$\"\"$

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The equations are $\"\"$ and $\"\"$ .

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Observe the diagram:

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Since the center of mass lies on the axis of symmetry, $\"\"$ .

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Find the area of semi circle.

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The area of the semi circle is $\"\"$ .

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Find the $\"\"$ -coordinate of the centroid.

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

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$\"\"$ .

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Therefore, centroid is $\"\"$ .

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$\"\"$

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$\"\"$ .