Graph the inequality subject to the nonnegative restrictions. 15x-24y <0, x ≥ 0, y ≥0 Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints. Click to enlarge graph -12-10 Ay 12- 10- 8- 6- -10- 10 12 A
Graph the inequality subject to the nonnegative restrictions. 15x-24y <0, x ≥ 0, y ≥0 Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints. Click to enlarge graph -12-10 Ay 12- 10- 8- 6- -10- 10 12 A
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
24
![### Graphing Inequalities with Nonnegative Constraints
#### Objective:
Graph the inequality subject to the nonnegative restrictions given.
\[ 15x - 24y < 0, \quad x \geq 0, \quad y \geq 0 \]
#### Instructions:
1. **Identify the Inequality:**
The inequality to be graphed is:
\[ 15x - 24y < 0 \]
2. **Nonnegative Restrictions:**
The graph must only show the area where:
\[ x \geq 0 \]
\[ y \geq 0 \]
3. **Graphical Representation:**
- On the right, there is a graph with \(x\)-axis and \(y\)-axis ranging from -12 to 12.
- Use the graph to accurately represent the inequality.
4. **Steps to Graph:**
- **Boundary Line:** Start by graphing the boundary line where \( 15x - 24y = 0 \). This can be rewritten to \( y = \frac{15}{24}x \) or \( y = \frac{5}{8}x \).
- **Shading the Region:** Since we have \( 15x - 24y < 0 \), shade the region below the boundary line because the inequality is less than 0.
- **Nonnegative Constraints:** Ensure that the shaded region is only in the first quadrant where both \( x \) and \( y \) are nonnegative.
#### Visual Tool:
- **Graphing Tool:**
- A clickable graphing tool icon is available to enlarge the graph for more detailed analysis.
5. **Interactive Activity:**
- Use the provided graphing tool to plot the boundary line and indicate the correct shaded region compliant with the inequality and constraints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d9df1eb-9cbe-4888-87d6-c14249115dd3%2F9efadee9-d294-43a1-8b98-c8926d1198c7%2Fvqeiiqp_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Inequalities with Nonnegative Constraints
#### Objective:
Graph the inequality subject to the nonnegative restrictions given.
\[ 15x - 24y < 0, \quad x \geq 0, \quad y \geq 0 \]
#### Instructions:
1. **Identify the Inequality:**
The inequality to be graphed is:
\[ 15x - 24y < 0 \]
2. **Nonnegative Restrictions:**
The graph must only show the area where:
\[ x \geq 0 \]
\[ y \geq 0 \]
3. **Graphical Representation:**
- On the right, there is a graph with \(x\)-axis and \(y\)-axis ranging from -12 to 12.
- Use the graph to accurately represent the inequality.
4. **Steps to Graph:**
- **Boundary Line:** Start by graphing the boundary line where \( 15x - 24y = 0 \). This can be rewritten to \( y = \frac{15}{24}x \) or \( y = \frac{5}{8}x \).
- **Shading the Region:** Since we have \( 15x - 24y < 0 \), shade the region below the boundary line because the inequality is less than 0.
- **Nonnegative Constraints:** Ensure that the shaded region is only in the first quadrant where both \( x \) and \( y \) are nonnegative.
#### Visual Tool:
- **Graphing Tool:**
- A clickable graphing tool icon is available to enlarge the graph for more detailed analysis.
5. **Interactive Activity:**
- Use the provided graphing tool to plot the boundary line and indicate the correct shaded region compliant with the inequality and constraints.
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