Question

Describe the set of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities.

a. 1 x2 + y2 + z2 25

b. x2 + y2 + z2 s25, x 20

A. The solid ball of radius 5 centered at (0,0,0) with the sphere of radius 1 centered at (0,0,0) removed.

B. The sphere of radius 5 centered at (0,0,0) together with the solid ball of radius 1 centered at (0,0,0).

C. The solid ball of radius 5 centered at (0,0,0) with the interior of the solid ball of radius 1 centered at (0,0,0) removed.

D. The sphere of radius 5 centered at (0,0,0) together with the sphere of radius 1 centered at (0,0,0).

Answer 1

The correct format of the question is

Describe the set of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities.

a. $1\leq x^2 + y^2 + z^2 \leq 25$

b. $x^2 + y^2 + z^2 \leq 25, x \geq 0$

Answer:

(C).The solid ball of radius 5 centered at (0,0,0) with the interior of the solid ball of radius 1 centered at (0,0,0) removed.

Step-by-step explanation:

These are the equation of Spheres

In the equation $1\leq x^2 + y^2 + z^2 \leq 25$, when we will take square root of 25 we will get radius as 5 so the Sphere is varying from radius 1 to 5, Which will make it into a Solid sphere with the center at (0, 0, 0)

In the equation $x^2 + y^2 + z^2 \leq 25, x \geq 0$ it is given that the sphere is less than

radius 5 units.

Also there will be no sphere with radius from 0 to 1 because the sphere is starting from radius 1 and increasing till radius 5.

Therefore, The sphere is a solid increasing from radius 1 to 5.

and another solid sphere is removed from inside with radius increasing from 0 to 1.