CIENCIAS III

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=amp Ann na zntzc n efjelm l~iacutea |nriumlm na ziumlz~ac oiacute| mjnl~mjcampnhugravef na efwn|zehmjcr I~mf Oeh~na Lmopmfmrec am lenflem |n ~|m nf am p~baelejmj jn amoe|om gcrom ~n |n ~zeaeym m ~f mlzcr gmoc|c c m ~f lmfzmfzn lcoc rn|pmajc jn lmaejmjjn ~f prcj~lzcamp e |n jeln nf ~f mf~flec ~n ~f prcj~lzc n|ziacute prcbmjc lenfziumlgelmonfzn|n |~pcfn ~n n| mahc wnrjmjnrc |n lrnn ~n na lcfcleoenfzc lenfziumlgelc n|ziacute prcbmjcoiacute| maaiacute jn zcjm j~jm ac ~n n| nrruumlfncamp Mjnoiacute| ac| p~baele|zm| |n mprcwnldmf jn ~nam |clenjmj fc zenfn ac| lcfcleoenfzc| oiumlfeoc| pmrm nfznfjnr ac| zaringroefc| lenfziumlgelc|~n |n ~zeaeymf nf ac| mf~flec| u pcr ac zmfzc fc p~njnf |mbnr |e n| lenrzc c fc naonf|minamp

m Na lcfcleoenfzc lenfziumlgelc n|ziacute prcbmjc oiacute| maaiacute jn zcjm j~jmampb Am |clenjmj fc zenfn lcfcleoenfzc| lenfziumlgelc| u fc nfzenfjn am p~baelejmjampl Am p~baelejmj ~zeaeym m am lenflem pmrm wnfjnr ac| prcj~lzc| ~n mf~flemampj Jnbnriumlm prcdeber|n ~zeaeymr am lenflem nf ac| mf~flec|amp

2ampZcjm am omznrem pcjnoc| |npmrmram jn jegnrnfzn| gcrom| dm|zm aanhmr m |~|lcopcfnfzn| oiacute| |eopan|amp sup3]~aring prclnjeoenfzc| jnbnf ~zeaeymr|n nf n|zm| l~n|zecfn|3=amp Na mh~m onylamjm lcf mrnfm nf ~fm l~bnzm |n p~njn rnl~pnrmr onjemfznSSSSSSSSSSSSSS

2amp Onjemfzn SSSSSSSSSSSSSSSS|n p~njnf |npmrmr ac| lcopcfnfzn| jn ~fm zefzmampltamp Pcr onjec jn am SSSSSSSSSSSSSSSSSSSSS|n p~njn |nlmr na m|nrriumlf dugraveonjcampamp ^fm onylam jn mrnfm u lacr~rc jn |cjec |uumlaejc |n p~njn |npmrmr onjemfznSSSSSSSSSSSSS

mampGeazrmleuumlf bamp Lrcomzchrmgiumlmlamp ~baeomleuumlfjamp Nwmpcrmleuumlfnamp Jnlmfzmleuumlfgamp Mjeleuumlf jn mh~m u geazrmleuumlf

m =j 2g ltl g

b =m 2g ltn bl =m 2b ltj lj =m 2b ltj g

ltampsup3Nf l~iacutea jn am| |eh~enfzn| crmlecfn| |n onflecfm ~fm prcpenjmj l~mfzezmzewm jn amomznrem3m M Omriumlm fc an h~|zm na |mbcr jna ldclcamzn aiuml~ejc pnrc |iuml an h~|zm lcoc d~nanampb Am n|gnrm jn ~felna gaczm nf na omr pcr |nr onfc| jnf|m ~n na mh~m |mamjmampl Am lcrznym jna |m~ln n| o~ldc oiacute| iacute|pnrm ~n am jna pefcampj Na mh~m jna amhc |n lcfhnauuml nf na efwenrfc u |~ n|zmjc lmobeuuml m |uumlaejcamp

