Taller # 2 Conmutacion

 

PMCCBV Do 6 Imrbd Mcbkmd`rm Dhýo Gorm Gñdham Mcbxmd`rm Umcbdahm

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Po Pogm gmd` d`o o cm tm tmfc fcm m `b Brcm Brcmdl dl F qub qub rbcm rbcmah ahod odm m bc tríe tríeha hao o oe oerb rbah ah`o `o bd eudahñd `bc dûgbro `b ahrauhtos y cm aodlbsthñd o pèr`h`ms `btbrghdb; m) Aodsh`brb ud lrupo `b =5 ahrauhtos bd = jorm phao aod ud tríehao oerbah`o `b =6 Brc `hlm ¿auíc bs bc vmcor aorrbspod`hbdtb m cm aodlbsthñd? y `btbrghdb qub shldheham bstb vmcor. V/ Qb ufham bd cm tmfcm cos vmcorbs `bc tríehao y bc dûgbro V/ Qb `b ahrauhtos qub dos pbrghthrí `behdhr bc vmcor `b cm aodlbsthñd qub bs m =>% =>%,, co qubbd bstb bs bc porabdtmkb `bhlumc profmfhch`m` `baumc qubshldheham cm ccmgm`m su prhgbr hdtbdto sbm fcoqubm`m.

 

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f) Qh sb thbdb ι 7 60> ccmgm`ms/jorm aod udm `urmahñd `b 1 ghdutos amcaucb cm `urmahñd progb`ho `b oaupmahodbs, bc tríehao aursm`o y bc tríehao rbajmzm`o.

V/ Qblûd cm baumahñd `b trmehao uthchzm`m sb jm po`h`o `btbrghdmr qub bc trmehao amusm`o y bc trmehao rbajmzm`o bs hlumc m =6 Brcmdl  Brcmdl  .

a) Aodsh`brb B 7 >.5== aod ud tríehao oerbah`o `b =0Brc `btbrghdb bc dûgbro `b ahrauhtos qub proporahodmd bstb vmcor `b aodlbsthñd.

6.

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Po Pogm gmd` d`o o cm tm tmfc fcm m `b Brcm Brcmdl dl F qub qub rbcm rbcmah ahod odm m cm ao aodl dlbs bsth thñd ñd a aod od bc dûgbro `b ahrauhtos `btbrghdb; m) Aodsh`brb ud lrupo `b 65 ahrauhtos bd = jorm phao aod ud aodlbsthñd `bc =% `hlm ¿auíc bs bc vmcor aorrbspod`hbdtb mc tríehao oerbah`o? V/ Qblûd cm tmfcm `b Brcmdl F y cm ufhamahñd bc trmehao oerbah`o bquhvmcb mc =5.85.

 

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f) Aodsh`brb udm aodlbsthñd `bc 2>% aod ud tríehao oerbah`o abramdo m 0>Brc `btbrghdb bc dûgbro `b ahrauhtos qub proporahodmd bstb vmcor `b aodlbsthñd. V/ Qblûd cm ufhamahñd `b cm aodlbsthñd rbspbato mc dugbro `b Brc, cos ahrauhtos sod 65

1.

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Po Pogm gmd` d`o o ccm m ttmf mfcm cm `b `b Brc Brcmd mdl lFq qub ub rbpr rbprbs bsbd bdtm tm cm am amrl rlm m gb` gb`hm hm por ahrauhto rbcmahodmd`o cm aodlbsthñd aod bc dûgbro `b ahrauhtos `btbrghdb; m) Aodsh`brb ud lrupo `b 62 ahrauhtos bd = jorm phao aod ud aodlbsthñd `bc 2% `hlm auíc bs bc vmcor aorrbspod`hbdtb mc tríehao aursm`o por ahrauhto.

 

V/ Bc trmehao amusm`o por bc ahrauhto bs =8,88

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0.

f) Aodsh`brb udm aodlbsthñd `bc =>% aod ud tríehao oerbah`o abramdo m >.518Brc `btbrghdb bc dûgbro `b ahrauhtos qub proporahodmd bstb vmcor `b aodlbsthñd. Rd lr lrup upo o `b ahra ahrauh uhto tos s au aurs rsm m :6> :6> ccmg ccmgm` m`ms ms p por or j jor orm, m, bc bc thb thbgp gpo o `b oaupmahñd bs `b 0 ghdutos `btbrghdb;

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m) Umcor `bc tríehao aursm`o

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f) Bd ud lrupo `b 5> ahrauhtos `btbrghdb cm aodlbsthñd y bc tríehao oerbah`o. V/ Qblûd co amcaucm`o sb pub`b `btbrghdmr qub aod 5> ahrauhtos y ud tríehao `b 20.555 Brcmdl, cm aodlbsthñd bs `b >.>2>:, bs `bahr 2.>:%

a) Amcaucmr bc dûgbro `b ahrauhtos pmrm qub cms pèr`h`m do bxab`m F 7 >.>>5. V/ Qblûd cm amcaucm`orm `b Brcmdl F cm amdth`m` `b ahrauhtos sod .555 Brcmdls * 0 7 6.555 Brcmdls 6.555

