Ejericicios Grupales
July 15, 2022 | Author: Anonymous | Category: N/A
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Olornmnmnfs Krupcaos 3.
]o mfrro ug bnsoóf ecmtfrnca = Û 0 mfg 38 rîpanmcs pcrc ngvostnkcr oa dngmdcinogtf boa mctcanzcbfr bospuîs bo ac oxtrusnýg og ac ec`rnmcmnýg bo `ftoaacs bo pfanotnaogf bo catc bogsnbcb. Oa mctcanzcbfr so utnanzc og ac f`togmnýg bo bnmdf pfanotnaogf. Afs ecmtfros ngvostnkcbfs sfg< ifabo (mfg bfs gnvoaos) y @< mctcanzcbfr (mfg tros gnvoaos). Afs bctfs f`tognbfs so iuostrcg og ac snkunogto tc`ac<
>= >0 >8 >3 >0 >3 >8 >3
Mctcanzcbfr @0 >0 >2 >8 >3 >8 >3 >0 >0
>= >8 44 44 4; 4; 44 4; 4; 4; 4; 44
>0 >3 >8 44 44 44 4> >8 4> 44 44 4>
@3
C3
Ifabo
C0
@= >? >2 >2 >2 >2 >; >? >5 >2 >5 >3 >8 >0 >8 >; 4> >8 >3 >3 >3
c) Xacgtoo acs dnpýtosns bo ngtorîs og osto prf`aoic y oa ifboaf ostcbéstnmf mfrrospfgbnogto. `) Mfgstruyc ac tc`ac bo cgãansns bo vcrncgzc y botoringo muãaos oeomtfs ostãg cmtnvfs. m) Bn`ulo acs krãenmcs bo iobncs pcrc afs bfs oeomtfs prngmnpcaos mfg afs iîtfbfs A]B quo mfgmausnýg f`tnogo. b) Dckc ac krãenmc bo ngtorcmmnýg. o) Botoringo muãa os oa iolfr trctcinogtf. ¶Muãa os oa dngmdcinogtf probnmdf og oa iolfr trctcinogtf6
e) Uornenquo afs supuostfs bo gfricanbcb y vcrncgzc mfgstcgto. k) _tnanmo ac krãenmc bo rosnbufs mfgtrc ecmtfros pcrc botomtcr pfsn`aos oeomtfs sf`ro ac bnsporsnýg boa dngmdcinogtf. ¶Og muãa ifabo pcromo quo os iogfr ac ac bnsporsnýg6
0.
Xcrc iolfrcr ac rosnstogmnc c ac tfrsnýg bo acs cbdosnfgos bo mfipfgogtos oaomtrýgnmfs sf`ro pacmcs, so ostubncrfg bfs tnpfs bo pokciogtfs ( 3 y 0) y tros toiporcturc toiporcturcss bo murcbf (58, 48 y 388¸M). Og mcbc mfi`ngcmnýg so cgcanzcrfg bfs mfipfgogtos y afs rosuatcbfs f`tognbfs sfg afs snkunogtos<
Xokciogtf C3 Xokciogtf C0
58 0.? 0.4 3.5 3.00
Murcbf 48 =.4 =.2 =.0 0.4
388 2.8 2.0 2.= 2.;
c) Xacgtoo acs dnpýtosns bo ngtorîs og osto prf`aoic y oa ifboaf ostcbéstnmf mfrrospfgbnogto. `) Mfgstruyc oa CGFUC y bomnbc muãaos oeomtfs ostãg cmtnvfs. m) Bn`ulo acs krãenmcs bo oeomtfs y botoringo mfg oaacs oa iolfr trctcinogtf. b) Ostnio ac rosnstogmnc c ac tfrsnýg og oa iolfr trctcinogtf. o) Uornenquo rosnbufs.
=.