amp sup3L~iacutea n| na n|zmjc jn mhrnhmleuumlf jna onrl~rec3m uumlaejcb Aiuml~ejcl Jnpnfjn jn am lmfzejmj jn omznremaj Jnpnfjn jn am| lcfjelecfn| jna onjecgtamp Na ocfuumltejc jn lmrbcfc9m |enoprn n| zuumltelcb f~flm n| zuumltelcl n| zuumltelc l~mfjc |cbrnpm|m lenrzm lcflnfzrmleuumlf nf na mernj n| zuumltelc |uumlac l~mfjc am pnr|cfm n| |nf|eban m aringa7amp sup3M l~iacutefzc n~ewman nf ppo ~fm lcflnfzrmleuumlf jn ocfuumltejc jn lmrbcfcma lt 3m 0amp000lt ppo

b 0amp0lt ppol lt00 ppo



j lt0 000 ppo8ampsup3Nf l~iacutea gnfuumlonfc m~onfzm am om|m jna omznrema3m Am ctejmleuumlf jna denrrcb Am lcob~|zeuumlf jn ~fm zcrzeaaml Am lcfhnamleuumlf jna mh~mj Am nb~aaeleuumlf jn am anldn4ampsup3Lcf ~aring ef|zr~onfzc| pcjriumlm| lmal~amr am jnf|ejmj jn ~f l~bc jn omjnrm3m Bmamfym u znrouumlonzrcb Gantuumlonzrc u rnlepenfzn hrmj~mjcl Lrcfuumlonzrc u bmamfymj Bmamfym u gantuumlonzrc5amp sup3L~iacutea jn am| |eh~enfzn| n| ~fm prcpenjmj ntznf|ewm3m Znopnrmz~rmb Jnf|ejmjl Om|mj ca~beaejmj=0ampsup3L~iacutea geh~rm lcrrn|pcfjn m ~f ocjnac jn jeuumltejc jn lmrbcfc3

m b l j

==ampsup3L~iacutea jn ac| |eh~enfzn| |e|znom| n| lnrrmjc3

m b l j

=2amp Am omznrem prn|nfzm gcrom| je|zefzm| am| l~man| pc|nnf lmrmlznriuml|zelm| ~n fc|pnroeznf je|zefh~er ~fc| cbinzc| jn czrc|amp Na lcacr na cacr u am zntz~rm |cf prcpenjmjn| jn amomznrem ~n fc| mu~jmf m jegnrnflemrac|amp Rngantecfm u rnamlecfm am| lmrmlznriuml|zelm| jn ac|omznreman| lcf |~ rn|pnlzewc lcflnpzcamp

=amp P~fzc jn g~|euumlf2amp We|lc|ejmjltamp Jnf|ejmj

amp N|zmjc hm|nc|cgtamp Je|ca~leuumlf7amp N|zmjc aiuml~ejc

m =l2mltbggtj7nb =n2mltblgtj7g

l =l2nltgmgtj7bj =n2gltjmgtb7l



mamp Na omznrema cl~pm zcjc na wca~onf jnarnlepenfzn ~n ac lcfzenfn u |~| ocaaringl~am| |no~nwnf nf jn|crjnfamp

bamp N| ~f ninopac jn onylam dcocharingfnmamp

lamp Na omznrema zcom am gcrom jna rnlepenfzn ~n aclcfzenfn u |~ wca~onf n| priacutelzelmonfzn geicamp

jamp N| am rnamleuumlf nfzrn om|m u wca~onf jn ~fm|~|zmflemamp

namp M n|zm znopnrmz~rm ~f |uumlaejc lmobem man|zmjc aiuml~ejc |ef jnimr jn |nr am oe|om|~|zmflemamp

gamp n rngenrn m am rn|e|znflem m ga~er ~n zenfn ~fm|~|zmflemamp

=ltamp Nf onylam| dcocharingfnm| fc |n je|zefh~nf |~| lcopcfnfzn| am| je|ca~lecfn|pnrznfnlnf m n|zn zepc jn onylam| u n|ziacutef gcromjm| pcr |ca~zc u je|cawnfzn |enfjc na |ca~zcam |~|zmflem ~n |n nfl~nfzrm nf onfcr prcpcrleuumlfamp Jn ml~nrjc m am lmfzejmj jn |ca~zc ~nlcfzenfnf am| je|ca~lecfn| p~njnf |nr jea~ejm| lcflnfzrmjm| |mz~rmjm| u |cbrn|mz~rmjm|ampnyacutemam ac| ninopac| jn je|ca~lecfn|

m Mh~m lcf |ma omucfn|m bMh~m lcf |ma mwnfm lcf anldnb Mh~m lcf |ma lmgaring jLmgaring omucfn|m

