Download - 5. ELEMENTI 16 GRUPE
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7/23/2019 5. ELEMENTI 16 GRUPE
1/75
CJCICH^M 01( K_SVC ,QM @-
L`jegkchm cjcichtm,h`dvmc z`stupjdchm u run`i`-
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^`ocj` ?( Chcrkmd` mghmz`bmdc m egcambmdcht cjcetrghck`tmvhgstm`tgi` cjcich`t` 01( krupc m rcnges pgtchbmd`jm hdmlgvml
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Emsmedc pjmh mdm su igjceujm nvg`tgihm( Rtv`r`hdcnvg`tgihml igjceuj` igkuc dc s`ig egn G zogk hdckgvgk
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RVGDCQM cst cjcetrgh` u z`nhdci ev`hthgi hgvgu4
imhmi`jhm stcpch gesmn`bmdc z` svc cjcichtc dc )?5
gsmi emsme`* pr`vc spgdcvc s` i`es( stcpchgi gesmn`bmdc %15
Rt`omjhm spgdcvm cjcich`t` gvc krupc mi`du stcpchc gesmn`bmdc4
)?*%?* %>* m %1(
emsme hc pr`vm spgdcvc s` pgzmtmvhmi stcpchgi gesmn`bmdc* gsmi s`
ajugrgi egdm dc cjcetrghck`tmvhmdm gn hdck`* prm ciu sc stv`r`nmgesmkchmje`tdgh G??%(
Rtcpch gesmn`bmdc )?4
u spgdcvmi` s` cjcichtmi` i`hdc cjcetrghck`tmvhgstm
spgdcvm s` vgnmegi* L?G* L?R* L?Rc* L? c(
Rt`omjhgst gp`n` u hmzu4 L?G L?R L?Rc L? c(
Ssjmdcn h`st`d`hd` vgnmegvc vczc egd` dc uzrgegv`h` vcjmegi
cjcetrghck`tmvhgu emsme`* ngj`zm ng `sgbmd`bmdc igjceuj` L?G* p` dcvgn` u hgri`jhmi usjgvmi` u tchgi st`hdu* nge su L?R* L?Rc m L? cpjmhgvm* hcprmd`thgk imrms` m gtrgvhm(
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Qgn` dc sj`og nmsgbmr`hm spgd m mstgvrcichg pge`zudc
pgndcnh`eg emscj` m o`zmh` svgdstv`4
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Vjmhgvmtm L?R* L?Rc m L?^c su tgpmvm u vgnm m gtgpmhc rc`kudu
emscjg zogk prgtgjmtmeml rc`ebmd`4
L?R L% % LR) ?L% %R?) E09
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Vgtg su L?R* L?Rc m L?^c sj`oc emscjmhc* tg su R?))*Rc?)) m ^c?))dghm d`ec eghdukgv`hc o`zc* p` r`stvgrjdmvm
gesmnm m sujamnm u vgnchmi r`stvgrmi` rc`kudu mzr`zmtgo`zmhg4
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M`eg sv`em gn l`jegkchml cjcich`t` mi` pg nv`
hcsp`rch` cjcetrgh`* ghm igku rc`kgv`tm icusgohgt`eg n` sc spgdc `hk`udum pg dcn`h cjcetrgh* ngenrukm cjcetrgh gst`dc z` gstv`rmv`hdc vcz` s` nrukmi
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Gv`e`v spgd dc h`trmdcv nmsujamn* H`?R?(
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stcpch gesmn`bmdc 6
Rpgdcvm stcpch` gesmn`bmdc %?
nml`jgkchmnm m gesmnm* suipgrgv ,MM- ljgrmn* RBj?5 tcjur,MM- gesmn`*
cG Rpgdcvm stcpch` gesmn`bmdc %2
suipgr,MMM- gesmn* R?G2* lmpgnmsujamth` emscjmh`* L?R?G> m hdchcsgjm lmpgnmsujamtm
Rpgdcvm stcpch` gesmn`bmdc %>
Gesmnm ,RG?* RcG?* ^cG?* VgG?- r`stv`r`hdci suipgrgvgk,MQ- gesmn` m scjchgvgk,MQ-
gesmn` u vgnm h`st`du emscjmhc sujamth` ,L?RG2- m scjchmth`,L?RcG2-4
RG?,k- % L?G L% % LRG2
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sujamtc* RG2?)* scjchmtc* RcG2
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Gesmn`bmdsem stcpch %? ) nml`jgkchmnm m gesmnm( Rvm
spgdcvm gvgk gesmn`bmdsegk orgd` su hcst`omjhm(
Nmajugrmnc hc pr`vc R* Rc* c m Vg* nmljgrmnm pgstgdcs`ig egn suipgr`* tcjur` m pgjghmd`* nmorgimnm egn
tcjur` m pgjghmd`* ` nmdgnmnm hm egn dcnhgk cjcicht`
gvc krupc(
Gesmnm s` stcpchgi gesmn`bmdc %? hmsu pgzh`tm( R`smkurhgu dc utvrchg pgstgd`hdc s`ig tcjur,MM-gesmn`* cG(
Rpgdcvc s` gesmn`bmdsemi orgdci %2 kr`nm s`ig
suipgr( g su suipgr,MMM- gesmn* R?G2* lmpgnmsujamth`emscjmh` L?R?G> m hdchc sgjm lmpgnmsujamtm(
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Rvm cjcichtm* mzuzcv G* kr`nc spgdcvc s` gesmn`bmdsemi
stcpchgi %>(
l`jgkchmnm RA> m RcOr>* gnkgv`r`dum gesmnm* emscjmhc egdc scmzvgnc mz gesmn` m hdmlgvc sgjm(
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Gesmnm suipgr`,MQ- m scjch`,MQ- sc j`eg gt`p`du u vgnm prm
ciu h`st`du sujamth` L?RG2 m scjchmth` L?RcG2 emscjmh`4
^cjur,MQ- gesmn* ^cG?* sc vrjg sj`og gt`p` u vgnm* gt`p` sc u
emscjmh`i` m o`z`i`* p` prci` tgic mi` `iagtcr`h e`r`etcr(
D`mh` gvml emscjmh` gp`n` u hmzu gn suipgr` prci` tcjuru*
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Rpgdcvm stcpch` gesmn`bmdc %1
Lces`ajugrmnm ,RA1* ^cA1 -
Gesmnm ,suipgr,QM- gesmn* RG2* scjch,QM- gesmn*RcG2* tcjur,QM- gesmn* cG2-
Emscjmhc ,suja`th`* L?RG>* scjch`th`* L?RcG>*
tcjur`th`* L1 cG1-
m nv` hmz` sgjm emscjmh` ,lmnrgkchsuja`tm m
lmnrgkchscjch`tm* suja`tm m scjch`tm-
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EMRME h`dr`sprgstr`hdchmdm cjcicht u zcijdmhgd egrm* i`schm unmg
>=*3#m s`nr`h u gojmeu smjme`t`* e`rogh`t`* agsa`t` m suja`t`( S `tigsacrm sc h`j`zm u sjgognhgi st`hdu* vgjuihm unmg u
zr`eu mzhgsm ?0 #* i`schm unmg ?2#(
s`nr`h u vgnm u vrjg vcjmemi egjmmh`i` u vcz`hgi st`hdu* `prmsut`h dc m cjcicht`rhm emsme r`stvgrch u vgnm(
emsme m hdckgvm spgdcvm ) mzuzcthg zh``dhm z` mvgt svml mvmlom`( Tr`e* td( sjgognhm emsme dc hcgplgn`h z` hdmlgvg nms`hdc(Nms`hdc dc sjgchm gesmn`bmdsem prgbcs prm egdci sc r`zvmd`tgpjgt`* z`lv`jdudum egdgd jdunseg tmdcjg mi` tcipcr`turu 21*3)2;gB(
T` dcn`h s`t gvdceu dc pgtrcohg vmc gn 366 ni
2
v`znul`( Omjdec u tgeu `smimj`bmdc trgc BG?` gsjgo``du emsme(
Vgdcnhgst`vjdchg gvm prgbcsm sc igku prcnst`vmtm 5
Bi,L?G-h % iG? iBG?,k- % hL?G % Chcrkmd`
Gv` nv` prgbcs` prcnst`vjd`du st`jhm eruhm tge u prmrgnm(
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Ngomv`hdc emsme`4
J`ogr`tgrmdsem4
`- ?EBjG2 ?EBj,s- % 2G?,k-
o- ?LkG,s- ?Lk % G?,k-
b- ;366B
?O`G?,s- ?O`G,s- % G?,k-
3666B
Mhnustrmdsem4
ue`pjdmv`hdci zr`e` mjm cjcetrgjmzgi vgnc
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Chcrkctsem nmd`kr`i igjceujseml gromt`j` z` G?