]o bosoc ngvostnkcr bo quî icgorc ceomtc oa tnoipf bo murcbf y oa tnpf boa cmoaorcgto c ac rosnstogmnc bo mcumdf vuamcgnzcbf. ]o rocanzc ug oxporniogtf y so f`tnogog afs snkunogtos bctfs88 2=88, =588
M =;88, 2388 =>88, 2888 =588, =488
c) ]oócao oa gfi`ro boa bnsoóf bo oxporniogtf utnanzcbf y su ifboaf ostcbéstnmf.
`) Efriuao macrciogto tfbcs acs dnpýtosns quo so puobog prf`cr. m) Pocanmo oa cgãansns ostcbéstnmf cprfpncbf pcrc prf`cr acs dnpýtosns quo efriuaý. b) ¶Dcy caküg tnoipf bo murc quo os iolfr pcrc cuiogtcr ac rosnstogmnc6 Crkuiogto su rospuostc. o) ¶Caküg cmoaorcgto os iolfr6 Oxpanquo. e) ¶Dcy cakugc mfi`ngcmnýg bo tnoipf y cmoaorcgto quo soc iolfr6 k) Oxpanquo bo icgorc krãenmc mýif so f`tuvf og ac mfiputcbfrc oa vcafr-p vcafr- ppcrc pcrc tnoipf bo murc. d) Uornenquo quo so muipacg afs supuostfs. Og mcsf bo quo gf so muipanorc oa supuostf bo vcrncgzc mfgstcgto pcrc oa tnoipf bo murc, ¶quî snkgnenmcréc osf y mýif pubnorc mfrroknrso6
2.
Og ugc eã`rnmc bo cmontos vokotcaos mfiostn`aos ac mcanbcb rosuatc ceomtcbc pfr ac mcgtnbcb bo nipurozcs bogtrf boa cmonto, yc quo îstcs mcuscg fxnbcmnýg, y oaaf ropormuto c su voz og acs mcrcmtoréstnmcs bo sc`fr y mfafr boa prfbumtf engca. Oa prfmosf bo ‑`a gquof’ os oa rospfgsc` rospfgsc`ao ao bo oaningcr tcaos nipurozcs, y ugc efric bo iobnr su
oenmcmnc os inbnogbf oa mfafr boa cmonto. Xcrc kogorcr ugc prniorc cprfxnicmnýg c ac sfaumnýg boa prf`aoic so bomnbo ostubncr oa oeomtf bo ac toiporcturc y oa pfrmogtclo bo crmnaac og oa mfafr boa cmonto ngnmncaiogto c gnvoa ac`frctfrnf. Oa bnsoóf y afs bctfs bo acs pruo`cs oxporniogtcaos so iuostrcg c mfgtngucmnýg mfgtngucmnýg..
Roiporcturc
Xfrmogtclo bo crmnaac
>8
8.4 ?.4 ?.>
8.> ?.2 ?.?
3 2.> ?.3
3.3 2.? 2.2
388 338
?.8 2.> 2.; 2.5
2.4 2.; 2.2 2.2
2.5 2.2 2.3 2.8
2.3 2.= =.; =.5
c) Mfgstruyc oa ifboaf ostcbéstnmf y efriuao acs dnpýtosns portngogtos. portngogtos. `) ¶Muãa os oa gfi`ro boa bnsoóf utnanzcbf6 utnanzcbf6 m) Xfr af kogorca, c mfgbnmnfgos rocaos so utnanzc 3.3% bo crmnaac y 388 krcbfs bo toiporcturc. ¶Xfr quî mroo quo so oanknorfg promnsciogto osfs gnvoaos bo pruo`c pcrc oa oxporniogtf6 oxporniogtf6 mfgmausnfgos. b) Pocanmo ug cgãansns bo vcrncgzc pcrc prf`cr acs dnpýtosns y f`togkc mfgmausnfgos. o) Cpfyãgb Cpfyãgbfso fso og acs krãenmcs bo oeomtfs, ¶muãa os ac roacmnýg kogorca ogtro oa mfafr y afs ecmtfros mfgtrfacbfs og su rcgkf bo oxporniogtc oxporniogtcmnýg6 mnýg6
e) C pcrtnr bo ac krãenmc bo ngtorcmmnfgos, ¶mroo quo dcyc ug oeomtf gf angoca6 k) Mfgsnborcgbf quo oa gnvoa iégnif cmoptc`ao bo `acgmurc os bo 2.4, ¶quî
trctcinogtf utnanzcréc6
?.
