Find an equation in rectangular coordinates for the cylindrical equation r = 6z
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
2.7.2
![**Problem Statement**
Convert the given cylindrical equation to rectangular coordinates:
\[ r = 6z \]
**Solution**
To convert from cylindrical to rectangular coordinates, use the following relationships:
- \( r = \sqrt{x^2 + y^2} \)
- \( z = z \)
Substitute these into the equation \( r = 6z \):
\[ \sqrt{x^2 + y^2} = 6z \]
Square both sides to eliminate the square root:
\[ x^2 + y^2 = (6z)^2 \]
\[ x^2 + y^2 = 36z^2 \]
This represents the equation in rectangular coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21e8a523-579f-40b9-8f0a-805524283a8d%2F3b222708-67d9-4175-8dbe-a0674962989b%2Fx5tkb8p_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Convert the given cylindrical equation to rectangular coordinates:
\[ r = 6z \]
**Solution**
To convert from cylindrical to rectangular coordinates, use the following relationships:
- \( r = \sqrt{x^2 + y^2} \)
- \( z = z \)
Substitute these into the equation \( r = 6z \):
\[ \sqrt{x^2 + y^2} = 6z \]
Square both sides to eliminate the square root:
\[ x^2 + y^2 = (6z)^2 \]
\[ x^2 + y^2 = 36z^2 \]
This represents the equation in rectangular coordinates.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
