Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a. x² + (y + 3)² + (z − 1)² = 9, x ≥ 0, y2-3, and z> 1 b. y² + (z+ 2)² = 4,0 ≤ x ≤ 2, and z<-2.

a. x² + (y + 3)² + (z − 1)² = 9, x ≥ 0, y2-3, and z> 1 b. y² + (z+ 2)² = 4,0 ≤ x ≤ 2, and z<-2.

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
See similar textbooks
icon
Related questions
Question
**Problem Description:** Describe and sketch the following sets of points defined by the given conditions. **a.** \( x^2 + (y + 3)^2 + (z - 1)^2 = 9 \), where \( x \geq 0 \), \( y \geq -3 \), and \( z \geq 1 \). **b.** \( y^2 + (z + 2)^2 = 4 \), where \( 0 \leq x \leq 2 \) and \( z \leq -2 \). --- **Explanation:** - **For part a:** - The equation \( x^2 + (y + 3)^2 + (z - 1)^2 = 9 \) represents a sphere with a radius of 3 centered at the point (0, -3, 1). - The constraints \( x \geq 0 \), \( y \geq -3 \), and \( z \geq 1 \) limit the sphere to a specific region, effectively taking only the part of the sphere that lies within these bounds. - **For part b:** - The equation \( y^2 + (z + 2)^2 = 4 \) represents a cylinder centered on the y-axis running parallel to the x-axis with a radius of 2. - The constraints \( 0 \leq x \leq 2 \) and \( z \leq -2 \) restrict this cylinder to a specific section along the x-axis and below \( z = -2 \). The tasks require sketching these geometric figures following the given constraints to visualize the shapes in the appropriate coordinate spaces.
Transcribed Image Text:**Problem Description:** Describe and sketch the following sets of points defined by the given conditions. **a.** \( x^2 + (y + 3)^2 + (z - 1)^2 = 9 \), where \( x \geq 0 \), \( y \geq -3 \), and \( z \geq 1 \). **b.** \( y^2 + (z + 2)^2 = 4 \), where \( 0 \leq x \leq 2 \) and \( z \leq -2 \). --- **Explanation:** - **For part a:** - The equation \( x^2 + (y + 3)^2 + (z - 1)^2 = 9 \) represents a sphere with a radius of 3 centered at the point (0, -3, 1). - The constraints \( x \geq 0 \), \( y \geq -3 \), and \( z \geq 1 \) limit the sphere to a specific region, effectively taking only the part of the sphere that lies within these bounds. - **For part b:** - The equation \( y^2 + (z + 2)^2 = 4 \) represents a cylinder centered on the y-axis running parallel to the x-axis with a radius of 2. - The constraints \( 0 \leq x \leq 2 \) and \( z \leq -2 \) restrict this cylinder to a specific section along the x-axis and below \( z = -2 \). The tasks require sketching these geometric figures following the given constraints to visualize the shapes in the appropriate coordinate spaces.
Expert Solution
Step 1

Advanced Math homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS