Describe in words the region of RR^{3} represented by the equation or inequality. z geq -1

Describe in words the region of RR^{3} represented by the equation or inequality. z geq -1

Question
Alternate coordinate systems
asked 2020-11-23
Describe in words the region of \(RR^{3}\) represented by the equation or inequality.
\(z \geq -1\)

Answers (1)

2020-11-24
\(RR^{3}\) is the three dimensional coordinate system which contains x, y, and z-coordinates.
The equation \(z \geq -1\ in\ RR^{3}\)
represents the set \({(x, y, z)|z \geq-1},\)
which is the set of all points in \(RR^{3}\) whose z-coordinate is greater than or equal to 8 and x, y-coordinates are any values.
The equation \(z = -1\) is sketched as shown below in Figure 1.
image
Thus, the equation \(z \geq -1\ in\ RR^{3}\)
represents a half-space that consists of all points which are on or above the plane \(z = -1.\)
0

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