Explanation Given: The inequalities are x 2 + y 2 > 1 and x 2 + y 2 < 4 . Graph: Consider the inequalities and substitute the equal symbol at the place of inequality and rewrite the equation as shown below: Now the equations are x 2 + y 2 = 1 And, x 2 + y 2 = 4 The first equation x 2 + y 2 = 1 represents a circle origin at ( 0 , 0 ) and radius 1 that can be rewritten as ( x − 0 ) 2 + ( y − 0 ) 2 = 1 2 . Plot the graph using the equation of this circle in rectangular coordinate system, origin at ( 0 , 0 ) and radius r = 1 . Now this circle divides the plane into three regions: the circle itself, the inner plane of the circle, and the outer plane of the circle. Now, take origin ( 0 , 0 ) as a test point and check the region in the graph to shade: Check whether the test point satisfies the inequality: x 2 + y 2 > 1 0 + 0 > ? 1 0 > 1 Since the test point does not satisfy the inequality, thus, shade the outer plane of the circle, that is, away from the origin ( 0 , 0 )

7th Edition

ISBN: 9780137394173

Author: Blitzer

Publisher: VST

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 8, Problem 9T

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To graph: The solution set of a system of inequality x2+y2>1 and x2+y2<4.

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Chapter 8, Problem 8T

Chapter 8, Problem 10T

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To graph: The solution set of a system of inequality x 2 + y 2 > 1 and x 2 + y 2 < 4 .

Solution Summary: The author illustrates the solution set of a system of inequality x2+y2.

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To graph: The solution set of a system of inequality x2+y2>1 and x2+y2<4.

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Chapter 8 Solutions

To graph: The solution set of a system of inequality x 2 + y 2 &gt; 1 and x 2 + y 2 &lt; 4 .

Solution Summary: The author illustrates the solution set of a system of inequality x2+y2.

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To graph: The solution set of a system of inequality x2+y2>1 and x2+y2<4.

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Chapter 8 Solutions

To graph: The solution set of a system of inequality x 2 + y 2 > 1 and x 2 + y 2 < 4 .