Answer :
Certainly! Let's work through the problem step by step.
### Part (a)
We're asked to complete a table using the relation [tex]\( F = \frac{9}{5} C + 32 \)[/tex], where [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit and [tex]\( C \)[/tex] is the temperature in degrees Celsius. We'll use this formula to fill in the missing values for [tex]\( F \)[/tex] for each given [tex]\( C \)[/tex].
Here is the completed table:
[tex]\[
\begin{array}{|l|l|l|l|l|c|c|c|c|}
\hline
{}^{\circ} C & 0 & 5 & 10 & 15 & 20 & 25 & 30 \\
\hline
{}^{\circ} F & 32.0 & 41.0 & 50.0 & 59.0 & 68.0 & 77.0 & 86.0 \\
\hline
\end{array}
\][/tex]
### Part (b)
This part involves drawing a graph. You can do this by following these steps:
1. Label the Axes:
- The horizontal axis represents degrees Celsius ([tex]\( {}^{\circ} C \)[/tex]), with a scale of 2 cm to 5 units.
- The vertical axis represents degrees Fahrenheit ([tex]\( {}^{\circ} F \)[/tex]), with a scale of 2 cm to 10 units.
2. Plot the Points:
- From the table, plot each pair of [tex]\((C, F)\)[/tex] values:
- (0, 32), (5, 41), (10, 50), (15, 59), (20, 68), (25, 77), and (30, 86).
3. Draw the Line:
- Connect the points with a straight line to show the linear relationship between [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
### Part (c)
To find the value of [tex]\( C \)[/tex] when [tex]\( F = 55 \)[/tex] degrees, you can either use the graph or calculate directly using the formula:
1. Using the Graph:
- Find 55 on the Fahrenheit axis and draw a horizontal line to intersect the graph line and then a vertical line down to the Celsius axis. Read the value of [tex]\( C \)[/tex].
2. Using the Formula:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
Substitute [tex]\( F = 55 \)[/tex]:
[tex]\[
C = \frac{5}{9} (55 - 32) = \frac{5}{9} \times 23 \approx 12.78
\][/tex]
So, when [tex]\( F = 55 \)[/tex] degrees, the temperature in Celsius is approximately [tex]\( 12.78 \)[/tex] degrees.
### Part (a)
We're asked to complete a table using the relation [tex]\( F = \frac{9}{5} C + 32 \)[/tex], where [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit and [tex]\( C \)[/tex] is the temperature in degrees Celsius. We'll use this formula to fill in the missing values for [tex]\( F \)[/tex] for each given [tex]\( C \)[/tex].
Here is the completed table:
[tex]\[
\begin{array}{|l|l|l|l|l|c|c|c|c|}
\hline
{}^{\circ} C & 0 & 5 & 10 & 15 & 20 & 25 & 30 \\
\hline
{}^{\circ} F & 32.0 & 41.0 & 50.0 & 59.0 & 68.0 & 77.0 & 86.0 \\
\hline
\end{array}
\][/tex]
### Part (b)
This part involves drawing a graph. You can do this by following these steps:
1. Label the Axes:
- The horizontal axis represents degrees Celsius ([tex]\( {}^{\circ} C \)[/tex]), with a scale of 2 cm to 5 units.
- The vertical axis represents degrees Fahrenheit ([tex]\( {}^{\circ} F \)[/tex]), with a scale of 2 cm to 10 units.
2. Plot the Points:
- From the table, plot each pair of [tex]\((C, F)\)[/tex] values:
- (0, 32), (5, 41), (10, 50), (15, 59), (20, 68), (25, 77), and (30, 86).
3. Draw the Line:
- Connect the points with a straight line to show the linear relationship between [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
### Part (c)
To find the value of [tex]\( C \)[/tex] when [tex]\( F = 55 \)[/tex] degrees, you can either use the graph or calculate directly using the formula:
1. Using the Graph:
- Find 55 on the Fahrenheit axis and draw a horizontal line to intersect the graph line and then a vertical line down to the Celsius axis. Read the value of [tex]\( C \)[/tex].
2. Using the Formula:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
Substitute [tex]\( F = 55 \)[/tex]:
[tex]\[
C = \frac{5}{9} (55 - 32) = \frac{5}{9} \times 23 \approx 12.78
\][/tex]
So, when [tex]\( F = 55 \)[/tex] degrees, the temperature in Celsius is approximately [tex]\( 12.78 \)[/tex] degrees.