]upfgkc ug bnsoóf ecmtfrnca 00, muyfs ecmtfros y gnvoaos sfg< toiporcturc (4, 08) y voafmnbcb (2, ;). Ac vcrnc`ao bo rospuostc os rogbninogtf. Mfgtosto acs snkunogtos prokugtcs 22 =? 04
@ @0 = ? 3 44 ;8 ;5 =4 00 05
@= 3 0 3 ;3 ;3 5> 0> 08 00
c) Ospomnenquo oa ifboaf ostcbéstnmf pcrc oa prf`aoic y acs dnpýtosns portngogtos. `) Dckc ug cgãansns bo vcrncgzc y f`togkc mfgmausnfgos. m) Ngtorproto mfg botcaao oa oeomtf bo ngtorcmmnýg, sn os snkgnenmctnvf. b) Uornenquo supuostfs. o) ¶Dcy ug trctcinogtf iolfr6 Crkuiogto mfg pruo`cs ostcbéstnmcs.
;.
C mfgtngucmnýg, so iuostrcg afs rosuatcbfs bo ug bnsoóf ecmtfrnca. Mfgtosto afs snkunogtos ngmnsfs sng utnanzcr ug sfetwcro mfiputcmnfgca, os bomnr, dckc acs fporcmnfgos bo Pîpanmc
icgorc
icguca. icguca.
C@NN NN NNN Rftca C@ C + -
@ +
N 40 ;4 ;3
NN 48 40 ;8
NNN 42 ;> 55
+
+
4>
44
>=
c) ¶Suî gfi`ro romn`o osto bnsoóf y pfr quî6 `) Cgfto oa ifboaf bo osto bnsoóf m) ¶Muãgtfs trctcinogtfs tnogo osto bnsoóf, ¶muãgtcs rîpanmcs6 b) Oxpanquo afs oeomtfs quo so puobog ostubncr c trcvîs bo osto bnsoóf. o) F`togkc afs mfgtrcstos pcrc afs oeomtfs prngmnpcaos bo C bo Cy y @, csé mfif pcrc ac ngtorcmmnýg. e)
Mcamuao afs oeomtfs prngmnpcaos y oa oeomtf bo ngtorcmmnýg.
k) Dckc acs krãenmcs bo afs oeomtfs prngmnpcaos bo C bo Cy y @, o ngtorprîtoacs. d)
Pocanmo ac krãenmc bo ac ngtorcmmnýg ogtro afs ecmtfros C Cy y @, o ngtorprîtoac mfg botcaao.
n) ¶Bosbo su pugtf bo vnstc oa ecmtfr @ @pcromo pcromo togor ngeauogmnc sf`ro ^ 6 Crkuiogto su rospuostc.
4.
]upfgkc ug bnsoóf ecmtfrnca 0=, y mfgtosto acs snkunogtos prokugtcs. prokugtcs. c) _tnanmo ac gftcmnýg bo ( ”, +) pcrc afs gnvoaos bo afs ecmtfros, y osmrn`c tfbfs afs trctcinogtfs quo efricg osto bnsoóf. bnsoóf. `) Poprosogto og efric kofiîtrnmc osto bnsoóf y roscato ac roknýg bo oxporniogtcmnýg. oxporniogtcmnýg. m) ¶Muãaos sfg tfbfs afs pfsn`aos oeomtfs quo so puobog ostubncr mfg osto bnsoóf6 bnsoóf6 b) Xcrc mcbc ugf bo afs oeomtfs cgtornfros, f`togkc su mfgtrcsto, afs oeomtfs y ac suic bo mucbrcbfs. mucbrcbfs.
>.
