To write: The inequalites to describe the region of a solid cylinder that lies on or below the plane displaystyle{z}={8} and on or above the disk in the xy - plane with the center at origin and radius 2.

Jaden Easton 2020-12-24 Answered
To write: The inequalites to describe the region of a solid cylinder that lies on or below the plane z=8 and on or above the disk in the xy - plane with the center at origin and radius 2.
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Expert Answer

casincal
Answered 2020-12-25 Author has 82 answers
R3 is the three dimensional coordinate system which contains x, y, and z - coordinates.
The equation z=8R3 represents the set {(x,y,z)|z=8}, which is the set of all points in R3 whose z - coordinate is 8 and x, y - coordinates are any values.
The inequality to describe the region in which all points lie on or below the plane z=8 is 0z8.
The equation to describe the region of cylinder with center at the origin and radius of 2 units on the xy-plane is x2+y2=4. But, it is required to describe the region in which all points lie on or above the disk in the xy - plane.
The inequality to describe the region of solid cylinder that lies on or above the disk in the xy - plane wiwth center at origin and radius of 2 units x2+y24.
Thus, the inequality to describe the region of solid cylinder that lies on or below the plane z=8 and on or above the disk in the xy - plane with center at the origin and radius 2 is x2+y24,0z8.
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