MTR_500_HW5 - KEY

MTR_500_HW5 - KEY - J (-- .' ..1 r; 1- (2 - -tJ) (2Q,- 0./...

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Unformatted text preview: J (-- .' ..1 r; 1- (2 - -tJ) (2Q,- 0./ /6 Ii, + Oa- . (Ato:)a: . :.: pCOl;. x- y= z = psin; a 2; p (x,y,:) x=2CO19()1 Q Q (0. I. - 4). = x.rsin8cos;~ y: rsin8sin; = ;= rcos8 . IO~13" R(.r.y.=) = x = 4sin9<1cos3C1 x = 4SlnYCrCOSJ(J' . 3.464. y = 3 sin 30' sin24f1 .2 = = roosS = 4cos9<JI . o. T(x.y.=) & Given P( t .-4.-3). 19 0.20/ a.. + 1 ~6(1 1 sin 120' .~ 80.16(,. P (0.5. 0.166. 2). 2 sin 9()1 . 1;-10. 3sin4.s- cos21(1 .- 1.137;- 1.061; IOsin 13,. sin9f1 . .2J2L R(- 1.&37,- 1.061. 2J21). T(3.464. 2. 0). convert to cylindrical and spherical values; )'--I . . tan-I -;. tan-I T. 284.Dr. :. P(p,t,z). (4J23,184"', - J Spherical: '..J~ +,,'; ;1. "'1+ 16+ 9. 8. tan-If. = tan-/~. /16.04'. % -J P(I'.8..>. p(J.D99. 126,Dr, 2U.D4'). t.~ %. p~l, y. pliDl, y. pz~~-1 sin~~;+ pzsin~ u. .X'1+yl+Z1+Y+2~ . ,.1 + r1Jin18sin1 ~+ 2,.1 ~ 8 . ~[1+ lin18sin1 ~+ 2~ 8 [ ] [ . ] D, ~+ sin + 0 ~: . - s:+ ~+ ~] [Z;Z D,. (.1'+ z)ain+ . (p~ + z).+ D.. (.1'+ z)~. . (P~. + z)~ 1>. (p COlt + z)[sint a,+ COlt a;J SpMrica/: [ Dr] [ ", .e.. "' J [ ] ~ . ,., ~e.. '" .1'+ J' ~ '" COl. .', 20 4J2J. . . (4123,184.048, - 3). S.099. pain;, Y' I sin;cos;+ pzsin; 0. = (x+ :)~9 sin. = r(sin8 sin. + cos9)cos9 sint. D. = (x+ :)cost = r(sinO cost + cosO)cos.. b. r(sin9 cost + cos9){sin9 sin. 0, + cos9 sint ci, + cost a.l CylirKirical: [ E, ] [ ~' lin' 0 ] [ Y-i' ] £, a - lID' ~; 0 .1)'% E: 0 0 1 ~ - ,:2 £,. ()I2 - .tJ)~;+ xyzsin' = pZ(sinl;- coal ~)~; ... ~za)S~sin1, . - ~ cos2;col~ ... p~z.in~ ;cos;....
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MTR_500_HW5 - KEY - J (-- .' ..1 r; 1- (2 - -tJ) (2Q,- 0./...

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