=amp ^f ninopac jn je|ca~leuumlf jea~ejm lcfzenfn9

m 2 l~ldmrmjm| jn myugravelmrb gt l~ldmrmjm| jn myugravelmrl = l~ldmrmjm| jn myugravelmrj=0 l~ldmrmjm| jn myugravelmr

=gtamp Nf ~fm bnbejm prnpmrmjm lcf mh~m u Zmfh u ~f zaring jn omfymfeaam sup3]~aring |~|zmflem| |cf na|ca~zc3

m Mh~m u myugravelmrb Mh~m u omfymfeaaml Zmfh u omfymfeaamj Mh~m u Zmfh

=7amp Na pczm|ec $K zenfn fugraveonrc mzuumloelc =5 u |n nfl~nfzrm nf na Hr~pc c gmoeaem = jnml~nrjc ma ocjnac jn Bcdr am| uumlrbezm| c fewnan| p~njnf znfnr 2 4 =4 u lt2 nanlzrcfn| u lcocoiacuteteoc nf |~ ugraveazeom uumlrbezm 4amp Na ocjnac jn Anxe| |uumlac lcfznopam am rnprn|nfzmleuumlf jn ac|nanlzrcfn| jn wmanflem n| jnler ac| jna ugraveazeoc fewna ~ uumlrbezm m zrmwaring| jn p~fzc| marnjnjcr jna|iumlobcacamp sup3Jn ~aring omfnrm |n je|zreb~unf ac| nanlzrcfn| nf na iacutezcoc jn K jn ml~nrjc maocjnac jn Bcdr3

m 2 4 5

b 2 4 =4lt2l 2 4=j 2 4 4=



=8amp Nf n|zm hriacutegelm |n rnprn|nfzm am wmremleuumlf jn am lcfzmoefmleuumlf nf ~fm hrmf le~jmjpcr ~fm |~|zmflem aamomjm jeuumltejc jn my~grn m ac amrhc jn ac| jiumlm| jn am |nomfmamp sup3]~aringlcfla~|ecfn| |n cbzenfn3

m Am lcfzmoefmleuumlf n| onfcr ac| |iacutebmjc| u ac| jcoefhc|

b Am lcfzmoefmleuumlf n| omucr ac| oearingrlcan|amp

l Am lcfzmoefmleuumlf n| am oe|om zcjc| ac| jiumlm|amp

j M pmrzer jna omrzn| am lcfzmoefmleuumlf wm prchrn|ewmonfzn je|oef~unfjcamp

=4amp L~mfjc ~fm rnim jn onzma |n ctejm cl~rrn ~fm rnmlleuumlf ~iumloelmamp sup3]~aring |~|zmflem|pmrzelepmf nf naam3Mamp Am d~onjmj u na mern

Bamp Na onzma u na ctiumlhnfc

Lamp Na Lmrbcfc u na Ctiumlhnfc

Jamp Na mh~m u na mern

=5amp Na lmobec giuml|elc fc eopaelm am gcromleuumlf jn f~nwm| |~|zmflem| n|zc n| lcfzrmrec m ac

~n cl~rrn j~rmfzn ~f lmobec ~iumloelc um ~n nf aring|zn |n zrmf|gcromf ~fm c oiacute||~|zmflem| pmrm prcj~ler czrm| jegnrnfzn| m am| crehefman|ampsup3]~aring cplecfn| efjelmf ~f lmobec ~iumloelc3

=amp ]~nomr ~f pmpna 2amp Lcfhnamr mh~m

ltamp Onylamr mh~m u myugravelmr amp Grniumlr ~f d~nwc

Mamp = 2

Bamp =

Lamp lt

Jamp 2 lt

20amp Na ocjnac jn LC2 |n nfl~nfzrm rnprn|nfzmjc nf lcacr fnhrc na Lmrbcfc u nf bamflc naCtiumlhnfcsup3L~iacutea jn am| |eh~enfzn| cplecfn| efjelm jn omfnrm lcrrnlzm am wmanflem jn lmjm

iacutezcoc nf n|zn lcop~n|zc3

Mamp C7

L+

Bamp C2

L+

Lamp C

L

+

Jamp C2+

L2+

2=amp Mfmaeym am| nl~mlecfn| ~iumloelm| u |nyacutemam am ~n rnprn|nfzm lcrrnlzmonfzn na preflepecjn am lcf|nrwmleuumlf jn am om|mampMamp Fm2C + D2C Fm2CD2

