To graph: The sketch of the solution set of system of nonlinear inequality

Chesley 2020-11-05 Answered

To graph: The sketch of the solution set of system of nonlinear inequality
[x2 + y2 9]
x2 + y2 25
y |x|

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Expert Answer

komunidadO
Answered 2020-11-06 Author has 86 answers

Graph:
Consider the inequalities [x2 + y2 9]
Since the equation is in the form of (x  h)2 + (y  k)2=r2,here(h, k) are the coordinates for the center and r is the radius of the circle.
The equation [x2 + y2=9] represents a circle with its center at [0 0]and radius 3 units.
The inequality [x2 + y2 9] denotes the region on and outside the circle [x2 + y2=9]
Test the point [0 0] which lies inside the circle as follows:
x2 + y2 9
02 + 02 9
0 9
This inequality does not hold true for the origin which lies inside the circle. Thus the region on and outside the represents the inequality.
Draw the graph of the inequality as follows:
Step 1: Mark the center of circle in the rectangular coordinate system. The center of the circle [x2 + y2=9]is[0 0]
Step 2: Mark the points at 3 units distance from the center. Mark the points [3 0],[0 3],[3 0],[0 3]
Step 3: Connect the points using a smooth circle with center at origin keeping the radius 3 units.
Step 4: Shade the region outside the circle to denote the solution set of the inequality.
Now, consider the inequality [x2 + y2 25]
Since the equation is in the form of (x  h)2+ (yk)2=r2,here(h, k) are the coordinates for the center and r is the radius of the circle.
The equation [x2 + y2=25] represents a circle with its center at [0 0] and radius 5 units.
The inequality [x2 + y2 25] denotes the region outside the circle [x2 + y2=25]
Test the point [0 0] which lies inside the circle as follows:
[x2 + y2 25]
02 + 02 25
0 25
This inequality holds true for the origin which lies inside the circle. Thus the region on and inside the circle represents the inequality.
Draw the graph of the inequality as follows:
Step 1: Mark the center of circle in the rectangular coordinate system. The center of the circle x2 + y2=25 is (0, 0)
Step 2: Mark the points at 5 units distance from the center. Mark the points (5, 0), (0, 5), (5, 0), (0, 5)
Step 3: Connect the points using a smooth circle with center at origin keeping the radius 5 units.
Step 4: Shade the region outside the circle to denote the solution set of the inequality.
Now, consider the inequality.
Consider the inequality

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