Find the mass and the center of mass of the lamina occupying the region $R$, where $R$ is the triangular region with vertices $( 0,0 ) , ( 5,2 )$, and $( 10,0 )$, and having the mass density $\rho ( x , y ) = x$.
A)
$$m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$$
B)
$$m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$$
C)
$$m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$$
D)
$$m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$$

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The Answer of Find the mass and the center of mass of the lamina occupying the region $R$, where $R$ is the triangular region with vertices $( 0,0 ) , ( 5,2 )$, and $( 10,0 )$, and having the mass density $\rho ( x , y ) = x$.
A)
$$m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$$
B)
$$m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 2 } { 3 } , \frac { 35 } { 6 } \right)$$
C)
$$m = 10 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$$
D)
$$m = 50 , ( \bar { x } , \bar { y } ) = \left( \frac { 35 } { 6 } , \frac { 2 } { 3 } \right)$$

Find the Mass and the Center of Mass of the Lamina