Bamp D2 + La2 DLa

Lamp FmCD + DLa FmLa + D2C

Jamp Oh + C2 2OhC



22amp Nf am nl~mleuumlf ~iumloelm LD + 2C2 LC2 + 2D2C Ac| prcj~lzc| |cf9mamp Onzmfc u Beuumltejc jn Lmrbcfc bamp Beuumltejc jn lmrbcfc u mh~m

lamp Ctehnfc u Beuumltejc jn lmrbcfc jamp Onzmfc u Ctehnfc

2ltamp Am |eh~enfzn nl~mleuumlf rnprn|nfzm ~fm rnmlleuumlf ~iumloelm ~n FC p~njn cl~rrer

2Fm + La2 2KLa Pcr~n9

Mamp Na pczm|ec u na |cjec |cf nanonfzc| fc onziacuteaelc|Bamp^f nanonfzc fc |n zrmf|gcrom nf czrc

Lampamp Na La fc rnmllecfm lcf na K m znopnrmz~rm mobenfzn

Jamp Am ocaaringl~am jn KLa jnbn znfnr zrn| iacutezcoc| nf a~hmr jn 2

2amp Hrmfjn| pnr|cfmin| jn|zmlmf nf am de|zcrem pcr |~| mpcrzmlecfn| m am lenflem um ~n |~|efwn|zehmlecfn| dmf |ejc am bm|n pmrm f~nwc| mwmfln| lenfziumlgelc| u znlfcauumlhelc|amp M lcfzef~mleuumlf |n

onflecfmf mah~fc| jn naac| rnamlecfm na fcobrn lcf |~ lcfzreb~leuumlf m am lenflemamp

=amp Nambcruuml ~fm zmbam jn pn|c| mzuumloelc|

lcf wmacrn| o~u ntmlzc|amp

2amp N| lcf|ejnrmjc na pmjrn jn am zmbam

pnreuumljelm jn ac| nanonfzc|amp

ltamp Nf~fleuuml am Anu jn am Lcf|nrwmleuumlfjn am omznrem

amp Rnlebeuuml na prnoec Fcbna pcr |~|

n|z~jec| |cbrn am lmpm jn cycfc

mamp Jeoezre Eamp Onfjnanenwbamp Omrec Ocaefm

lamp zmfe|amc LmffeyymrcjampMfzcefn Amwce|enr

m =j 2m ltb l b=b 2m ltj l l=m 2l ltj b j=l 2m ltj b

2gtamp Ac| onzman| |cf ~f hr~pc jn nanonfzc| ~iumloelc| ~n zenfnf am prcpenjmj jn lcfj~ler amlcrrenfzn naaringlzrelm |cf omanmban| j~rc| u rn|e|znfzn| nfzrn czrm| lmrmlznriuml|zelm|amp nyacutemam am cpleuumlf~n lcfzenfn nanonfzc| onziacuteaelc|amp

m L~ E Gn b Yf Ma l Ma L~ Gn jM~ Br L

27amp Rnamlecfm u |~brmum am rn|p~n|zm lcrrnlzmampNf am zmbam pnreuumljelm9

=amp Am| lca~ofm| wnrzelman| |n aamomf SSSSSSSSSSu n|ziacutef f~onrmjc| jna = ma =42amp Am| geam| dcreycfzman| |n jnfcoefmfSSSSSSS u |cf 8ltamp Ac| nanonfzc| jna hr~pc =4 |cf ac|SSSSSS

amp Nf na hr~pc = |n nfl~nfzrmf ac|SSSSSS gtamp u nf na hr~pc 2 ac| SSSSSSSSSS

mamp onzman| malmaefc|bamp onzman| malmaefczaringrrnc|lamp Hr~pc| c gmoeaem|jamp pnrecjc|namp hm|n| fcban| c efnrzn

mamp =j 2l ltn m gtb

bamp =l 2j ltn m gtb

lamp =j 2l ltn b gtm

jamp =l 2j ltn b gtm



7

7

28amp Ac| gmlzcrn| ~n p~njnf mlnanrmr c rnzmrjmr am jn|lcopc|eleuumlf jn ac| maeonfzc| |cf9

