Answer :
To successfully illustrate the annual energy-output at different tilt angles for the seven solar panels, we'll need to create a bar graph. Here is a detailed step-by-step process on how to go about this:
### Step-by-Step Solution
1. Collect Data:
- Tilt Angles (degrees): [tex]\( [0^{\circ}, 10^{\circ}, 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 90^{\circ}] \)[/tex]
- Energy-Outputs (kWh/year): [tex]\( [350, 370, 390, 410, 385, 360, 220] \)[/tex]
2. Create Axes:
- Horizontal Axis (X-axis): This will represent the different tilt angles.
- Vertical Axis (Y-axis): This will represent the energy output in kWh/year.
3. Bar Graph Elements:
- Bars: Each bar in the graph will represent the energy output of a solar panel at a specific tilt angle.
- Titles and Labels:
- Title of the Graph: "Annual Energy Output at Different Tilt Angles"
- Label for X-axis: "Tilt Angle (degrees)"
- Label for Y-axis: "Total Annual Energy Output (kWh/year)"
4. Plot the Bars:
- For each tilt angle, draw a bar corresponding to the energy output value.
### Example Bar Graph:
Here is a textual description of how to construct the graph without actually drawing it.
#### Graph Elements:
- X-axis:
- Mark the axis with the tilt angles: [tex]\(0^{\circ}, 10^{\circ}, 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 90^{\circ}\)[/tex]
- Y-axis:
- Create a scale from the minimum energy output (let’s say start from 0) to a little above the maximum energy output (around 420 to cover 410 for space).
#### Bars:
- For [tex]\(0^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(350\)[/tex] kWh/year.
- For [tex]\(10^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(370\)[/tex] kWh/year.
- For [tex]\(20^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(390\)[/tex] kWh/year.
- For [tex]\(30^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(410\)[/tex] kWh/year.
- For [tex]\(40^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(385\)[/tex] kWh/year.
- For [tex]\(50^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(360\)[/tex] kWh/year.
- For [tex]\(90^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(220\)[/tex] kWh/year.
### Verbal Illustration:
- Title: "Annual Energy Output at Different Tilt Angles"
- X-axis: Tilt Angle (degrees)
- Y-axis: Total Annual Energy Output (kWh/year)
The bars will then be:
- A bar at [tex]\(0^{\circ}\)[/tex] reaching 350 kWh/year.
- A bar at [tex]\(10^{\circ}\)[/tex] reaching 370 kWh/year.
- A bar at [tex]\(20^{\circ}\)[/tex] reaching 390 kWh/year.
- A bar at [tex]\(30^{\circ}\)[/tex] reaching 410 kWh/year.
- A bar at [tex]\(40^{\circ}\)[/tex] reaching 385 kWh/year.
- A bar at [tex]\(50^{\circ}\)[/tex] reaching 360 kWh/year.
- A bar at [tex]\(90^{\circ}\)[/tex] reaching 220 kWh/year.
### Conclusion:
By plotting these values on a bar graph with the specified labels and title, you will have a clear visual representation of how the annual energy output varies with different tilt angles for the solar panels. This visual tool will help in determining the optimal tilt angle for maximum energy output over a year, which in this case is [tex]\(30^{\circ}\)[/tex].
### Step-by-Step Solution
1. Collect Data:
- Tilt Angles (degrees): [tex]\( [0^{\circ}, 10^{\circ}, 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 90^{\circ}] \)[/tex]
- Energy-Outputs (kWh/year): [tex]\( [350, 370, 390, 410, 385, 360, 220] \)[/tex]
2. Create Axes:
- Horizontal Axis (X-axis): This will represent the different tilt angles.
- Vertical Axis (Y-axis): This will represent the energy output in kWh/year.
3. Bar Graph Elements:
- Bars: Each bar in the graph will represent the energy output of a solar panel at a specific tilt angle.
- Titles and Labels:
- Title of the Graph: "Annual Energy Output at Different Tilt Angles"
- Label for X-axis: "Tilt Angle (degrees)"
- Label for Y-axis: "Total Annual Energy Output (kWh/year)"
4. Plot the Bars:
- For each tilt angle, draw a bar corresponding to the energy output value.
### Example Bar Graph:
Here is a textual description of how to construct the graph without actually drawing it.
#### Graph Elements:
- X-axis:
- Mark the axis with the tilt angles: [tex]\(0^{\circ}, 10^{\circ}, 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 90^{\circ}\)[/tex]
- Y-axis:
- Create a scale from the minimum energy output (let’s say start from 0) to a little above the maximum energy output (around 420 to cover 410 for space).
#### Bars:
- For [tex]\(0^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(350\)[/tex] kWh/year.
- For [tex]\(10^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(370\)[/tex] kWh/year.
- For [tex]\(20^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(390\)[/tex] kWh/year.
- For [tex]\(30^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(410\)[/tex] kWh/year.
- For [tex]\(40^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(385\)[/tex] kWh/year.
- For [tex]\(50^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(360\)[/tex] kWh/year.
- For [tex]\(90^{\circ}\)[/tex] tilt angle, plot a bar reaching up to [tex]\(220\)[/tex] kWh/year.
### Verbal Illustration:
- Title: "Annual Energy Output at Different Tilt Angles"
- X-axis: Tilt Angle (degrees)
- Y-axis: Total Annual Energy Output (kWh/year)
The bars will then be:
- A bar at [tex]\(0^{\circ}\)[/tex] reaching 350 kWh/year.
- A bar at [tex]\(10^{\circ}\)[/tex] reaching 370 kWh/year.
- A bar at [tex]\(20^{\circ}\)[/tex] reaching 390 kWh/year.
- A bar at [tex]\(30^{\circ}\)[/tex] reaching 410 kWh/year.
- A bar at [tex]\(40^{\circ}\)[/tex] reaching 385 kWh/year.
- A bar at [tex]\(50^{\circ}\)[/tex] reaching 360 kWh/year.
- A bar at [tex]\(90^{\circ}\)[/tex] reaching 220 kWh/year.
### Conclusion:
By plotting these values on a bar graph with the specified labels and title, you will have a clear visual representation of how the annual energy output varies with different tilt angles for the solar panels. This visual tool will help in determining the optimal tilt angle for maximum energy output over a year, which in this case is [tex]\(30^{\circ}\)[/tex].
