# describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities. x^2 + y^2 + z^2 <= 1

Question
describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities. $$\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}\le{1}$$

2021-02-12
As $$\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}={1}$$ represent a sphere. Which have radius 1 and center at the point (0,0,0). So that,
The inequalities $$\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}\le{1}$$ represents all the points inside the sphere.

### Relevant Questions

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) $$\displaystyle{x}\le{y}^{2},{0}\le{z}\le{2}.$$
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$\displaystyle{x}^{{2}}+{\left({y}-{1}\right)}^{{2}}+{z}^{{2}}={4},{y}={0}$$
Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points (if any).
$$\displaystyle{x}+{y}\ge{5}{\left({1}\right)}$$
$$\displaystyle{x}\le{10}{\left({2}\right)}$$
$$\displaystyle{y}\le{5}{\left({3}\right)}$$
$$\displaystyle{x},{y}\ge{0}{\left({4}\right)}$$
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$\displaystyle{x}^{{2}}+{y}^{{2}}={4},{z}={y}$$
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. All vectors (x, y, z) in $$V_3$$ whose components satisfy a system of three linear equations of the form:
$$a_{11}x+a_{12}y+a_{13}z=0$$
$$a_{21}x+a_{22}y+a_{23}z=0$$
$$a_{31}x+a_{32}y+a_{33}z=0$$
An objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$
Describe the graphs of the equations and inequalities. $$x^{2}+y^{2}=0$$
Describe the graphs of the equations and inequalities. $$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={0}$$
$$\displaystyle{5}\le{3}+{\left|{2}{x}-{7}\right|}$$
Describe the solution set to the system of inequalities. $$\displaystyle{x}\ge{0},{y}\ge{0},{x}\le{1},{y}\le{1}$$