   Chapter 8, Problem 78RE

Chapter
Section
Textbook Problem

Centroid In Exercises 77 and 78, find the centroid of the region bounded by the graphs of the equations using any method. ( x − 1 ) 2 + y 2 = 1 ,   ( x − 4 ) 2 + y 2 = 4

To determine

To calculate: The centroid that is bounded by graphs of region for the equations (x1)2+y2=1 and (x4)2+y2=4.

Explanation

Given:

The region is bounded by (x1)2+y2=1 and (x4)2+y2=4.

Formula used:

The centroid point is:

x¯=A1x1+A2x2A

Where, A=A1+A2 is the area of the region.

Here, x1 is centroid of region 1 and x2 is the centroid of region 2.

Calculation:

The equation of circle with radius 1 and centre (1,0) is (x1)2+y2=1.

The equation of circle with radius 2 and centre (4,0) is (x4)2+y2=4.

∴, the graph obtained is:

The graph obtained has two circles with radius1 and radius 2

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