Og ugc eã`rnmc bo bnogtos so tnogo prf`aoics mfg ac mcanbcb< pfrfsnbcb (`ur`ulcs bo cnro bogtrf bo afs bnogtos), icgmdcs `acgmcs, bnogtos sumnfs, bnogtos quo`rcbfs. Og afs ngtogtfs pfr rosfavor afs prf`aoics dcg domdf mci`nfs og cakugfs ecmtfros f vcrnc`aos
boa prfmosf. Mfg `cso og ac iotfbfafkéc boa
BBO
so bomnbo mfrror ug bnsoóf bo
oxporniogtfs 0=. Afs ecmtfros y gnvoaos sfg< toiporcturc bo progscbf (>8, 3=8¸M), tnoipf bo progscbf (4 y 3? ingutfs) y tcicóf bo pcrtémuac (sng tcinzcr y mfg tcinzcbf), ac vcrnc`ao bo rospuostc euo pfrmogtclo bo bnogto `uogf og mcbc mfrrnbc (ug afto bo prfbummnýg). Afs bctfs sfg afs snkunogtos8 3=8 >8 3=8 >8 3=8 3=8
Rnoip f 4 4 3? 3? 4 4 3? 3? 3?
R. bo pcrtémuac ]ng tcinzcr ]ng tcinzcr ]ng tcinzcr ]ng tcinzcr Mfg tcinzcbf Mfg tcinzcbf Mfg tcinzcbf Mfg tcinzcbf tcinzcbf
Xfrmogtclo bo bnogto `uogf ;5.2, ;5.> ;5.=, ;5.> 48.2, 43.8 ;;.>, ;>.5 42.2, 42.5 42.;, 42.? 40.;, 4=.0 4?.8, 42.; 42.;
c) Ostnio tfbfs afs pfsn`aos oeomtfs y bnkc muãaos sfg snkgnenmctnvfs. `) Pocanmo ug cgãansns bo vcrncgzc bo ostfs bctfs y f`togkc mfgmausnfgos kogorcaos. m) Uornenquo rosnbufs, ¶quî f`sorvc quo soc gftfrnf6 b) ¶Dcy ug trctcinogtf kcgcbfr6 o) ¶Suî mfgbnmnýg bo prfmosf suknoro oipaocr c euturf6 Rfio og muogtc, cboiãs, quo, c icyfr tnoipf y icyfr toiporcturc, iãs mfstfs. e) Acs mfgbnmnfgos quo so utnanzc`cg cgtos boa oxporniogtf orcg< toiporcturc bo 3=8¸M y tnoipf bo 3? ingutfs. ¶Xfr quî mroo quo so oanknorfg gnvoaos ngeornfros bo pruo`c pcrc ostfs ecmtfros6 k) Ostfs rosuatcbfs, cugquo pfsntnvfs, gf sfg suenmnogtos: pfr af tcgtf, quî suknoro ustob, ¶oxpafrcr iãs gnvoaos bo afs ecmtfros yc ostubncbfs6, ¶mfgsnborcr ftrcs mcuscs6 f ¶quî6 Crkuiogto.
38.
]upfgkc ug bnsoóf ecmtfrnca 02, y mfgtosto acs snkunogtos prokugtcs. prokugtcs. c) Cgfto oa ifboaf bo osto bnsoóf. `) Cgfto ac ictrnz bo bnsoóf, os bomnr, dckc ugc anstc bo tfbfs afs trctcinogtfs quo efricg osto bnsoóf. m) ¶Xfr quî osto bnsoóf romn`o tca gfi`ro6
b) ¶Muãaos sfg tfbfs afs pfsn`aos oeomtfs quo so puobog ostubncr mfg osto bnsoóf6 o) Mfg rospomtf ca cgãansns, ¶og quî mfgsnsto y muãa os oa f`lotnvf bo f`togor oa iolfr CGFUC6 e) F`togkc oa mfgtrcsto pcrc oa oeomtf prngmnpca bo B y pcrc oa oeomtf bo ngtorcmmnýg MB MB.. k) ¶Xuobo bcrso oa mcsf bo quo oa oeomtf prngmnpca bo C bo Cgf gf soc snkgnenmctnvf, y oa oeomtf bo ac ngtorcmmnýg ngtorcmmnýg C@ C@sé sé af soc6
33.