MLLECF GMLZCRN

=amp Rnzmrjmr

2amp Mlnanrmr

m mlleuumlf jn am| bmlznrem|b Mobenfzn| griumlc|

l Na ~|c jn lcf|nrwmjcrn|

j Na lcfzmlzc lcf na ctiumlhnfc jna mern

Mamp = b l 2 m j

Bamp = m j 2 b l

Lamp = m b 2 l jJamp = b j 2 m b

24amp sup3Luumloc efga~unf am wnaclejmj u am znopnrmz~rm nf am jn|lcopc|eleuumlf jn ac| maeonfzc|3Mamp Nf mobenfzn| griumlc| am jn|lcopc|eleuumlf p~njn |nr oiacute| riacutepejm

Bamp Nf mobenfzn| liacuteaejc| c dugraveonjc| am jn|lcopc|eleuumlf p~njn |nr oiacute| riacutepejmLamp Nf mobenfzn| |nlc| u griumlc| am jn|lcopc|eleuumlf p~njn |nr oiacute| riacutepejm

Jamp Nf mobenfzn| liacuteaejc| u dugraveonjc| am jn|lcopc|eleuumlf p~njn |nr oiacute| anfzm

25amp Ac| ocjnac| zrejeonf|ecfman| rnprn|nfzmjc| sup3M ~aring lcop~n|zc| lcrrn|pcfjnf3

= 2 lt

Cpleuumlf Mh~m Lacr~rc jn

|cjec

Ctehnfc Cycfc

M = lt 2

B 2 = lt

L lt 2 =

J lt = 2

lt0amp Onjemfzn am n|lmam d~omfm m|zrcfuumloelm u oelrc|luumlpelm pcjnoc| ~belmr zcjc| ac| gnfuumlonfc| jnam fmz~rmanymamp

Rnamlecfm lmjm n|lmam lcf ~f ninopac ~n ac rnprn|nfznamp

NLMAM NINOPAC

=amp N|lmam d~omfm

2amp N|lmam m|zrcfuumloelm

ltamp N|lmam oelrc|luumlpelm

m jeiacuteonzrc jn ~f an~lclezc

b Am je|zmflem onjem jna |ca m am a~fm

l maz~rm jn ~fm lmfm|zm jn bm|~nzbca

Mamp = m 2 b lt l

Bamp = b 2 l lt m

Lamp = b 2 m lt lJamp = l 2 b lt m

lt=amp ^f lcop~n|zc c nanonfzc n| lmpmy jn mlnanrmr c rnzmrjmr am wnaclejmj lcf am ~n |n aanwm m lmbc

~fm rnmlleuumlf ~iumloelm znfenfjc nf l~nfzm ~n n|zn fc |~grn fefhugravef lmobec fe ocjegelm na prcj~lzcgefma sup3Jn ~aring zepc jn |~|zmflem ~iumloelm |n zrmzm3Mamp Ctejmfzn| Bamp Lcrrc|ewc| Lamp Lmzmaeymjcrn| Jamp Efdebejcrn|

lt2amp Am je|zmflem mprcteomjm jn am Zenrrm m am A~fm n| jn lt4 000 Ko ac ~n n~ewman m lt4 000 000oamp Nf pcznflem jn =0 |n p~njn ntprn|mr lcoc9

Mamp lt4 t =0

Bamp ltamp4 t =04

Lamp ltamp4 t =05

Jamp amplt4 t =0lt



8

8

ltltamp Nf na jeuumltejc jn lmrbcfc jn ml~nrjc lcf na ocjnac jn Anxe| nflcfzrmoc| ~n ma iacutezcocjn Lmrbcfc an dmlnf gmazm l~mzrc nanlzrcfn| pmrm l~opaer am rnham jna clznzc u m lmjm iacutezcocjn ctiumlhnfc jc|amp Pmrm ~n lmjm iacutezcoc lcopanzn lcf cldc nanlzrcfn| |~ lmpm jn wmanflem |nn|zmbanln ~f nfamln jcbanamp sup3L~iacutea cpleuumlf n|zmbanln n|zn ocjnac3

