Question

6. Find the volume of the house, as shown above, sitting on the cy-plane, walled by the cz-plane, the yz-plane, and the plane 2x + y = 2, and with roof provided by the plane 2 + 2y + z = 6. (1) 13/3 (2) 9/4 (3) 11/7 (4) 7/8 (5) None of the above

Answer 1

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&z=(6-x-2g solution: Given the region is sounded by the planess az-plave (y=0 yz-plane (x=0) and the sey. plane (7:0), 2x+y=2 3 y: 12-28 ideas x+2y+z=6 And roof leeelings is provided by etagez :. 052(b=rry) osy< (2-2x) And: intersection with az-plane gives: 2-2x =0 3X=1 ::0<xsi. Tefle,4,3): 0<x<!, C osys 2-2), i volume: 02Z < 6-2-24 V: 535dv= 5S Se da dyan a fi o og je 2012. ayeta" x=0 yzo zão. s' slenza) (2)/6-X=24 dydza! 9 m -2-24; dupla - J'{<6-239- 6}\x69.com = 5" (160)(z-za)– (en aj") eta = '12 (6-)(1-x) -4 (1-*).ax : s' 2(-) (678-2 +2x) dx :!'alim2)(4+2).042 2478-42-x3 4x 2'114-3x=xy dx =2(42-3x ? ) 2(4-%-%)= {(24-9-2)= $x13 - Loption:1). And xo so x=0 yao