Question

Find the mass and center of mass of the solid E with the given density function p. E is the tetrahedron bounded by the planes x = 0, y = 0, z = 0, x + y + z = 2; p(x, y, z) = 9y. m = (7,5,7) = ( [

Answer 1

E := tetrahedron bounded by the planes x = 0, y=0,370 X+Y+ 3 =2; and density play,z)=gy 12 Volume of the tetrahedoon (0,02) m Je P(X,Y 8). dr. v (200,0) X 2 2-2 ২-২-১) qy d3 dy dx CH 60,2,0) x+y=2 X50 Y10350 2-X 19 9 9.(2-x-4) dy de X=0 y=0 2 2.x ag 29_ay_y") dy da 1 . Xoo yoo ora ég 20 S [3 - 22 e dx S [42-23 (2-23- 2-x33] da & 750 2 6-3x - 2+1 da 99 (2-4 -X) 6 X=0 = No 3 2 (3-23 (4-22) dx $ (2_139 dx doo 3 3 x=0 E 3, 4 12 3

Sap dri m. 12 f² / 2x po ugy dis dy ose 2050 Y=0 780 2-2 gx.y (2-x-4) dy da X50 YEo 1² 12 SA (89- wy=5*3 * SS . (9_73* di. Yoo 'see first Part ) a 3. x=0 co NA G1 will Á 2-1 (2-H-y У da dy dre 4.94 12 a=0 Yoo fro 2-X (242 xyz_y3 ) dy dre E 9 12 ) não y co -x)" Jax 4 (2-23°- {.(2-0) 370 (3-833 8=48-6 +32 12 .) dx 4 (8 - + 3 Et s ' (2-1) (2 -803 Atze XEO KO toi 39 5 allen 16

Z oth lapar - لا -2 لا لا -1 . 3.gyda dy dre = 0 = 0 = 0 9 رولا -7-2) dy doc 2 x=0 90 از -2م ( الا وه ( 9+ (1-2) و2 - (2-2) و 29 24 Xe6 y=0 -2- و در 3-2) 2- و(27)) » و( قوم 24 =0 90 (2) dx (2-3) (2) (2) ( 4 24 ہلا 2-X) da 9 24 12 =0 เรา Adre 32 0 م ۱) - او 92 ( 3 ) : (3ر5 * Here arhat of m89 5