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Numerade Educator

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Problem 31 Easy Difficulty

Describe in words the region of $ \mathbb{R}^3 $ represented by the equation(s) or inequality.

$ x^2 + y^2 = 4 $, $ z = -1 $

Answer

$x^{2}+y^{2}=4, z=-1$ is a circle with radius 2 and center $(0,0,-1)$ lying on
the plane $z=-1$

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Video Transcript

Okay, so if we take a look at this here, if we look at this picture in the X Y plain, this part is a cylinder Dillinger. But on ly at Z equals negative one. So it's taking one slice of a cylinder. So one slice of cylinder and one slice of a cylinder is a circle. So it's a circle, uh, down here with the radius one at Z equals negative one.