Describe the sets of points in space whose coordinates satisfy the inequality or combination of equations and inequalities. 1≤x2+y2+z2≤4

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Describe the sets of points in space whose coordinates satisfy the inequality or combination of equations and inequalities.     1≤x2+y2+z2≤4

Karly Logan · Accepted Answer

The given combinations of equations and inequalities is    1≤x2+y2+z2≤4    Write the standard equation for the sphere of radius a and center    (x0,y0,z0) is (x−x0)2+(y−y0)2+(z−z0)2=a2    The equation (x−0)2+(y−0)2+(z−0)2=1    Compare the equations, the center C is (0,0,0) and radius a is 1.    The equation (x−0)2+(y−0)2+(z−0)2=22    Compare the equations, the center C is (0,0,0) and radius a is 2.    For 1≤x2+y2+z2≤4 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 1≤x2+y2+z2≤4 is the solid enclosed between the sphere of radius 1 unit and 2 unit centered at the origin.

Describe the sets of points in space whose coordinates satisfy

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