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Emsme sc sp`d` s` vcmhgi cjcich`t` u VR ,gsmi s`pjcichmtmi k`sgvmi`* ajugrgi* ljgrgi* orgigi*mgngi* zj`tgi m pj`tmhgi-)prgbcs gesmn`bmdc(
@tgi emsme` sc vcc prctchg egv`jchthmi vcz`i`s` nrukmi `tgimi`* m tg t`eg n` mhm nvmdc prctchgegv`jchthc vczc(
@tgi emsme`* ` pghce`n m igjceuj` emsme`* igcprmimtm nv` cjcetrgh`* prm ciu h`st`du dghm s` nv`hck`tmvh` h`ogd`* G?)* gnhgshg G?
?) * kndc dc vcz`emsme` s` nrukmi `tgimi` prctchgdghse`( ^`evmspgdcvm igku h`st`tm s`ig s cjcichtmi` h`di`hdc
cjcetrghck`tmvhgstm( _mdcteg* `tgi emsme` igc mzkuomtm cjcetrgh ,hpr( u
spgdu G?%VtA1
) -(
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mst emsme dc gp`s`h k`s dcr sc u hdciu tv`rm j`ecgesmnmr`du m ogjdc kgrc(
Num ogr`v`e u `tigsacrm ocz emsme` ngvgnm ngprcst`h`e` mvgt` gvdcmdck grk`hmzi`(
@eg eghbchtr`bmd` emsme` u v`znulu sp`nhc h` 0;#*
hmsu prmidcchc tcthc pgsjdcnmbc(
mst emsme igc sc unms`tm er`teg vrmdcic oczpgsjdcnmb` m upgtrcojd`v` sc egn gmvjd`v`hd`n`vjdchme`* gsgo` trgv`hml BG m u sju`du gsj`ojdchgk
r`n` pju`( Vrm nuci unms`hdu mstgk emsme` tdcjcsh` tcipcr`t(
h`kjg r`stc zogk uorz`hd` ict`ogjmeml prgbcs`(
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Emsme mi` zh``dhu prmidchu u icnmbmhm* e`n` sucvmnchthc pgtcegc u nms`hdu* hpr( prm trgv`hdu
gtrgvhmi pjmhgvmi` mjm egn up`jc pju`( ^ n` sc egrmstmsidcs` emsme` m zr`e` u gidcru 040(
Ridcs` G?%BG?sc prmidchdudc egn vdct`egknms`hd`* u `vmghgi`* pgnigrhmb`i`(
Emsme sc egrmstm u gesm`bctmjchsemi kgrmghmbmi` z`pgstmz`hdc vmsgeml tcipcr`tur` tg mi` prmidchu urcz`hdu m z`v`rmv`hdu ict`j`(
Vgrcn `tgi` emsme` s` i`sgi 01* pgzh`t su mzgtgpm
s` i`s`i` 0; m 0
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Gzgh G
2trg`tgih` igjceuj` emsme`* nruk` `jgtrgpse`
ignmame`bmd`* vrjg `etmvh` m hcpgstgd`h`(
Egjmmh` gzgh` icu igjceuj`i` emsme` dc pr`etmhgz`hci`rjdmv`(
@eg sc pgvc`v` tcipcr`tur`* egjmmh` gzgh` uk`sgvmtgi emsmeu gst`t c kgtgvg mst`(
Icutmi* ngvgchdci chcrkmdc u hcegi nrukgigojmeu ,cjcetrmh` chcrkmd` mjm chcrkmd` r`nmd`bmdc-*
egjmmh` gzgh` u r`vhgtcm s emsmegi zh`thg r`stc( H`st`h`e gzgh` mz `tgi` m igjceuj` emsme` dc
ckzgtcrih` rc`ebmd`(
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Gzgh* G2 h`st`dc rc`ebmdgi4
G?,k- ?G,k- rL 9 >=> eD'igj?G,k- % ?G?,k- ?G2,k- rL 9 )?6= eD'igj
2 G?,k- ?G2,k- rL 9 ? eD'igj
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M emsme m gzgh su d`e` gesmn`bmdse` srcnstv`4
G?,k- % >L% % >c) ?L?G C
6 9 %0*?2 Q
G2,k- % ?L% % ?c) ?L?G % G?,k- C
6 9 %?*6; Q
Gzgh dc r`stvgrjdmv u vgnm m hdckgv` r`stvgrmvgst dc 36xvc` hckg dc r`stvgrjdmvgst emsme` u vgnm(
pjmh pj`vg ng pj`vgjduom`stc ogdc* u i`jmi egjmmh`i` vrjgprmd`thgk imrms`* ` u vcmi imrms` h` omdcjm jue mjm ljgr(
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7/23/2019 5. ELEMENTI 16 GRUPE
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gzgh dc mzuzcthg d`eg gesmn`bmdseg srcnstvg* dcnmhg dcajugr d`m gesmn`hs gn G2(
Gzgh gesmnmr` segrg svc cjcichtc( Sspdchg uhmt`v` o`etcrmdc* mzodcjdudc grk`hsec ogdc*
j`eg gesmnmr` hcz`smchc grk`hsec spgdcvc( Egrmstm sc z` stcrmjmz`bmdu vgnc m z` omdcjdchdc(
Mhtchzmvhg `psgroudc SQ)zr`ectg dc gn pgscohgkzh``d` z` mvgt h` zcijdm( Gzghsem sjgd egdm sc h`j`zmu vmmi sjgdcvmi` `tigsacrc tmtm pgvrmhu zcijdc gntcthgk ndcjgv`hd` suhcvgk SQ)zr`chd`( Gzghsec
rupcegdc su sc pgd`vmjc z`nhdml ncsctjdc` suukj`vhgi mz`zv`hc ndcjgv`hdci spgdcv` mz krupcarcgh` egdm ngspmdcv`du u `tigsacru mz urc`d` z`lj`chdc m sprcd)ogmb`(
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gzgh gesmn`bmdgi uhmt`v` o`etcrmdc* upgtrcojd`v` sce`g nczmhacebmghg srcnstvg z` prcm`v`hdc vgnc
vcml vgngvgn`( Nczmhameudc vgnuh` t`d h`mh tggesmnmc grk`hsec tv`rm(
Gzghmzgv`hm v`znul sc upgtrcojd`v` z` vchtmj`bmdu
r`nhml prgstgrmd`* pgnzcihml cjdczhmb` m vcmlnvgr`h`(
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RVGDCQM EMRME@
stcpch gesmn`bmdc?4
Gesmnm4 B`G* RG?* m gesm)spgdcvmH`?RG>* L2VG> mtn(
Ej`smame`bmd` gesmn`4 h` gshgvu emscjg)o`zhml e`r`etcrmstme` mpgigu strueturhml e`r`etcrmstme`(
0( h` gshgvu emscjg)o`zhml e`r`etcrmstme`4 emscjm* o`zhm * `iagtcrhm mhcutr`jhm
`- Emscjm gesmnm4 u vgnchmi r`stvgrmi` n`du emscju rc`ebmdu5 r`stv`r`dusc u o`z`i`5 nmrcethg hcutr`jmu o`zc 4
RG2 u vgnchmi r`stvgrmi` n`dc emscju rc`ebmdu4
RG2,k- % L?G L% % LRG>) Gnhgshg nmrcethg hcutr`jmc o`zc4
RG2,k- % GL) LRG>)
RmG?tgpjdchdci igc hcutr`jms`tm o`zc4RmG
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% ?H`GL,j-
H`?
