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Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² + (z-1)² = 9, x ≥-2/y20 and z > 1

Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² + (z-1)² = 9, x ≥-2/y20 and z > 1

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Please describe the surface and its orientation and sketch it showing the points. Please read all question’s instructions.
**Problem 1: Analyzing a Geometric Set** **Objective:** Describe and sketch the set of points defined by the given conditions. **Given Equations and Conditions:** 1. \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) 2. \(x \geq -2\) 3. \(y \geq 0\) 4. \(z \geq 1\) **Explanation:** - The first equation \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) describes a sphere centered at \((-2, 0, 1)\) with a radius of 3. - The additional conditions \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\) restrict this sphere to specific regions, forming a subset of the sphere. **Sketching Guidance:** - Begin with the complete sphere centered at \((-2, 0, 1)\). - Apply the conditions as constraints, sketching only the part of the sphere that satisfies all three inequalities. - This can be visualized as an upper quadrant portion of the sphere in the positive \(y\) and \(z\) directions, and to the right of the plane \(x = -2\).
Transcribed Image Text:**Problem 1: Analyzing a Geometric Set** **Objective:** Describe and sketch the set of points defined by the given conditions. **Given Equations and Conditions:** 1. \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) 2. \(x \geq -2\) 3. \(y \geq 0\) 4. \(z \geq 1\) **Explanation:** - The first equation \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) describes a sphere centered at \((-2, 0, 1)\) with a radius of 3. - The additional conditions \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\) restrict this sphere to specific regions, forming a subset of the sphere. **Sketching Guidance:** - Begin with the complete sphere centered at \((-2, 0, 1)\). - Apply the conditions as constraints, sketching only the part of the sphere that satisfies all three inequalities. - This can be visualized as an upper quadrant portion of the sphere in the positive \(y\) and \(z\) directions, and to the right of the plane \(x = -2\).
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