Og ugc oiprosc aomdorc so dcg tognbf prf`aoics mfg ac vnsmfsnbcb bo mnortc `o`nbc bo mdfmfacto. ]o mroo quo mfg tros ngkrobnogtos quo so ckrokcg og poquoócs mcgtnbcbos so puobo rosfa vor osto prf`aoic, pfr af quo os gomoscrnf oxpafrcr ac sntucmnýg: pcrc oaaf so mfrro ug oxporniogtf 0 = mfg bfs rîpanmcs. C mfgtngucmnýg so cpromncg afs rosuatcbfs f`tognbfs< Ngkrobnogto C C ”3 +3 ”3 +3 ”3 +3 ”3 +3 +3
Ngkrobnogto @ @ ”3 ”3 +3 +3 ”3 ”3 +3 +3 +3
Ngkrobnogto M M ”3 ”3 ”3 ”3 +3 +3 +3 +3 +3
Unsmfsnbcb 3=.=, 3=.> 32.;, 32.2 32.5, 32.> 32.=, 32.3 35.>, 3;.0 3?.?, 3?.3 3;.2, 3;.3 34.>, 3>.0 3>.0
c) Ostnio tfbfs afs pfsn`aos oeomtfs y bnkc muãaos sfg snkgnenmctnvfs. `) Pocanmo ug cgãansns bo vcrncgzc bo ostfs bctfs y f`togkc mfgmausnfgos kogorcaos. m) Ngtorproto c botcaao afs oeomtfs snkgnenmctnvfs. b) ¶Dcy ug trctcinogtf kcgcbfr pcrc ingninzcr6 o) Uornenquo rosnbufs, ¶quî mfgsnborc bostcmcbf6
30.
_g ec`rnmcgto bo `fascs bo pcpoa bosoc cgcanzcr ac rosnstogmnc ca rcskcinogtf ( ^), pcrc af muca utnanzc ugc osmcac guiîrnmc. Oxcingc tros ecmtfros, mcbc ugf og bfs gnvoaos, xa 9pcpoa, x0 9 duiobcb, x= 9 bnrommnýg boa rcskuóf. Bomnbo f`togor tros f`sorvcmnfgos (rîpanmcs) og mcbc mfi`ngcmnýg, acs insics quo so iuostrcg og ac snkunogto tc`ac<
x3 + + +
x0 + + -
x= + +
+
+ +
+ +
=.4 5.5 =.2 =. 2 5.4 0.= 2.;
Posnstogmnc =.3 4 3.; 4.0 =.3 =.?
0.0 5.4 =.4 5 8.; 2.2
0.3 2.0
3.3 2.;
=.5 0.>
c) Dckc oa cgãansns bo vcrncgzc pcrc ostfs bctfs. `) Ngtorproto afs oeomtfs snkgnenmctnvfs y ogmuogtro oa iolfr trctcinogtf. m) Uornenquo afs supuostfs boa ifboaf
3=.
]o qunoro cuiogtcr oa rogbninogtf bo ug prfmosf, y pcrc oaaf so ostubncg tros ecmtfros mfg bfs gnvoaos mcbc ugf. ]o dcmog tros ropotnmnfgos og mcbc trctcinogtf boa bnsoóf ecmtfrnca 0= rosuatcgto. Ac vcrnc`ao bo rospuostc quo so inbo os rogbninogtf. Afs bctfs sfg afs snkunogtos<
Rrctcinogtfs 3 c ` c` m cm `m c`m
3 00 =0 =? ?? 22 28 58 =>
Popotnmnýg 0 =3 2= =2 2; 2? =; ?8 23
= 0? 0> ?8 25 =4 =5 ?2 2;
c) ¶Muãaos oeomtfs ostãg cmtnvfs6 `) ]n f`tuvf ugc ngtorcmmnýg nipfrtcgto, nipfrtcgto, ngtorprîtoac mfg botcaao. m) Botoringo acs mfgbnmnfgos bo fporcmnýg quo icxninzcg oa rogbninogtf. b) ¶Muãa os ac rospuostc osporcbc og oa iolfr trctcinogtf6 o) Uornenquo afs supuostfs boa ifboaf.
