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Chapter 9: Q. 12 (page 730)

Explain why the inequality 0鈮�r鈮�2 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 , 0鈮�r鈮�1with radius 1 .

Step by step solution

01

Given information

The inequality 0鈮�r鈮�2

02

Simplification

Consider the inequality 0鈮�r鈮�2of 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 .

\

The inequality 0鈮�r鈮�2 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 0鈮�r鈮�1represents a circle with radius 1 and the values of the inequality lies inside the circle.

Thus, the inequality 0鈮�r鈮�2describes the points inside the circle with radius 2 .

The inequality 0鈮�r鈮�1describes the points inside the circle with radius 1 .

Therefore, the answer is Inside the circle ,0鈮�r鈮�1 with radius 1 .

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