The Cartesian equation associated with a sphere of radius 2 centred at (0, 0, 2) is x² + y² + 22 – 4z = 0. (a) Show that the sphere of radius 2 centred at (x, y, z) = (0, 0, 2) can be represented by p = 4 cos(4) using Spherical Coordinates. (b) What is the distance from the origin to the point (x, y, z) = (0,2, 2), which is on the bottom boundary of the upper hemisphere? [Hint: Use the distance formula involving p².] (c) State restrictions on o and 0 so that the equation developed in part (a) will generate the upper hemisphere.
The Cartesian equation associated with a sphere of radius 2 centred at (0, 0, 2) is x² + y² + 22 – 4z = 0. (a) Show that the sphere of radius 2 centred at (x, y, z) = (0, 0, 2) can be represented by p = 4 cos(4) using Spherical Coordinates. (b) What is the distance from the origin to the point (x, y, z) = (0,2, 2), which is on the bottom boundary of the upper hemisphere? [Hint: Use the distance formula involving p².] (c) State restrictions on o and 0 so that the equation developed in part (a) will generate the upper hemisphere.
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 Cartesian equation associated with a sphere of radius 2 centred at (0, 0, 2) is x² + y²+
2² – 4z = 0.
(a) Show that the sphere of radius 2 centred at (x, y, z) = (0,0, 2) can be represented by
p = 4 cos(4) using Spherical Coordinates.
(b) What is the distance from the origin to the point (x, y, z) = (0,2, 2), which is on the
bottom boundary of the upper hemisphere?
[Hint: Use the distance formula involving p².]
(c) State restrictions on o and 0 so that the equation developed in part (a) will generate the
upper hemisphere.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb092f731-30ff-4674-aac4-3dfd738c2223%2Fba10a244-c149-4481-b70d-40e97c5603c9%2F6bjiivn_processed.png&w=3840&q=75)
Transcribed Image Text:The Cartesian equation associated with a sphere of radius 2 centred at (0, 0, 2) is x² + y²+
2² – 4z = 0.
(a) Show that the sphere of radius 2 centred at (x, y, z) = (0,0, 2) can be represented by
p = 4 cos(4) using Spherical Coordinates.
(b) What is the distance from the origin to the point (x, y, z) = (0,2, 2), which is on the
bottom boundary of the upper hemisphere?
[Hint: Use the distance formula involving p².]
(c) State restrictions on o and 0 so that the equation developed in part (a) will generate the
upper hemisphere.
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