Describe the sets of points in space whose coordinates satisfy

Hailee Cline

Hailee Cline

Answered question

2022-01-24

Describe the sets of points in space whose coordinates satisfy the inequality or combination of equations and inequalities.
1x2+y2+z24

Answer & Explanation

Karly Logan

Karly Logan

Beginner2022-01-25Added 11 answers

The given combinations of equations and inequalities is
1x2+y2+z24
Write the standard equation for the sphere of radius a and center
(x0,y0,z0) is (xx0)2+(yy0)2+(zz0)2=a2
The equation (x0)2+(y0)2+(z0)2=1
Compare the equations, the center C is (0,0,0) and radius a is 1.
The equation (x0)2+(y0)2+(z0)2=22
Compare the equations, the center C is (0,0,0) and radius a is 2.
For 1x2+y2+z24 in the Cartesian coordinate system represents that the solid sphere enclosed between the radius 1 and radius 2 which centered at the origin (0,0,0).
Hence, the set of points in space whose coordinates satisfy the given combinations 1x2+y2+z24 is the solid enclosed between the sphere of radius 1 unit and 2 unit centered at the origin.

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