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29) A) Bounded B) Unbounded -10 :-5 5 10 -10 5 10 Q Unbounded D) Bounded -103 10 10 3 10

29) A) Bounded B) Unbounded -10 :-5 5 10 -10 5 10 Q Unbounded D) Bounded -103 10 10 3 10

Advanced Engineering Mathematics
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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The image displays a mathematical problem related to systems of inequalities and graph analysis. It features the following elements: **Problem Statement:** 29) - \( y > -4 \) - \( x \leq 3 \) **Graphical Solutions:** The image contains four different graphs, labeled A through D, each illustrating a possible solution set for the inequalities. The graphs display a coordinate plane with shaded regions representing the solution areas. **Detailed Graph Descriptions:** - **Graph A) Bounded:** - No shading is visible. It incorrectly suggests a bounded solution which does not align with the inequalities given. - **Graph B) Unbounded:** - The graph shows a vertical line at \( x = 3 \) with shading to the left (for \( x \leq 3 \)) and above a horizontal line at \( y = -4 \) (for \( y > -4 \)). The shaded region is a half-plane extending indefinitely. - **Graph C) Unbounded:** - Similar to Graph B, it shows shading above the line \( y = -4 \) and to the right of \( x = 3 \), which does not correctly represent the constraints \( x \leq 3 \). - **Graph D) Bounded:** - This graph displays the correct shading for \( x \leq 3 \) and \( y > -4 \). The shaded region is located to the left of \( x = 3 \) and extends upwards from \( y = -4 \), forming an unbounded solution. Each graph includes axes marked with numbers from -10 to 10, providing a clear view of the coordinate plane.
Transcribed Image Text:The image displays a mathematical problem related to systems of inequalities and graph analysis. It features the following elements: **Problem Statement:** 29) - \( y > -4 \) - \( x \leq 3 \) **Graphical Solutions:** The image contains four different graphs, labeled A through D, each illustrating a possible solution set for the inequalities. The graphs display a coordinate plane with shaded regions representing the solution areas. **Detailed Graph Descriptions:** - **Graph A) Bounded:** - No shading is visible. It incorrectly suggests a bounded solution which does not align with the inequalities given. - **Graph B) Unbounded:** - The graph shows a vertical line at \( x = 3 \) with shading to the left (for \( x \leq 3 \)) and above a horizontal line at \( y = -4 \) (for \( y > -4 \)). The shaded region is a half-plane extending indefinitely. - **Graph C) Unbounded:** - Similar to Graph B, it shows shading above the line \( y = -4 \) and to the right of \( x = 3 \), which does not correctly represent the constraints \( x \leq 3 \). - **Graph D) Bounded:** - This graph displays the correct shading for \( x \leq 3 \) and \( y > -4 \). The shaded region is located to the left of \( x = 3 \) and extends upwards from \( y = -4 \), forming an unbounded solution. Each graph includes axes marked with numbers from -10 to 10, providing a clear view of the coordinate plane.
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