Mg= SS x(3x+ xy) dydx= ! 3x +x y dydx 3x y+ X5 S bx'+ 8 x dx 3. 6. Find the center of mass of the lamina with density function p(x) = 2y + 6x in the region R = {(x,y)|0 < x < 2,0 < y< 3}. 33 (3) 23 145.5= My 9x + 18 x] 9(1) + 9 (2)" = 18+ 36 =541 ique i %3D ng the define 23 2. s (s'+ bx(3)-(6)dx= S 9+18xdx . easier if we ith respect J 18+ 27xdx = 19% +27 x = 18(4) + 22 (2) = 36 +54 = My !{ x(2y+bx)dydz = 2x4+ by' dydx = lx O23 %3D 90 (2)* 3 ice th d% = ntrod achi = 18 + 48 = 54 9= 90 54 3 5 ysis

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Please Solve correctly in 1 hour and get the thumbs up please show neat and clean work and provide by hand solution only please

An open tank has the shape of a right circular cone, as indicated in the figure to the right. The tank is 8 feet across the top and 6 feet high. Initially, the tank is completely filled with a liquid with a density of 12 pounds per cubic foot. The tank is emptied by pumping the liquid out from the top of the tank. How much work is done to remove all of the liquid? 64 6- y Ay Show work by graphing the corresponding cross- section of the tank and using that graph to write your work integral. -4 2.