 ^B7

0

0! 0

∝  H 7>

6.555

h!

h

  7>.=5:5

Cm profmfhch`m` `b qub bc lrupo `b 0 ahrauhtos sb bdaubdtrb oaupm`o bs `b =5.:5% ahrauhtos. Bc tríehao lbdbrm`o por cos bgpcbm`os `b ud `çm tçphao bs bc shluhbdtb;

=) Bc tríehao por ccmgm`ms coa coamcbs mcbs orhlhdm` orhlhdm`ms ms por cm bgprbsm bgprbsm

 

.  M 72>>

Y  W

 Ccmg ∜6 .2 j  j 76>.:11 Brcmdls ghd 5>

 Y W

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6) Bc tríehao por ccmgm`ms coamcbs rbahfh`ms por cm bgprbsm

 M 70:>

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Y  W

 Ccmg ∜6.2 j  j 76> Brcmdl  Brcmdlss 5> ghd

 Y W

1) Bc tríehao totmc por ccmgm`ms coamcbs  MPotmc  MP otmc 76>.:1 Brcmdl + 6> Brcmdl 7 0>.:11 Brcmdl

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0) Bc tríehao por ccmgm`ms `b C.@. orhlhdm`ms por cm bgprbsm

 M 71>

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 Y W

2) Bc tríehao por ccmgm`ms `b C.@. rbahfh`ms por cm bgprbsm

 M 7 =>

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Y  W

 Ccmg ∜=.> j  j 7>.2 Brcmdl  Brcmdlss ghd 5>

Y  W  Ccmg j

∜= .2

5>

 Y W  j ghd

 Brcmdls

7 6>

5) Bc tríehao totmc por ccmgm`ms `b C.@.  MPotmc  MP otmc 7>.2 Brcmdl + >.=55 Brcmdl 7 >.555 Brcmdl

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.:11 Brcmdl + >.=55 Brcmdl =6> Ahrauhtos

 

7>.10

 Brcmdls

:) ¿Auíc bs bc thbgpo gb`ho `b cms ccmgm`ms orhlhdm`ms (bd

 

ghdutos)?  M 6>.:11 Brcmdl+ >.2 Brcmdl 7>.>0 jorms 76.0 ghdutos j7   7  ι ccmg orhlhdm`ms 21> j

Y  W

:. Rd shstbgm `b pèr`h`m qub thbdb => ahrauhtos, bd cm jorm phao rbahfb udm hdtbdsh`m` progb`ho `b =2> ccmgm`ms. Bc thbgpo gb`ho `b oaupmahñd bs `b 1 ghdutos. Qupodhbd`o qub bc dûgbro `b usumrhos bs hdehdhto amcaucmr; m) Mo

 M o 7=2>

Y  W

 Ccmg ∜1 ghd j   7< .2 Brcmdls 5> ghd

f) B 8. Cos susarhptorbs `b ud sbrvhaho `b aodbxhñd m Hdtbrdbt maab`bd mc HQ^ (Hdtbrdbt Qbrvhab ^rovh`br) m trmvès `b cm VP^A (Vb` Pbcbeñdham ^ûfcham Aodgutm`m). Bc HQ^ aubdtm aod 12> pubrtos `b maabso y bd progb`ho, cm aodbxhñd `b ud susarhptor `urm 02 ghdutos y rbmchzm trbs (1) aodbxhodbs por `çm (pmrm bstb profcbgm sb togmd =2 jorms aogo bc dûgbro bebathvo `b jorms `b ud `çm). Bc HQ^ lmrmdthzm qub cm profmfhch`m` `b fcoqubo bs -1`b => , ¿Auíc bs bc gíxhgo dûgbro `b susarhptorbs qub pub`b tbdbr bc HQ^?

 

1>2.58 Brcmdl >.=2 Brcmdl

  76>1: Qusarhptorbs

=>. Rd shstbgm `b bspbrm qub thbdb => ahrauhtos, bd cm jorm phao rbahfb udm hdtbdsh`m` progb`ho `b =2> ccmgm`ms. Bc thbgpo gb`ho `b oaupmahñd bs `b 1 ghdutos. Qupodhbd`o qub bc dûgbro `b usumrhos bs hdehdhto amcaucmr;

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m) Mo

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f) B

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a) ^rofmfhch`m` `b to`os cos ahrauhtos oaupm`os y do jmym aocm

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`) ^rofmfhch` ^rofmfhch`m` m` `b qub jmym `os ccmgm`m bd aocm

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b) ^rofmfhch` ^rofmfhch`m` m` `b qub jmym 0 o gís `b ccmgm`ms bd aocm