RmG2,j-
% L?
G,k-
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o- O`zhm gesmnm4 u vgnchmi r`stvgrmi` n`du o`zhu rc`ebmdu5 r`stv`r`du sc uemscjmh`i`5 nmrcethg hcutr`jmu emscjmhc 4
H`trmd)gesmn* H`?G r`stv`r`hdci u vgnm n`dc o`zhu rc`ebmdu4
H`?G,s- % L?G ?H`% % ?GL)
Hcutr`jmc emscjmhc4H`?G,s- % ?L% ?H`% % L?G
E`nimdcv gesmn* BnG sc hc r`stv`r` u vgnm* `jm sc r`stv`r` u emscjmh`i`prm ciu dc hcutr`jmzmr`4
BnG,s- % ?L% Bn?% % L?Gb-@iagtcrhm gesmnm4 igku sc r`stv`r`tm m u emscjmh`i` m u o`z`i`*
gnhgshg igku hcutr`jms`tm m emscjmhc m o`zc4
Ro>G1hcutr`jmc m emscjmhc m o`zc4
Ro>G1,s- % 0?L%
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% 1L?GRo>G1,s- % >GL
) >RoG?) % ?L?G
n- Hcutr`jhm gesmnm4 hc rc`kudu s vgngi5 hc r`stv`r`du sc hm u emscjmh`i`hm u o`z`i`5 hc igku hcutr`jms`tm hm emscjmhc hm o`zc ,BG* H?G m HG-(
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7/23/2019 5. ELEMENTI 16 GRUPE
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Ngomv`hdc gesmn`40( Nmrcethgi smhtczgi mz cjcich`t`4
?B ,s- % G?,k- ?BG,k-B ,s- % G?,k- BG?,k-
?B` ,s- % G?,k- ?B`G,s-
?( Nclmnr`t`bmdgi hceml lmnrgesmn` ,ukj`vhgiprmdcj`zhml cjcich`t`-4?Ac,GL-2 ,s- Ac?G2,s- % 2L?G,k-Th,GL-? ,s- ThG,s- % L?G,k-
2( T`krmd`v`hdci hceml spgdcv` ,e`rogh`t`* hmtr`t`* omlrgi`t`* suja`t`-4
B`BG2 ,s- B`G,s- % BG? ,k-Vo,HG2-? ,s- VoG,s- % ?HG? ,k- % 0'?G?,k-Ac?,RG>-2 ,s- Ac?G2,s- % 2RG2 ,k-
,HL>-?Br?G; ,s- Br?G2,s- % H?,k- % >L?G,k-
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>( Vrchdci sujamn` ,gesmn`bmdgi h` zr`eu-4ThR,s- % 0*3G?,k- ThG,s- % RG? ,k-
3( Qrjg d`emi z`emscjd`v`hdci hceml sgjm ,vgjar`i`t`-4[G>
?) % ?L% [G2,s- % L?GQgn dc h`dv`hmdm gesmn(
Mghm B`?%* Ik?% m Ac?%stv`r`du hcr`stvgrjdmvc prgnuetctvrn` vgn`(^vrng` vgnc )ueup`h s`nr`d `hgrk`hseml supst`hbm u vgnm(
prgj`zh` mjm e`rogh`th`* prmsut`h mgh LBG2) m pgichutm mghm5
st`jh` mjm hce`rogh`th`* prmsut`h hcem nrukm `hmgh ` hcLBG2
) * m pgichutm mghm
^vrng` vgnc sc idcrm stcpchmi` tvrngc4 )0 hdci`em stcpch tvrngc gnkgv`r` egjmmhm ict`jhml dgh` egd` dc
cevmv`jchth` i`schgd eghbchtr`bmdm B`G gn 06 ik ni)2*
)0 ar`hbusem stcpch tvrngc gnkgv`r` egjmmhm ict`jhml dgh` egd` dc
cevmv`jchth` i`schgd eghbchtr`bmdm B`BG2 gn 06 ik ni)2(
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7/23/2019 5. ELEMENTI 16 GRUPE
27/75
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7/23/2019 5. ELEMENTI 16 GRUPE
28/75
Igjceuj` vgnc dc trgeut`stc strueturc* s` ukjgi gn 06>*3gmzicu nvmdc G)L)vczc( Togk vcjmec r`zjmec u cjcetrghck`tmvhgstmmzicu vgnme` m emsme`* igjceuj vgnc dc nmpgjhgk e`r`etcr`* tc suigjceujc vgnc `sgbmr`hc*e`eg u tchgi* t`eg m u vrstgist`hdu(
@h`jmzgi jcn` rchnkchsemi zr`e`i` dc ust`hgvjdchg n` sc geg
sv`egk `tgi` G h`j`zc ctmrm `tgi` L* nv` vcz`h`egv`jchthgi vczgi m nv` vgnmegvgi ,lmnrgkchgvgi- vczgi*
tg prgstgrhg n`dc tctr`cn`rseu strueturu( ^ctr`cnrm sc n`jdc egiomhmr`du u prgstgru pgput s`` stv`r`dum
lces`kgh`jhc upjdmhc* zogk egdml jcn mi` i`hdu kustgugnvgnc(
Vrgidch` kustgc vgnc prm pgvmchdu tcipcr`turc sc hc nc`v`eghtmhumr`hg( gpjdchdci jcn` sc h`ru`v` tctr`cn`rse`sruetur`( H` 2*=
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7/23/2019 5. ELEMENTI 16 GRUPE
29/75
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7/23/2019 5. ELEMENTI 16 GRUPE
30/75
Qgn` mi` vcjmeu rcj`tmvhu pcrimtmvhgst m ngo`r dc r`stv`r` prmdcsvck` z` supst`hbc s` dghsegi m pgj`rhgi egv`jchthgivczgi( S t`evmi r`stvgrmi`* gsmi mhtcr`ebmd` Q`h ncr[``jsgvgk tmp`* pgstgdc m d`c vczc* dcr vgn` igc omtm m jmk`hn(
ihgkc supst`hbc prm r`stv`r`hdu rc`kudu s` vgngi( Vrmermst`jmz`bmdm supst`hbm mz vgnchgk r`stvgr`* igc ngm ngukr`nhdc igjceuj` vgnc u ermst`jhu rccteu) h`st`du spgdcvmermst`jglmnr`tm( S ermst`jglmnr`tmi`* ermst`jh` vgn` igc omtmvcz`h` lmnrgkchgvgi vczgi mjm eggrnmh`bmdsegi vczgi(