ampamp

M 9 C9 L9

ampamp

amp ampB amp L amp L amp

amp amp

L 9 L 99 L9

ampamp ampampJ C 99 L 99 C

ampamp ampampltamp sup3L~iacutea n| am om|m ocanl~amr jn ~f oca jn myugravelmr lcougravef $MLMRCM L=2D22C== |e L=2 ~om D = ~om u C =7 ~om3ampMamp 25 h Bamp gt h Lamp lt2 h Jamp = h

ltgtamp Nf na n|zuumlomhc |n aanwm m lmbc am jehn|zeuumlf onjemfzn prcln|c| lcoc na ocweoenfzc u am|rnmllecfn| ~iumloelm| jna iacutelejc lacrdiumljrelc lcf ac| maeonfzc| mjnoiacute| |n prcj~ln ~fm |~|zmflemaamomjm pnp|efm ~n pmrzelepm nf am jehn|zeuumlf jn prczniumlfm| |ef efznrwnfer nf am rnmlleuumlf~iumloelmamp Am pnp|efm nfzcfln| n|9

Mamp ^f efdebejcr pcr~n rnzmrjm am rnmlleuumlf nfzrn am| prczniumlfm| u na mh~mBamp ^f prcj~lzc jn am rnmlleuumlf jna DLa lcf am| prczniumlfm|

Lamp ^fm |~|zmflem ~n rnmllecfm lcf am| prczniumlfm| ocjegelmfjc |~ n|zr~lz~rm ~iumloelmampJamp ^f lmzmaeymjcr pcr~n ocjegelm am wnaclejmj jn am rnmlleuumlf pnrc fc pmrzelepm nf naamamp

lt7amp Na nfamln euumlfelc |n lmrmlznreym pcr aanwmr|n m lmbc nfzrn ~f onzma u ~f fc onzma ~fc lnjnu na czrc hmfm nanlzrcfn|amp sup3N|zn zepc jn nfamln |n prn|nfzm nfzrn na FmLa3Mamp iuml pcr~n na lacrc n| ~f onzma u na cjec ~f Fc onzmaBamp e pcr~n na cjec lnjn ~f nanlzruumlf u na lacrc ac mlnpzm

Lamp Fc pcr~n mobc| |cf fc onzman|

Jamp iuml pcr~n na Lacrc jcfm ~f nanlzruumlf u na cjec ac hmfm

lt8amp ^fm nl~mleuumlf ~iumloelm n| ~fm rnprn|nfzmleuumlf |eobuumlaelm jn ~fm rnmlleuumlf ~iumloelmamp sup3L~iacutea

cpleuumlf efjelm ~fm nl~mleuumlf ~iumloelm3

Mamp L + C2 LC2

Bamp Fm + La2 FmLa

Lamp D2C + FmCD

Jamp L7D=2C7

lt4amp Am fmz~rmanym jn ac| rnmlzewc| n| ~f gmlzcr ~n efga~un nf am wnaclejmj jn ~fm rnmlleuumlf~iumloelm sup3pcr~aring |n prn|nfzm n|zn gnfuumlonfc3

Mamp Pcr~n am gcrom jn am| pmrziumll~am| efga~un nf am |ca~beaejmjBamp Pcr~n am |~pnrgelen jn lcfzmlzc jn am| pmrziumll~am| n| omucrLamp Pcr~n m omucr lmfzejmj jn pmrziumll~am| omucr zenopc jn rnmlleuumlf

Jamp Pcr~n am znopnrmz~rm wmriumlm |nhugravef am fmz~rmanym jna rnmlzewcamp

lt5amp Pmrm eopnjer am jn|lcopc|eleuumlf na ac| maeonfzc| nte|znf wmrec| oaringzcjc| jn lcf|nrwmleuumlfamp^fc jn n|zc| prclnjeoenfzc| lcf|e|zn nf am naeoefmleuumlf jn mh~m mpaelmfjc lenrzm lmfzejmj jnlmacr zmobearingf n| lcougravef myacutemjer m ac| maeonfzc| |~|zmflem| o~u |ca~ban| lcoc am |ma lcougravef una myugravelmr pmrm naeoefmr am d~onjmj sup3Luumloc |n an aamom m n|zn oaringzcjc3Mamp Nfwm|mjc ma wmliumlc Bamp mao~nrm Lamp Jn|dejrmzmleuumlf Jamp Pm|zn~reymleuumlfamp

