Question

10. Find the center of mass of the region E with constant density p that is bounded by the paraboloids z=x² + y2 and 2 = 32 – 7x - 7y. Set up and label all the necessary integrals. Use technology to evaluate the integrals. Give the exact answer.

Answer 1

solution of Co-ordinates pg Given, constant density e. In cylindrical E is described by of region ²2 232.782 OL8L2 20 e 21, & Moment about the ny plane USE ze dv 20 2 32-782 z erdz dr do si to rzo 2=12 25 2 z r dr dr do 0 12 G 32-702 r drdo Y2 O 2 s (32-7823-8") ar do I (10248 gr - 4488²-8) de 20 D 27 (1024 x +40 rs_ 448 83) ar dB (2017-11) 215 (2048 + 512 - 1792) do l. 25 (256-1792) - 1534 me

Moment about the yz plane JS. xe du E 21 2- 32-712 al 1 s orar doch D Y 20 12 2.0 2- e O 20 (32-88²) 1² ose de dr e J Cod de j 2) cose do 6:09 e l wodo. ( 32.8 - 2. 32) 20 Р 32.8 (3-4) oso do 20 Cosodo = 2.3 2.8 C 15 How Moment about the g Zx plane Ille Man 2012 yld 32-772 Y sind.l. rdrdo da D 2 . 2 el (32-782-8²) r² sud droo = el sud do 2 Į (32re - gr ) dr

Men- 29-3 0 They Center of mass is D 64 ne lune 1536 til bune Centre of mass ( 0, 0,24) Mass of region, M= edv E 2 27 32-782 s dr do dz D 0 2.1 (32-78282) rardo 00 II (328-883) drao -l 20 ej Į (64-32) de 32 21. P 64 en -