Hcec supst`hbc mi`du vcjmem `amhmtct prci` vgnm* st`d`hdci
`psgroudu vj`ku mz zr`e` m prcj`zc u r`stvgr)pgd`v`ncjmevcsbchbmdc(
Ruprgt`h prgbcs gtput`hd` vgnc mz ermst`jglmnr`t` )cajgrcsbchbmd`(
S tcrignmh`imegi simsju* vgn` dc mzuzcthg st`omj`h spgd* `jm
vc h` sgohgd tcipcr`turm igc rc`kgv`tm s` ihgkmisupst`hb`i`( S vcmhm rc`ebmd` s` vgngi* pgn utmb`dci vgnc ngj`zm ng
emn`hd` pgj`rhml egv`jchthml vcz` u spgdcvmi`)rc`ebmdclmnrgjmzc*i`n` sc u uci simsju pgn lmnrgjmzgipgnr`zuimdcv`du rc`ebmdc sgjm m vgnc(
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7/23/2019 5. ELEMENTI 16 GRUPE
31/75
Vrgj`zh` mjm e`rogh`th` tvrng` uej`hd` sc4`- eul`hdci vgnc dcr sc gnvmd` pgvr`th` rc`ebmd` p` sc mz
r`stvgr` uej`hd` BG?4
B`BG2,s- % L?G % BG? B`?% % ?LBG2
)
o- uej`hd`hdci B`?% )mgh` mz r`stvgr` ngn`tegi sgnc*H`
?
BG2
prm ciu sc t`jgm hcr`stvgrjdmvm B`BG2
4
B`?% % BG2?)
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mgh egdm ghn` t`jgm B`?%
LBG2) % GL) BG2?) % L?G
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7/23/2019 5. ELEMENTI 16 GRUPE
32/75
c- ngn`tegi e`jbmd lmnrgesmn` ,pgstup`e s v`phgi m sgngi-4
B`?% % ?LBG2) % B`?% % ?GL) ?B`BG2 ,s- % ?L?G
Ik?% % ?GL) Ik,GL-? ,s-
Ac?% % ?GL) Ac,GL-? ,s-
a- pgstupbm s mghsemi mzidchdmv`mi` Upcriutmt* H`,@jRmG>-( L?G mzcgjmt H`,@jRm?G1-( L?G Y4
B`?% % ?H`% ?H`% % B`?%
k- pgstupbm s` smhtctsemisigjhmi mzidchdmv`mi` ,ngomdc scncmghmzmr`h` vgn`-4
E`tmghse` mzidch`vcu sc ict`jhm ` gsjgo``du vgnmegvm
mghm4?L)sigj` % B`?% B`)sigj` % ?L%
@hmghse` mzidch`vcu sc `hmghm ` gsjgo``du GL) mghm egdmhcutr`jmu L%)mghc4
?GL)sigj` % RG>?) % ?L% RG>)sigj` % ?L?G
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7/23/2019 5. ELEMENTI 16 GRUPE
33/75
dghgmzidchdmv`m su vmsgegpgjmicrmzmr`hc grk`hsec supst`hbcegdc s`nrc emscjc hpr( _)RG2)L
%) mjm o`zmhc hpr( _)H,BL2-2%GL
)) krupc(
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H`egh z`sm`v`hd`* dghgmzidchdmv`m sc rckchcrmr`duprgput`hdci eghbchtrmr`hml r`stvgr` emscjmhc mjm o`zc(
Vrcm`v`hdc vgnc z` pmc ) sjgch prgbcs* s`stgdm sc mz a`z`4ljgrmr`hdc* ajgeuj`bmd`* scnmicht`bmd`* amjtrmr`hdc* trctmr`hdc`etmvhmi ukjdchgi m pghgvhg ljgrmr`hdc(
Auhebmd` prvgk ljgrmr`hd` dc uej`hd`hdc p`tgkchml o`etcrmd` mvmrus`( Ajgeuj`bmdgi sc uej`hd`du suspchnmr`hc m egjgmnhcsupst`hbc( S vgnu sc ngn`du @j,MMM- m Ac,MMM- sgjm* egdc
lmnrgjmzmr`du stv`r`dum kcjgvc lmnrgesmn` egdm `nsgroudu nrukcegjgmnc4@j?,RG>-2 % 1 L?G ? @j,GL-2,s- % 2 L?RG>
^rctmr`hdc `etmvhmi ukjdchgi sjum z` uej`hd`hdc r`stvgrchmlgrk`hseml supst`hbm( Nrukg ljgrmr`hdc mi` auhebmdu sprdc`v`hd`z`k`mv`hd` pmd`c vgnc u vgngvgnhgd ircm(
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7/23/2019 5. ELEMENTI 16 GRUPE
34/75
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7/23/2019 5. ELEMENTI 16 GRUPE
35/75
stcpch gesmn`bmdc
0
Vcrgesmnm spgdcvm u egdmi` sc vcz` emsme)emsme r`zomd` prm vmsgegdtcipcr`turm(
Ngomv`hdc o`rmdcvgk pcrgesmn`* O`G?* z`krmd`v`hdcicjcicht`rhgk o`rmd` s emsmegi n`jdmi z`krmd`v`hdci sc r`zj`c4
O`G?,s- ?O`G % G?,k- rL 9 012 eD'igj
Ndcjgv`hdci emscjmhc h` pcrgesmn h`st`dc vgnmegv pcrgesmnO`G?,s- % ?L
% O`?% % L?G?Kcgictrmd` igjceujc lmnrgkch pcrgesmn` u vrstgi st`hdu4
Mhnustrmdseg ngomv`hdc4
`- `hgnhgi gesmn`bmdgi L?RG>
E`tgn` ?L% % ?c) O`?% % L?G?@hgn` ?LRG>
) L?R?G< % ?c)
,pcrgesgnmsuja`th` ems(-
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7/23/2019 5. ELEMENTI 16 GRUPE
36/75
T`krmd`v`hdci L?R?G< lmnrgjmzmr` h`dprmdc u pcrgesgsuja`thuemscjmhu* L?RG3
L?R?G< % L?G L?RG3 % L% % LRG>)
z`tmi L?RG3 lmnrgjmzmr` n`jdc h` L?G?