32.
Mfgsnboro ugc ngvostnkcmnýg aaovcbc c mc`f pcrc ostubncr oa oeomtf quo tnogo ac mfgmogtrcmnýg bo ug rocmtnvf y ac prosogmnc bo ug mctcanzcbfr sf`ro oa tnoipf bo
rocmmnýg bo ug prfmosf quéinmf. ]oc ac mfgmogtrcmnýg boa rocmtnvf C mfg bfs gnvoaos bo ngtorîs, 3?
y 0? . Oa mctcanzcbfr mfgstntuyo oa ecmtfr ecmtfr @, oa gnvoa catf f supornfr supornfr bogftc
oa usf bo bfs scmfs bo mctcanzcbfr y oa gnvoa `clf f ngeornfr bogftc oa usf bo ug sfaf scmf. Oa oxporniogtf so rocanzc = ropanmcs y afs bctfs sfg mfif snkuo<
c) Cgfto oa ifboaf bo osto bnsoóf `) ¶Muãgtfs trctcinogtfs tnogo osto bnsoóf, ¶muãgtcs rîpanmcs6 m) Oxpanquo afs oeomtfs quo so puobog ostubncr c trcvîs bo osto bnsoóf. b) F`togkc afs mfgtrcstos pcrc afs oeomtfs prngmnpcaos bo C bo Cy y @, csé mfif pcrc ac ngtorcmmnýg. o) Uornenquo afs supuostfs 3?.
_gc oiprosc oi`ftoaacbfrc bo roerosmfs ostã ngtoroscbc og f`togor caturcs bo aaogcbf iãs ugnefrios ugnefrios bo acs `ftoaacs quo so ec`rnmcg og su prfmosf prfmosf bo icgnecmturc. Oa ngkognorf boa prfmosf puobo mfgtrfacr tros vcrnc`aos burcgto oa prfmosf bo aaogcbf< oa pfrmogtclo bo mcr`fgctcmnýg(C), ac prosnýg bo fporcmnýg bo aaogcbf (@) y acs `ftoaacs prfbumnbcs pfr ingutf c rcpnboz bo aégoc (M). Oa ngkognorf puobo mfgtrfacr ac mcr`fgctcmnýg og 0 gnvoaos (38,30), oanko bfs gnvoaos pcrc ac prosnýg (0? y =8) y bfs gnvoaos pcrc ac rcpnboz bo ac aégoc ( 088 y 0?8). Oa ngkognorf bo`o mfrror 0 rîpanmcs. Ac vcrnc`ao rospuostc f`sorvcbc os ac bosvncmnýg prfiobnf bo ac caturc boa aaogcbf f`lotnvf quo so f`sorvc og ugc mfrrnbc bo prfbummnýg bo `ftoaacs mfg mcbc mfglugtf bo mfgbnmnfgos. Og ac snkunogto tc`ac iuostrc afs bctfs quo rosuatcrfg boa oxporniogtf. Xrosnýg bo Fporcmnýg (@) Xfrmogtclo bo Mcr`fgctcmnýg (C)
38 30
0? X]N
=8 X]N
Pcpnboz bo aégoc (M) 088 0?8 -= -3 -3 8 0 8
Pcpnboz bo aégoc (M) 088 0?8 -3 3 8 3 0 5
3
3
=
?
c) Cgfto oa ifboaf bo osto bnsoóf `) ¶Muãaos oeomtfs ostãg cmtnvfs6 m) ]n f`tuvf ugc ngtorcmmnýg nipfrtcgto, ngtorprîtoac mfg botcaao. b) ¶Muãa os ac rospuostc osporcbc og oa iolfr trctcinogtf6 o) Uornenquo afs supuostfs boa ifboaf.
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