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Find Mx,My , and xˉ\bar{x} yˉ\bar {y} ) for the Lamina of Uniform Density

Question 2

Multiple Choice

Find Mx,My , and ( xˉ\bar{x} , yˉ\bar {y} ) for the lamina of uniform density ρ\rho text bounded by the graphs


A)
Mx=1,0245,My=0xˉ=11213,yˉ=73\begin{array} { l } M _ { x } = \frac { 1,024 } { 5 } , M _ { y } = 0 \\\bar { x } = \frac { 112 } { 13 } , \bar { y } = \frac { 7 } { 3 }\end{array}
B)
Mx=1285ρ,My=8,19211ρxˉ=11213,yˉ=145\begin{array} { l } M _ { x } = \frac { 128 } { 5 } \rho\\ , M _ { y } = \frac { 8,192 } { 11 } \rho \\ \bar { x } = \frac { 112 } { 13 } , \bar { y } = \frac { 14 } { 5 }\end{array}
C)
Mx=1,0245ρ,My=8,19211ρ,xˉ=11211,yˉ=145\begin{array} { l } M _ { x } = \frac { 1,024 } { 5 } \rho , M _ { y } = \frac { 8,192 } { 11 } \rho , \\\bar { x } = \frac { 112 } { 11 } , \bar { y } = \frac { 14 } { 5 }\end{array}
D)
Mx=5125ρ,My=8,19211ρxˉ=11211,yˉ=73\begin{array} { l } M _ { x } = \frac { 512 } { 5 } \rho\\ , M _ { y } = \frac { 8,192 } { 11 } \rho \\\bar { x } = \frac { 112 } { 11 } , \bar { y } = \frac { 7 } { 3 }\end{array}
E)
Mx=0,My=8,19211ρ M_{x}=0, M_{y}=\frac{8,192}{11} \rho
xˉ=1129,yˉ=563 \bar{x}=\frac{112}{9}, \bar{y}=\frac{56}{3}

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