L?RG3 % L?G L?G? % L% % LRG>)
o- lmnrmr`hdc `htr`emhgh` m gesmn`bmd` h`st`jgk `htr`emhgj`
mstm L G dc oc ogdh` tchgst egd` sc j`eg r` j`c pg rc`ebmdm
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7/23/2019 5. ELEMENTI 16 GRUPE
37/75
mstm L?G?dc oczogdh` tchgst egd` sc j`eg r`zj`c pg rc`ebmdm
)0 )? 6
L?G? ? L?G % G?,k- S vgnchmi r`stvgrmi` dc sj`o` emscjmh` egd` nmsgbmr` u nv`
stcpch`L?G? L
% % LG?) ?L% % G?
?)
u pgrcchdu s` vgngi mi` vmu tcipcr`turu ejdu`hd`
,036gB-* vcu kustgu m vmsegzhgst( E`g m egn vgnc* igjceujc L?G?su m u tchgi m vrstgi st`hdu
pgvcz`hc vgnmegvmi vcz`i`(
pgstgdc spgdcvm egdm su `h`jgkhm ermst`jglmnr`tmi` m egdm sc zgvu
pcrlmnr`tm* hpr( H`?BG2xL?G? Lmnrgkchpcrgesmn sc prmidchdudc e`g nczmhacebmdseg srcnstvg m
srcnstvg z` omdcjdchdc(
A`ri`bcutseu prmidchu mi` h`dcc 2#)thm r`stvgr egdm
r`z`r` ihgkc p`tgkchc o`etcrmdc(
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7/23/2019 5. ELEMENTI 16 GRUPE
38/75
Vcrgesmnhm mgh dc d`e` o`z` egd` prgtgjmtmem rc`kudc svgngi
G??) % ?L?G L?G? % ?GL)
Vcrgesmnm ndcjudu e`g gesmn`bmdse` srcnstv`* prmi`ducjcetrghc m prcj`zc u stcpch gesmn`bmdc?
L?G? % ?L% % ?c) ? L?G C69 %0*;; Q
Gorhutg* pcrgesmnm ndcjudu e`g rcnuebmdse` srcnstv`*gtput`du cjcetrghc m prcj`zc u stcpch gesmn`bmdc 6
,cjcicht`rhm emsme-
L?G? G?,k- % ?L% % ?c) C69 ) 6*1= Q
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7/23/2019 5. ELEMENTI 16 GRUPE
39/75
Mz r`stvgr` dgnmn` mzjuudu cjcicht`rhm dgnL?G? % ?M
) % ?L% M?,s- % ?L?G
_cnueudc emscjc r`stvgrc pcri`hk`h`t`3L?G? ?IhG>
) % 1L% 3G?,k- % ?Ih?% %
-
7/23/2019 5. ELEMENTI 16 GRUPE
40/75
L?G? )gesmn`bmdseg srcnstvg* srcnstvg z` omdcjdchdc(
S icnmbmhm sc upgtrcojd`v` 2# r`stvgr e`g nczmhacebmdsegsrcnstvg( Nczmhacebmdseg ndcjgv`hdc L?G?pgtmc gnh`sbchthgk emsme` egdm sc gsjgo`` r`sp`n`hdci L?G? (
Mz 0 k 2# L?G?gsjgo`` sc ?6 bi2 G? (
_`sp`n`hdc L?G m gsjgo``hdc emsme` dc h`rgmtgmhtchzmvhg h` khgdhmi r`h`i` zogk prmsustv` acrich`t`
e`t`jmzc m pcrgesmn`zc egdm mhtchzmvmr`du r`sp`n`hdc L?G? (
A`ri`bcutseu prmidchu mi` h`dcc 2#)thm r`stvgr
L?G? egdm uspdchg r`z`r` ihgkc p`tgkchc o`etcrmdc(
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7/23/2019 5. ELEMENTI 16 GRUPE
41/75
stcpch gesmn`bmdc
0'?
Rupcrgesmnm* spgdcvm tmp` IG? s` cjcichtmi` 0( krupc
,E* _o m Bs-E`jmd)supcrgesmn h`st`dc mzk`r`hdci E u strudm emsme`
6 6 %0 )0'?
E ,s- % G?,k- EG?,s-
)Hcst`omjhm spgdcvm* u vgnm nmsprgpgrbmghmr`du h` L?G?*
gnhgshg LG?) m cjcicht`rhm emsme
)0'? 6?EG?,s- % L?G G?,k- % LG?) % ?E%% GL)
RSIVG_
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7/23/2019 5. ELEMENTI 16 GRUPE
42/75
RSIVG_ i`schm unmg u Tcijdmhgd egrm 9 6*63#
d`vjd` sc sjgogn`h m u gojmeu suja`t` m sujamn`
u vcz`hgi gojmeu h`j`zm sc h`dcc u imhcr`jmi`4 pmrmtu*AcR?* l`jegpmrmtu* BuAcR?* k`jchmtu* VoR* kmpsu* B`RG>x ? L?G m nr(
Cjcicht`rhm suipgr dc gomhg vuje`hsegk pgrmdcej` mjm sch`j`zm u h`sj`k`i` mspgn pmdcse` m si`tr` sc n` dc
h`st`g o`etcrmdsemi r`zj`k`hdci e`jbmdcvgk suja`t`( Vrgbcs h`st`d`hd` cjcicht`rhgk* vuje`hsegk suipgr`*
sc igc god`shmtm icusgohmi ndcjgv`hdci nv` pjmhgvmt`suipgrh` spgd` suipgrvgnme`* L?R m suipgr,MQ- gesmn`RG?(
prmsut`h m u suipgrhmi vgn`i` u egdmi` sc h`j`zmr`stvgrchm L?R(
u i`jmi egjmmh`i` h`j`zm sc u hcemi odcj`hcvmh`i`pgtrcohmi z` jdunsem mvgt(
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7/23/2019 5. ELEMENTI 16 GRUPE
43/75
Ngomv` sc h` ? h`mh`40( Ar`sblgvmi pgstupegimz prmrgnhml jcmt` ,mstgc =1 eD'igj
Ngomvchm R dc r`st`jdch
gh g s s` c z` g v`h c pg
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7/23/2019 5. ELEMENTI 16 GRUPE
44/75
gh g s s` c z` g v`h c pgAr`sblu
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7/23/2019 5. ELEMENTI 16 GRUPE
45/75
Bj`usgv pgstup`e z` ngomv`hdc suipgr`
-
7/23/2019 5. ELEMENTI 16 GRUPE
46/75
R dc h` sgohgd tcipcr`turm u vrstgi st`hdu* svmdctjgut* ocz ueus` m imrms`
hcr`stvgrjdmv u vgnm* r`stvgrjdmv u ihgkmi grk`hsemir`stv`r`mi` ,BR?* BBj>-(
Rj`og prgvgnm tgpjgtu m cjcetrmbmtct(
Vrmidch`4 z` prgmzvgnhdu suipgrhc emscjmhc* z`
vuje`hmz`bmdu kui` m z` prgmzvgnhdu o`rut`5 z`ngomv`hdc spgdcv` ,BR?* R?Bj?- m e`g auhkmbmn u
pgjdgprmvrcnm(
Vr`vm spgdcvc s hck`tmvhmi m pgzmtmvhmi stcpchmi`
gesmn`bmdc(
Ignmame`bmdc cjcicht`rhgk s ipgr`