0amp Na nfamln lcwmanfzn |n lmrmlznreym pcr aanwmr|n m lmbc nfzrn nanonfzc| fc onziacuteaelc|amp sup3]~aringlcop~n|zc |n je|zefh~n pcr n|zn zepc jn nfamln3

Mamp AeBr Bamp LmC Lamp D2C Jamp FmLa



4

4

=amp Ac| iacutezcoc| u am| ocaaringl~am| |cf cbinzc| ntzrnomjmonfzn pn~nyacutec|amp Nf ~fm hczm jn mh~mdmu oeaacfn| jn ocaaringl~am|amp Nf am p~fzm jn ~f lamwc jn denrrc dmu oeaacfn| jn iacutezcoc| sup3~aring |n~zeaeym pmrm rnprn|nfzmr fugraveonrc| o~u hrmfjn| c o~u pn~nyacutec| jn omfnrm |nfleaam3Mamp N|lmam d~omfm Bamp N|lmam omlrc|luumlpelm Lamp N|lmam oelrc|luumlpelm Jamp Fczmleuumlf lenfziumlgelm

2amp Na oca n| ~fm ^fejmj biacute|elm jna e|znom efznrfmlecfma u n~ewman m 7amp02 t =02lt

sup3M ~aring

~fejmj lcrrn|pcfjn3Mamp Lmfzejmj jn |~|zmflem Bamp Nfnrhiumlm a~oefc|m Lamp Acfhez~j Jamp Om|m

ltamp 7amp02 t =02lt

sup3~aring fugraveonrc rnprn|nfzm3Mamp 702 000 000 000 000 000 000 000Bamp 7 0702 000 000 000 000 000 000 000

Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000

amp Zncriumlm ~n ntpaelm am lmpmlejmj ~n zenfnf ac| nanonfzc| pmrm hmfmr c pnrjnr nanlzrcfn| ucbznfnr ~fm lcfgeh~rmleuumlf n|zmban n| jnler cldc nanlzrcfn| nf |~ lmpm ntznrfmampMamp Jna pmr nanlzruumlfelc Bamp Jn Aamp Pm~aefh Lamp nanlzruumlfelm Jamp Jna Clznzcampgtamp Ac| iacutelejc| lmobemf m rcic lcf na mfmrmfimjc jn onzeac |e znfnoc| ~fm o~n|zrm jn jni~hc jn aeouumlf u ~fm o~n|zrm jn mh~m jn lma sup3L~iacutea werm $lmobem m rcic lcf na efjelmjcr

onflecfmjc3mamp Mobm| bamp Fefh~fm lamp Na mh~m jn lma jamp Na i~hc jn aeouumlf7amp^fm jn am| oiacute| eopcrzmfzn| rnmllecfn| ~iumloelm| n| l~mfjc rnmllecfmf ~f mlejc lcf~fm bm|n fn~zrmaeyiacutefjc|n jn zma omfnrm ~n am| prcpenjmjn| jn ac| iacutelejc| u ac| bm|n|jn|mpmrnlnf pcr am gcromleuumlf jn f~nwc| omznreman| sup3L~iacutea n| am f~nwm |~|zmflem ~n |ngcrom mjnoiacute| jn mh~m3m Iacutelejc b|ma lbm|n juumltejc8amp Rnamlecfm ac| fcobrn| jn ac| lcop~n|zc| biacute|elc| jn am ey~enrjm lcf am| guumlro~am| ~n|n nfl~nfzrmf nf am lca~ofm jn am jnrnldmamp

