Question

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

Answer 1

Dute: # Saint- 3 = 202 2 ty 2 Z = 32- 742–742 7e ?tyza 32-722-742 2 > aze at dy? 232 2) 222tyz 2.4 Slny z = flan Sthat's None. Mass ? I (214, z) dlv E I s. dv 32-7(72+42) IS f de dredy my z = x2 + y2 lol eff 32 -7(72+y2) - (224y2) Johody Duy I (3 8(x2785) alreally muy 2

2 Date: In polory Coordination Drey rez scago 8 2 osno 22ty 24 olr32 olocar + S (2-882).razdo Ozo rzo 2 883) dodo oso J20 2n = 22 of 2 ) de = f( (164 2*1235) -o) (202 1664 32) 2д. 32 2. ñ m 64 T

ol None Muz S gg du 32-7(2²+42) yg dlzosedy Duy Z=2²742 = 1/5 (32 - 8622742) yolzedly muy In polosy Coroodtonats) 2 127 32- rsinoordoody ozo 820 ? 0200720 (32 082) 22. sinododr. John Sme Asmodo o
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Date: / 1 -tru ч + 2 dt do 2. 14 (970 -t: 30- 2) т 2. so I do ч, ус 2 3 с 5 K Те th [q 3 12 2 x 2 Х ХК 4 2 - 2 43-323) л 3 14 7 г. 2 6 х 7 ( x 32769 — 42 yo ho Г// + 6. 4 5 x 59 *f 42-

Date: اله May (from ma = 64x504 42 64T WI 50 252 24 212 4.2 12 ho 127 Hence the Center af mass co, o, 12 Ang