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7/23/2019 5. ELEMENTI 16 GRUPE
47/75
Ignmame`bmdc cjcicht`rhgk suipgr`
Gshgvh` struetur` prstch`st` R
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7/23/2019 5. ELEMENTI 16 GRUPE
48/75
H`dzh``dhmdc su trm `jgtrgpsec ignmame`bmdc suipgr`*rgipsem* ighgejmhsem m `igrahm(
H` gomhgd tcipcr`turm* st`omj`h dc rgipsem suipgr* egdmh` =3*3gB rcvcrzmomjhg prcj`zm u ighgejmhsem ,mi`du
igjceuju R
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7/23/2019 5. ELEMENTI 16 GRUPE
49/75
d p k d d dh`kjg glj`nm* prcj`zm u ireu cj`stmhu i`su tzv( `igrahm mjmpj`stmhm suipgregdm sc s`stgdm mz nukgk hmz` R)`tgi`( Ngomv`sc numi z`krmd`v`hdci r`stgpjdchgk suipgr` m ujmdcv`hdci ulj`nhu vgnu(
S a`ri`bmdm ngj`zc trm agric mstgk suipgr`4 sujaur ncpur`tui,prcmchm suipgr-* sujaur suojmi`tui ,ngomvch prgbcsgisuojmi`bmdc- m sujaur prcbmp`t`tui,ngomvch t`jgchdci-(Rujaur suojmi`tui sc ngomv` suojmi`bmdgi suipgr` h` 0?3 B(
Rujaur ncpur`tuisc pgsjmdc gor`udc s` HL>GL* t`eg n` scprmsuthc emscjmhc prcvgnc u `ighmdcvc sgjm* ` @s?R2 m @s?G2 scprcvgnc u `ighmdcv `rschmt m `ighmdcv suja`rschmt4
@s?R2 % 1 HL>GL ,HL>-2@sR2 % ,HL>-2@sG2 % 2 L?GSpgtrcojd`v` sc mhtcrhg e`g purk`tmvhg srcnstvg( S brmdcvmi`h`st`dc L?R egdm h`nr`udc zmngvc brmdcv` m pgnstmc pcrmst`jtmeu(
Rpgjd` sc upgtrcojd`v` z` jmdcchdc r`zhml eghml ogjcstm(^`jgchm suipgr ,sujaur prcbmpmt`tui- sc ngomv` kr`chdcipgjmsujamn` m hdmlgvmi r`z`r`hdci ,vrjg smt`h-( Spgtrcojd`v` scspgjd` u gojmeu i`stm m mhtcrhg( Gtgpjdch u ujdu u gojmeu mhdcebmd`upgtrcojd`v` sc z` jmdcchdc lrghmhgk rcui`tmzi`(
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7/23/2019 5. ELEMENTI 16 GRUPE
50/75
stcpch gesmn`bmdc
?
Rujamnm* sgjm vgnchgk r`stvgr` L?R ,m lmnrgkchsujamnm-4Ruipgrvgnme* r`stv`r` sc u vgnm* rc`kudc emscjg4
L?R,k-L% % LR)?L
% % R?)
Qgnchm r`stvgr L?R dc sujamnh` emscjmh` ,suipgrgvgnmh`-
Ngomv` sc ngn`tegi L%
)mgh`4
ThR,s-% ?L%
Th?% % L?R,k-
_cnuebmghg ndcjudc u prgbcsmi` s` sj`omdmi gesmn`bmdsemi
srcnstvmi` prm ciu sc L?R gesmnmr` ng cjcicht`rhgksuipgr`4
)? 6
?Ac2% % L?R,k- ?Ac?% % R,s- % ?L%
t L R t d d e e mnm m R, ?-
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7/23/2019 5. ELEMENTI 16 GRUPE
51/75
r`stvgr L?R st`d`hdci h` zr`eu sc gesmnmr` mz R,)?- ucjcicht`rhm suipgr4
?L?R,k- % G? ?R,s- % ?L?G
s d`mi ges( srcnstvmi`* gesmn`bmd` mnc n`jdc ng %> mjm %1* uzngvgjd`h prmstup zr`e`4
)? %>
?L?R,k- % 2G?,k- ?RG?,k- % ?L?G,k-
` s` cjcicht`rhmi Bj?* Or? m IhG>) )dghgi h`st`dulmnrgkchsuja`tm4
LR)% >Bj?,k- % >L?G,k- LRG>) % L
% 3LRG>) %
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7/23/2019 5. ELEMENTI 16 GRUPE
52/75
RujamnmNgomv`hdc4
0( ndcjgv`hdci L?R mjm tgpjdmvml sujamn` h` ict`jhc mghc
Bu?% % R?) BuR ,s-?Om2% % 2R?) Om?R2 ,s-
?( nmrcethmi sp`d`hdci cjcich`t`
B,s-
% ?R,k-
BR?,k-
Ac,s- % R,s- AcR,s-
2( rcnuebmdgi suja`t` s ukjdmegi prm vmsgegd tcipcr`turm
%1 )? %?
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> t jm md n ml t je jmd eml jamn L R
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7/23/2019 5. ELEMENTI 16 GRUPE
53/75
>( hcutr`jmz`bmdgi vgnchml r`stvgr` `je`jmdseml sujamn` s L?R
?H`% % ?GL) % L?R,k- ?H`% % R?) % ?L?G
Rujamnhm mgh u vgnchmi r`stvgrmi` d`eg lmnrgjmzmr`4
R?)% L?G LR) % GL)
p` sc ngomdc H`?R(=L?G mjm H`LR
( 2L?G
Rujamnm sc r`zjmeudu pg r`stvgrjdmvgstm u vgnm4
j`eg r`stvgrjdmvm4 sujamnm `je`jhml m zcihg`je`jhml ict`j`
sujamnm egdm sc r`stv`r`du ngn`tegi L% )mgh`4 ThR m AcR
i`jg r`stvgrjdmvm4 BuR* VoR* Om?R2* @k?R* RhR m h`di`hdcr`stvgrjdmv LkR egdm sc r`stv`r` u b`rsegd vgnm mjmzj`tgtgpem ,0 nmg eghb( LHG2 m 2 nmdcj` eghb( LBj-
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7/23/2019 5. ELEMENTI 16 GRUPE
54/75
stcpch gesmn`bmdc0 m gst`jm hck`tmvhm stcpchm gesmn`bmdc
Nmsujamnm ,pcrsujamnm- m pgjmsujamnm
Vcrsujamnm* ,AcR?- spgdcvm `h`jgkhm pcrgesmnmi`4
U 4R)R4 Y?)
igku ndcjgv`tm gesmn`bmdsem4
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Mjm rcnuebmdsem4
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vmegi suipgr` ,H`?Rx kndc dc x9 gn ? ng 3* i`x( =-
t e mn md 0
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7/23/2019 5. ELEMENTI 16 GRUPE
55/75
stcpch gesmn`bmdc %0
Ruipgrhm l`jgkchmnm tmp` R?\?*
Ruipgr,M- ljgrmn* R?Bj?
stcpch gesmn`bmdc %?
