex]$C=25$[/tex], [tex]$F=77$[/tex].
- For [tex]$F=104$[/tex], [tex]$C=40$[/tex].
- For [tex]$F=50$[/tex], [tex]$C=10$[/tex].
- For [tex]$F=62.6$[/tex], [tex]$C \approx 17$[/tex].
This completes the step-by-step conversion process.
