Question

Describe, in words, the region of r 3 represented by the inequality x 2 y 2 z 2 > 2y.

Answer 1

The region represented by the inequality x^2 + y^2 + z^2 > 2y is all the points outside a sphere with radius 2, centered at (0, 1, 0).

Step-by-step explanation:

The inequality x^2 + y^2 + z^2 > 2y represents a region in 3-dimensional space. Let's break it down:

1. If we take the equation x^2 + y^2 + z^2 = 2y, it represents a sphere with radius 2 and centered at (0, 1, 0).
2. However, since we have the inequality symbol '>', it means the region is outside this sphere, i.e., the space around the sphere but not including the sphere itself.

So, in words, the region represented by the inequality is all the points in 3-dimensional space that are outside a sphere with radius 2, centered at (0, 1, 0).