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Explain why the inequality 0r2 describes the points inside or on the circle with radius 2 and centered at the origin. Use a similar inequality to describe the points in the annulus shown here:

Short Answer

Expert verified

The answer is Inside the circle , 0r1with radius 1 .

Step by step solution

01

Given information

The inequality 0r2

02

Simplification

Consider the inequality 0r2of the annulus.

The objective is to show an inequality to describe the points in the annulus. The given annulus is with center (0,0) and of radius 4 .

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The inequality 0r2 represents a circle with radius 2 .

Thus, the points of the inequality represent the values less than 2 which are inside the circle.

Now the inequality 0r1represents a circle with radius 1 and the values of the inequality lies inside the circle.

Thus, the inequality 0r2describes the points inside the circle with radius 2 .

The inequality 0r1describes the points inside the circle with radius 1 .

Therefore, the answer is Inside the circle ,0r1 with radius 1 .

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