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2 2 X + 9 16 2 x²+(-4)² ≥4 -≥1 X =) X Ś

2 2 X + 9 16 2 x²+(-4)² ≥4 -≥1 X =) X Ś

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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**Graphing Solutions to a System of Inequalities** The problem is to graph the solution to the following system of inequalities: 1. \(\frac{x^2}{9} + \frac{y^2}{16} \geq 1\) 2. \(x^2 + (y - 4)^2 \geq 4\) **Graph Explanation** - **Coordinate Plane:** The graph is plotted on a standard Cartesian coordinate plane with \(x\)- and \(y\)-axes ranging from \(-6\) to \(6\). - **Inequalities:** - The first inequality represents an outside area of an ellipse centered at the origin with semi-major axis length 4 along the \(y\)-axis and semi-minor axis length 3 along the \(x\)-axis. - The second inequality represents the outside region of a circle centered at \((0, 4)\) with a radius of 2. - **Graphing Tools:** - Various tools are available for drawing and editing geometric figures such as lines, curves, and shapes. This information is essential for visualizing and understanding the solution set of the given system of inequalities on a graph.
Transcribed Image Text:**Graphing Solutions to a System of Inequalities** The problem is to graph the solution to the following system of inequalities: 1. \(\frac{x^2}{9} + \frac{y^2}{16} \geq 1\) 2. \(x^2 + (y - 4)^2 \geq 4\) **Graph Explanation** - **Coordinate Plane:** The graph is plotted on a standard Cartesian coordinate plane with \(x\)- and \(y\)-axes ranging from \(-6\) to \(6\). - **Inequalities:** - The first inequality represents an outside area of an ellipse centered at the origin with semi-major axis length 4 along the \(y\)-axis and semi-minor axis length 3 along the \(x\)-axis. - The second inequality represents the outside region of a circle centered at \((0, 4)\) with a radius of 2. - **Graphing Tools:** - Various tools are available for drawing and editing geometric figures such as lines, curves, and shapes. This information is essential for visualizing and understanding the solution set of the given system of inequalities on a graph.
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