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categoryرياضيات
schoolبكالوريوس
event_available2026-07-14
السؤال
Transcribed Image Text:
(a) Describe the surface r = constant in the cylindrical coordinate system.
For a positive constant c, the surface is a cylinder perpendicular to the xy plane
plane parallel to the xy plane is a circle of radius c. If c = 0, the surface is the --Select---; if c < 0, --Select---
with axis the z axis
and such that the intersection of this cylinder with any
Describe the surface = constant in the cylindrical coordinate system.
The surface is a plane perpendicular to the ---Select---. The intersection with this plane is ---Select---
Describe the surface z = constant in the cylindrical coordinate system.
For a positive constant c, the surface is a plane parallel to the ---Select-- c units ---Select--- the plane. If c < 0, the plane is |c| units ---Select--- the
-Select-
(b) Describe the surface p = constant in the spherical coordinate system.
For a positive constant c, the surface is a sphere with radius
--Select-
Describe the surface = constant in the spherical coordinate system.
If c 0, the surface is ---Select---
If c < 0, the surface is
The surface is a plane perpendicular to the ---Select---. The intersection with this plane is --Select--
Describe the surface = constant in the spherical coordinate system.
If p = 0, the surface is ---Select---
If л, the surface is ---Select---
÷
If q?
the surface is the cone z = a√√√x² + y² + z², where
a = cos(q). If q?
the surface is the plane z = 0.
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