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}.

Kaycee Roche 2020-11-05 Answered
To determine:
Find the sets of points in space whose coordinates satisfy the given combinations of equation and inequalities:
a) yx2,z0,
b) xy2,0z2.
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Expert Answer

Aamina Herring
Answered 2020-11-06 Author has 85 answers

a)
Generally, the plane is determined by the coordinated axis is the xy-plane, whose standard equation by z=0.
From equation yx2,z0,y=x2 represent the parabola curve in the xy-plane and all point above the region z=0.
Figure 1 shows for yx2,z0 in the Cartesian coordinate system.
image
Thuse, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for yx2,z0 is the region inside the parabola yx2 in the xy-plane.
b)
From equation xy2,0z2,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=0z=2.
Figure 2 shows for xy2,0z2 in the Cartesian coordinate system.
image
Thus, the sets of points in space whose coordinates satisfy the given combinations of equations and inequalities for xy2,0x2 is the region on or to the left the parabola xy2 in the xy-plane and all points from z=0z=2.

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