Find the Center of Mass of a Thin Plate Covering $y = \frac { 8 } { x }$

question 254

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region between the curve $y = \frac { 8 } { x }$ and the $x$ -axis from $x = 1$ to $x = 9$ , with density $\delta ( x ) = \sqrt { x }$

• A) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 4 } { 3 }\)
• B) \(\bar { x } = 5 , \bar { y } = \frac { 8 } { 3 }\)
• C) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 128 } { 3 }\)
• D) \(\bar { x } = \frac { 13 } { 3 } , \bar { y } = \frac { 8 } { 5 }\)

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