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Seven solar panels were installed in an open field. Each panel was installed at a different fixed tilt angle. The energy output of the seven panels was then measured over a period of exactly one year (365 days).

The results can be found in the table below:
\begin{tabular}{|c|c|c|}
\hline
Panel number & \begin{tabular}{c}
Tilt (angle with the \\ horizontal plane)
\end{tabular} & \begin{tabular}{c}
Total annual energy output of the panel \\ (kWh/year)
\end{tabular} \\
\hline
1 & [tex]$0^{\circ}$[/tex] & 350 \\
\hline
2 & [tex]$10^{\circ}$[/tex] & 370 \\
\hline
3 & [tex]$20^{\circ}$[/tex] & 390 \\
\hline
4 & [tex]$30^{\circ}$[/tex] & 410 \\
\hline
5 & [tex]$40^{\circ}$[/tex] & 385 \\
\hline
6 & [tex]$50^{\circ}$[/tex] & 360 \\
\hline
7 & [tex]$90^{\circ}$[/tex] & 220 \\
\hline
\end{tabular}

4.1 Draw a bar graph to illustrate the annual energy output at different tilt angles for the seven solar panels. (6)

4.1.1 Which tilt angle gives the highest annual energy output? (1)



Answer :

GinnyAnswer
### Solution:

#### 4.1 Drawing a Bar Graph:
To illustrate the annual energy output at different tilt angles for the seven solar panels, we need to plot a bar graph. Here are the steps to create it manually:

1. Prepare the data from the table:
- Tilt angles: [tex]\( 0^\circ, 10^\circ, 20^\circ, 30^\circ, 40^\circ, 50^\circ, 90^\circ \)[/tex]
- Energy outputs: 350, 370, 390, 410, 385, 360, 220 (in kWh/year)

2. Set up the axes:
- The x-axis will represent the tilt angles (in degrees).
- The y-axis will represent the annual energy output (in kWh/year).

3. Label the axes:
- x-axis: "Tilt Angle (degrees)"
- y-axis: "Annual Energy Output (kWh/year)"

4. Title the graph: "Annual Energy Output at Different Tilt Angles"

5. Draw bars to represent energy output for each tilt angle. For each angle on the x-axis, draw a bar extending up to the respective energy output value on the y-axis.

Here is a rough sketch of the bar graph:

```
Annual Energy Output at Different Tilt Angles

| 450+-----------------------------------------------------+
| | x |
| 400+| x |
| | x |
| 350+| x x |
| | x x |
| 300+| x x |
| +-----x-----x-----x-----x-----x-----x-----x----------+
| 0° 10° 20° 30° 40° 50° 90°
Tilt Angle (degrees)

```

In the graph above:
- Each 'x' represents the top of the bar for respective tilt angles.

#### 4.1.1 Which tilt angle gives the highest annual energy output?

To determine which tilt angle provides the highest annual energy output, we need to look at the energy outputs provided for each tilt angle and find the maximum value.

Here are the given energy outputs:
- [tex]\(0^\circ\)[/tex]: 350 kWh/year
- [tex]\(10^\circ\)[/tex]: 370 kWh/year
- [tex]\(20^\circ\)[/tex]: 390 kWh/year
- [tex]\(30^\circ\)[/tex]: 410 kWh/year
- [tex]\(40^\circ\)[/tex]: 385 kWh/year
- [tex]\(50^\circ\)[/tex]: 360 kWh/year
- [tex]\(90^\circ\)[/tex]: 220 kWh/year

By comparing these values:

- The highest energy output is 410 kWh/year.

This occurs at a tilt angle of [tex]\(30^\circ\)[/tex].

### Answer:
The tilt angle that gives the highest annual energy output is [tex]\(30^\circ\)[/tex].

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