Nml`jgkchmnm* suipgr,MM- ljgrmn* RBj?* suipgr,MM-gesmn* RG
stcpch gesmn`bmdc %2
Gvm l`jgkchmnm hc pgstgdc ,R?G2-
Lmpgnmsujamtm R?G>?)
su st`omjhm u vrstgi st`hdu* uo`zhgd srcnmhm su d`e` rcnuebmdse` srcnstv`
stcpch gesmn`bmdc %>
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7/23/2019 5. ELEMENTI 16 GRUPE
56/75
stcpch gesmn`bmdc %>
^ctr`l`jgkchmnm* suipgr tctr`ajugrmn mjm suipgr,MQ- ajugrmn*RA>* suipgr nmgesmn* RG? m sujamth` emscjmh`* L?RG2 mhdczmhc sgjm(
Ruipgrgv,MQ- gesmn ,suipgrgv nmgesmn-* RG?h`st`dc mzk`r`hdci R s` emsmegi mz zr`e`4
R,s- % G?,k- RG?,k- rL 9 )?
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7/23/2019 5. ELEMENTI 16 GRUPE
57/75
Ruipgrgv,MQ- gesmn* RG? dc h` sgohgd tcipcr`turm k`sgvmt*gtrgv`hgtrgk* hcukgnhgk* ogbe`vgk imrms`
j`eg rc`kudc s vgngi ,emscj` rc`ebmd`- n`dum dghc4
LRG2) ) lmnrgkchsujamt* RG2?) )sujamt* R?G3?) )nmsujamt*hmdc utvrchg pgstgd`hdc sujamthc ,suipgr`stc- emscjmhc*L?RG2
Rgjm sujamthc emscjmhc4
hgri`jhm sujamtm I?
MRG2
m IMMRG2
m lmnrgkchsujamtm
egdm kuomtegi vgnc prcj`zc u nmsujamtc I?MR?G3(
H`trmdcv sujamt* H`?RG2* egrmstm sc e`g rcnuebmdseg srcnstvgm z` omdcjdchdc u tcestmjhgd mhnustrmdm
e`jbmdcv lmnrgkchsujamt* B`,LRG2-? mi`khczmdcv lmnrgkchsujamt Ik,LRG2-? *
egrmstc sc u prgmzvgnhdm p`pmr`( ngomd`du sc u gojmeu
vgnchgk r`stvgr`4
B`,GL-?
% ?RG?,k-
B`,LRG2
-?
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7/23/2019 5. ELEMENTI 16 GRUPE
58/75
RG? dc pgj`rh` igjceuj`* j`eg sc ue`pjdudc(
^chm RG?sc egrmstm e`g r`stv`r` z` ihgkcsupst`hbc hpr( M
?* V* R* EM* EOr m nr(
Vrm msp`r`v`hdu trgm zh`thu egjmmhu tgpjgtc* egrmstm sc u`p`r`tmi` z` lj`chdc(
egrmstm sc z` stcrmjmz`bmdu sulgk vg` m vmhsec our`nm* dcr
pgscohg gtrgvhg ndcjudc h` hmc grk`hmzic( struetur`sc igc prcnst`vmtm rczgh`hthmi lmormngi
ngimh`hth` agriuj`
R
G
G
R
G
G
% %
)
)
4 4
4
4
4
4((
((
((
((
((
((
R
G G
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7/23/2019 5. ELEMENTI 16 GRUPE
59/75
Ruipgrgv nmgesmn
nr`m m h`p`n` sjuzhmbu(
ndcjudc nczmhacebmghg* uomd` kjdmvmbc m o`etcrmdc(
d`e ervhm gtrgv5 sirt h`stup` zogk kuchd`5
egn `euthml trgv`hd` ngj`zm ng vcml gtcchd`
sjuzgegc gmdu m hgs`(omjdec su d`eg gsdctjdmvc h` pgvc`hc eghbchtr`bmdc
RG? u v`znulu(
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7/23/2019 5. ELEMENTI 16 GRUPE
60/75
stcpch gesmn`bmdc %14
h`dv`hmdm4 lces`ajugrmn RA1* R?A06* suipgrgv,QM-gesmn* suipgrh` emscjmh` m hdczmhc sgjm* l`jgkch)
ncrmv`tm suja`thc emscjmhc* tc pcrgesgsuja`thc emscjmhc
Ruipgrgv,QM- gesmn,suipgrgv trmgesmn-* RG2ngomd` sc gesmn`bmdgi RG? s emsmegi
?RG? % G?,k- ?RG2,k- rL 9 )?;6 eD'igj
rc`ebmd` dc ckzgtcrih` m pgr`stgi tcipcr`turc RG2sc r`sp`n`
J o t md em n om md d nm ja t
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7/23/2019 5. ELEMENTI 16 GRUPE
61/75
J`ogr`tgrmdsem sc ngomv` z`krmd`v`hdci nmicc suja`thcemscjmhc4
L?R?G; L?RG> % RG2,k-
Mjm z`krmd`v`hdci e`jmd lmnrgkchsuja`t`4
?ELRG>,s- E?R?G; % L?G,k-E?R?G;,s- E?RG>,s- % RG2,k-
Mjm ncstmj`bmdgi AcRG> mjm Ac?,RG>-2
Ac?,RG>-2,s- Ac?G2,s- % 2RG2,k-
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7/23/2019 5. ELEMENTI 16 GRUPE
62/75
H` sgohgd tcipcr`turm RG2 dc u tchgi st`hdu*r`slj`mv`hdci h` 01*
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7/23/2019 5. ELEMENTI 16 GRUPE
63/75
Ruipgrh` ,suja`th`- emscjmh * L?RG>
Ngomv`hdc4
r`stv`r`hdci RG2 u vgnm4
RG2,k- % L?G L?RG> rL 9 ) Vrmhbmp4 gesmn`bmd` RG?pgigu hmtrgzhgkk`s` egdm sc
ukj`vhgi s`stgdm gn HG?* ngomdchgk ndcjgv`hdci eghb(suja`thc emscjmhc h` eghbchtrmr`hu hmtr`thu emscjmhu(
Gesmn`bmd` pgigu hmtrgzhgk k`s` sc vrm u prmsustvuvgnc( H`st`jm HG sc gesmnmr` u HG? egdm prcnst`vjd`prchgsmgb` emsme` u prgbcsu( Gvmi pgstupegi sc ngomd`emscjmh` mdm dc i`esmi`jhm i`schm unmg ;6#(
-
7/23/2019 5. ELEMENTI 16 GRUPE
64/75
?( eght`ethm pgstup`e
e`t`jmz`tgr ,v`h`nmdcvm gesmnm-
?RG?,k- % G?,k- ?RG2,k- rL 9 )0
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7/23/2019 5. ELEMENTI 16 GRUPE
65/75
Rgjm L?RG>4
Lmnrgkchsuja`tm ,u vgnchgi r`stvgru rc`kudu emscjg-* H`LRG>m ELRG>5 z`krmd`v`hdci prcj`zc u nmsuja`tc ,pmrgsuja`tc-4
?H`LRG>,s- H`?R?G;,s- % L?G,k-
m n`jdmi krmd`hdci u suja`tc m RG24
H`?R?G;,s- H`?RG>,s- % RG2,k-
Gsjgogchm RG2rc`kudc s hctgpjdmvmi gesmngi stv`r`dumtgpjdmvm suja`t4
Br?G2,s- % 2RG2,k- Br?,RG>-2,s-
Ruja`tmsu r`stvgrjdmvm u vgnm*
lmnr`tmzmr`hm s hcp`rhmi orgdci igjceuj` vgnc* ,k`jmbc-4IMMRG>
;L?G ,IMM 9 Ih?%* Bg?%* Hm?%* Th?%* Ac?% - mjm
BuRG> 3)2)0 L?G5
nvgstruem suja`tm4
`j`uhm mjm stmpsc s`st`v` IMIMMM,RG>-?0?L?G m
chmtms`st`v` I?MIMM,RG>-?1L?G
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7/23/2019 5. ELEMENTI 16 GRUPE
66/75
Rvgdstv` L?RG>4 mst` emscjmh` dc oczogdh`* ujd`st`tchgst( R` vgngi sc imdc` u sv`egi gidcru* `jm dc
hdchg r`stv`r`hdc u vgnm vrjg ckzgtcrihg(`- emscjmhseg ndcjgv`hdc
L?RG> L% % LRG>)
LRG>) L% % RG> ?)
