   Chapter 12.1, Problem 35E

Chapter
Section
Textbook Problem

# Describe in words the region of ℝ3 represented by the equation(s) or inequality.35. 1 ≤ x2 + y2 + z2 ≤ 5

To determine

To describe: The representation of equation 1x2+y2+z25 in 3 .

Explanation

3 is the three dimensional coordinate system which contains x, y, and z-coordinates.

Consider a sphere with center C(h,k,l) and radius r.

Formula:

Write the expression for a sphere with center C(h,k,l) and radius r.

(xh)2+(yk)2+(zl)2=r2 (1)

Here,

(h,k,l) is the center of a sphere and

r is the radius of a sphere.

The equation x2+y2+z2=1 is also written as follows.

(x0)2+(y0)2+(z0)2=12 (2)

As the equation (2) is similar to the equation (1), the equation x2+y2+z2=1 represents a sphere with radius 1 and the center is at the origin (0,0,0)

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