To determine: Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities: a) y≥x2,z≥0, b) x≤y2,0≤z≤2.

Question

To determine:  Find the sets of  points in space whose coordinates satisfy the given combinations of equation and inequalities:  a) y≥x2,z≥0,  b) x≤y2,0≤z≤2.

Aamina Herring · Accepted Answer

a) Generally, the plane is determined by the coordinated axis is the xy-plane, whose standard equation by z=0. From equation y≥x2,z≥0,y=x2 represent the parabola curve in the xy-plane and all point above the region z=0. Figure 1 shows for y≥x2,z≥0 in the Cartesian coordinate system.  Thuse, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for y≥x2,z≥0 is the region inside the parabola y≥x2 in the xy-plane. b) From equation x≤y2,0≤z≤2,x=y2 represent the parabola curve in the xy-plane in the region on or to the left of the parabola and also have all point above the region from z=0→z=2. Figure 2 shows for x≤y2,0≤z≤2 in the Cartesian coordinate system.  Thus, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for x≤y2,0≤x≤2 is the region on or to the left the parabola x≤y2 in the xy-plane and all points from z=0→z=2.

To determine: Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities: a) displaystyle{y}ge{x}^{2},{z}ge{0}, b) displaystyle{x}le{y}^{2},{0}le{z}le{2}.

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