MTR_500_HW6 - KEY

MTR_500_HW6 - KEY - dl = pd £ dl = rsin 9d J It,sin9 dJ rd...

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Unformatted text preview: dl = pd;; £. dl = rsin 9d;; J. It- : ,sin9 dJ: rd; L. dl. , . dS=pd;dz Ids = pIId;dz. s. dS = Pdp~ . J '4 K P Ids. I ptip I~ = -(-); = ~ J 0 4 2 In spberi~ d S - r2 sinO ~ cS ~ h J 1. - Ids= 100 Isin9tJJ I~= l00(2KX-cosO) i . 0 !- " 4 dS- rdrtJJ . 4 1 Irti'I 0 ! J JiB = s= 46 p.3 3(1t .. k-- -) . -. 2.356 244- 1, 9- 3(1; ra d; . (1)8in30'[(~)- 0]. ~~~ II' R' 4R' 4(2-6)- -'3 = ~ , j. j d; 0 !. J ~.S.236 6- .. .. 2 (5)[-- -] 2 3 2 = = 200.(0.5- 07071)- 7.58.4- " C I I 81 .. - (-- -)= -. 4J89 2236- 1 (0) dV = drtiydz I r I 2 J I V = Idxdjldz= Idx ltiyIdz= (I) (2- IX3- -3)-! I 0 I -) , (b) dV = P~dpd= S I ~ W I p-' t' I' I 2. V = Pdp I d:. ,'+ S -t. (4- -fx- - -). -(25- 4X5X-) = 35. = L1Q-' ,! 2. J 1 J J (c) dV = r-' sine dr,A)~ ~ ! J _ I j ,J r' IJ 1t - f/ = I,-'dr sine t:4 = )1, (- C:OS9)l(2- 6) I ! ! 1 , J J - 26- = -(27- lX-X-)- -= 4..538 3 1 J 18 - ~:;~fi~C . , . y Ip.dY . , I X\'* I <x-'y + 1 n . J-+ j = . . I 47 + xy)dydx ~ I J 0 >dx' = I (x" + T)dr 1 17-8- 11 60 0.2833 . . I iI.iII = I (x'dx+ y' dy) L But on L, y. x' dy. 2%d% 1- - I I 1 4 xJ ~ , J J H.d/. (X +x .2x~. -+2---+-.'.6667 J 6 J J ~- -....
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MTR_500_HW6 - KEY - dl = pd £ dl = rsin 9d J It,sin9 dJ rd...

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