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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