?L?RG> L2RG>% % LRG>)
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7/23/2019 5. ELEMENTI 16 GRUPE
67/75
o- gesmn`bmdseg ndcjgv`hdc
Emscjmh` eghb( 0 igj'ni2
dc srcnhdc d`eg gesmn`b(srcnstvg* nge dc eghbchtrgv`h` emscjmh` d`eg
gesmn`bmdseg srcnstvg egdc gt`p` ict`jc
6 %1 %>
Bu,s- % 2L% %LRG>) Bu?% % RG?,k- % L?G
gesmnmr` cjcicht`rhm R4
6 %1 %>R,s- % ?L?RG> 2RG?,k- % ?L?G,k-
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7/23/2019 5. ELEMENTI 16 GRUPE
68/75
b- nclmnr`t`bmdseg ndcjgv`hdc
mst` emscjmh` vcc h` scoc vgnu ,srcnstvg z`
suchdc-* h`st`du t`hg ncamhms`hm lmnr`tm4L?RG>* L?RG>L?G* L?RG> ?L?G* L?RG>>L?G
gnuzmi` vj`ku grk`hsemi supst`hb`i`* ` grk`hsec
supst`hbc sc prm tgic ukjdchmu4
B0?L??G00,s- 0? B,s- % 00 L?G
ccr ,s`l`rgz`-
L`jgkchsem ncrmv`tmsuja`thc emscjmhc4
ighg)ncrmv`tm ,l`jgkchgsuja`thc emscjmhc h`st`duz`idchgi dcnhc GL)krupc- m
nm)ncrmv`tm ,l`jgkchgsujagh`thc emscjmhc h`st`du
z`idchgi nvmdc GL)krupc-(
L RG? >
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7/23/2019 5. ELEMENTI 16 GRUPE
69/75
L`jgkchgsuja`thc emscjmhc,ajugrgsuja`th`* LRG2A m ljgrgsuja`th`* LRG2Bj-
h`st`du ndcjgv`hdci l`jgkchgvgnme` h` gjcui4
RG2 % LBj LRG2BjRG2 % LA LRG2A
Vcrgesgjuja`thc emscjmhc4Vcrgesgnmsuja`th` emscjmh` ,pcrgesgnmsuipgrh`-* L?R?G4
?LRG>) R?G
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7/23/2019 5. ELEMENTI 16 GRUPE
70/75
^mgemscjmhc ,gesm)spgdcvm u egdmi` dc dcn`h mjm vmc `tgi`emsme` z`imdchdchg `tgimi` suipgr`-4
lmpgtctse` tmgsuipgrh` emscjmh`* L?R?G2m hdch` sgH`?R?G2
egd` sc ngomd` eul`hdci h`trmd sujamt` s` cjcicht`rhmi R4
RG2?)
% R,s- R?G2?)
Rtrueturh` agriuj` tmgsuja`thgk mgh`4
R?G2?)dc srcnhdc d`e rcnubchs4
?R?G2?)
R>G1?) %?c) C6 9 %6*6< Qprm ciu sc stv`r` tctr`tmgh`thm mgh* R>G1?)
RCJCH
-
7/23/2019 5. ELEMENTI 16 GRUPE
71/75
RCJCH
rmdcn`e cjcicht* e`g zj`tg
pr`tmj`b suipgr` m scjchmn`
ngomv` sc e`g husprgnuet prm cjcetrgjmtsegd r`amh`bmdm
o`er`
Rc
-
7/23/2019 5. ELEMENTI 16 GRUPE
72/75
Rcjch dc sjm`h suipgru m dcnh`eg e`g suipgr pgd`vjdudcsc u hcegjmeg `jgtrgpseml ignmame`bmd`(
H`dc` dc brh` ignmame`bmd` scjch` s` `igrahgistrueturgi(
Brvch` ignmame`bmd` mjm brvchm scjch sc s`stgdm gn
prstch`stml igjceuj` Rc
-
7/23/2019 5. ELEMENTI 16 GRUPE
73/75
Rcjchgvgnme* L?Rc dc pjmh hcukgnhgk imrms`*r`stv`r`hdci u vgnm n`dc emscjmhu egd` nmsgbmr` u nv`stcpch`4
L?Rc L% % LRc) ?L% %Rc?)
Rcjchgv nmgesmn mjm scjch,MQ- gesmn* RcG?* dc vrst`supst`hb` egd` sc r`stv`r` u vgnm n`dum scjchmthuemscjmhu ,scjch`stu-* L?RcG2(
Rcjchgv,QM- gesmn* RcG2
Rcjch`th` ,scjchse`- emscjmh * L?RcG>*d`eg gesmn`bmghg m nclmnr`t`bmghg srcnstvg* Rj`omd` dc gnsuja`thc ems(* `jm dc d`eg gesmn`bmdseg srcnstvg m d`c gnsuja`thc emscjmhc Cg90*03Q* igc n` gesmnmr` m pjcichmtcict`jc(
^CJS_
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7/23/2019 5. ELEMENTI 16 GRUPE
74/75
^CJS_
rmdcn`e e`g scjch* rdcm pr`tmj`b R
tcjurmnm su pr`tmgbm sujamn` o`er` m gjgv`^cjurgvgnme* L?^c dc gtrgvhm k`s hcukgnh` imrms`*r`stv`r` sc u vgnm
^cjurgv nmgesmn mjm tcjurgv,MQ- gesmn* ^cG?* sj`og scr`stv`r` u vgnm n`dum tcjurmthu emscjmhu ,tcjur`stu-L?^cG24
cG? % L?G L? cG2
Rgjm tcjurmthc emscjmhc4 lmnrgkchtcjurmtm m tcjurmtm
^cjur`th` emscjmh` ,tcjurh - L1^cG1,L?^cG>-h pgjmict`tcjur`th` ems(
Rvm spgdcvm Rc m c su gtrgvhm* dcnh`eg e`g m suipgrgvm spgdcvm )lcimd`gvml spgdcv` hmdc ngvgjdhg mzuch`(Imrms scjch` m tcjur` dc hcpgnhgjdmv* j`eg sc upmdc u egu m spgrggnstr`hdudc(
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7/23/2019 5. ELEMENTI 16 GRUPE
75/75
VGJGHMD r`nmg`etmv`h* vrjg gp`s`h* prmsut`h u run`i` ur`h`(
Vrvm put ngomvch cestr`ebmdgi mz gvml run`(
N`h`s sc ngomv` msejdumvg vdct`emi putci(
Hci` zh``dhmdu prmidchu(