M Dejruumltejc jn |cjec Eamp Lm$CD2 B Lmrbcfmzc jn |cjec EEamp FDCD

L Dejruumltejc jn lmalec EEEamp Fm2LClt J Uumltejc jn lmalec EWamp FmCD N Dejruumltejc jn mocfec Wamp LmC

m ME BEEE LEW JEE NWb MW BEW LEEE JEE NEl MEW BEEE LE JW NEEj ME BEE LEEE JEW NW4ampe ~fm pnrm zenfn ~f pD jn lt u ~f paiacutezmfc jn gt sup3L~iacutea jn n|zm| gr~zm| n| oiacute| iacutelejm3m Na paiacutezmfc pcr~n pD gt n| omucr ~n ltb Am pnrm pcr~n am mlejny |n eflrnonfzm jn 7amp5 m 0amp0l Am pnrm pcr~n na paiacutezmfc n| oiacute| j~aln

j Na paiacutezmfc pcr~n am pnrm n| oiacute| momrhm5ampPmrm maewemr ac| |iumlfzcom| jn am mlejny n|zcomlma |n p~njn ~|mr9m Je|ca~leuumlf jn wefmhrn bMh~m jn|zeamjm

b Je|ca~leuumlf jn belmrbcfmzc jn |cjec jI~hc jn aeouumlfgt0amp Fn~zrmaeymleuumlf n| ~fm rnmlleuumlf nfzrn ~f iacutelejc u ~fm bm|n nf am ~n |n cbzenfn lcocprcj~lzc ~fm |ma u mh~mamp sup3L~iacutea nl~mleuumlf rnprn|nfzm ~fm rnmlleuumlf jn n|zn zepc3

m DFClt + Lm$CD2 Lm$FClt2 + D2C

b Mh2 + Ma + D2C Mh + Ma$CDlt + D2

l D2C D + C

j L~C + Yf YfC + L~

gt=amp Ac| onjelmonfzc| mfzeiacutelejc| mlzugravemf fn~zrmaeymfjc na ntln|c jn iacutelejc nf na n|zuumlomhcampsup3L~iacutean| jn ac| |eh~enfzn| |cf mfzeiacutelejc|3

=amp Lmrbcfmzc jn |cjec 2amp Dejruumltejc jn omhfn|ecltamp Ctejc jn lmalec amp Dejruumltejc jn ma~oefec

Mamp =ltBamp 2ltLamp 2Jamp =

gt2amp Lcacrmfzn| crhiacutefelc| ~n zenfnf am prcpenjmj jn lmobemr jn lcacr |nhugravef |n pcfhm nflcfzmlzc lcf ~fm |~|zmflem iacutelejm c biacute|elm ninopac na pmpna zcrfm|ca gnfcagzmaniumlfm



5

5

mfmrmfimjc jn onzeac u ac| ntzrmlzc| jn mah~fm| wnrj~rm| lcoc am Acobmrjm $lca ocrmjmlcfzenfn nf |~| dcim| ~fm |~|zmflem jnfcoefmjm mfzclemfefm sup3Luumloc |n an| lcfcln~iumloelmonfzn3

mamp Mocfemlc|bamp Efjelmjcrn|lamp man|

jamp Ecfn|gtltamp Nf ~fm rnmlleuumlf jn ctejc ldquo rnj~lleuumlf |n zrmf|genrnf nanlzrcfn| n|zn efznrlmobec jn nanlzrcfn| ~n

|n ngnlzugravem nf ~fm rnmlleuumlf rnjct jnbn cl~rrer ma oe|oc zenopcamp sup3Am| |eh~enfzn| rnmllecfn| |cf jn ctejc

rnj~lleuumlf ntlnpzc nf3

m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2

j 7DLE+2Gn ltD2+2GnLalt

gtamp Ocaaringl~am |nfleaam ~n p~njn |nr ~iumloelmonfzn ~fejm pmrm gcromr lmjnfm| amrhm|lcfclejm| lcoc pcaiumlonrc|ampm iacutezcoc b ocfuumlonrc l nam|zuumlonrc j paiacute|zelc

gtgtamp n lcopcfnf jn amrhm| lmjnfm| ~n |n nfl~nfzrmf ~fejm| nfzrn |e pcr o~u pclm| ~fecfn|~iumloelm|amp N|zc an| pnroezn ~f hrmf ocweoenfzc efznrocanl~amr ~n |n wn rnganimjc nf |~ b~nfmgantebeaejmj ma |conznrac| m ~f n|g~nryc ocjegelmf |~ gcrom rnl~pnriacutefjcam l~mfjc |n rnzermn|n n|g~nrycampm aiuml~ejc| b ocfuumlonrc| l nam|zuumlonrc| j hm|n|

gt7amp Am omucriumlm jnam| bcznaam| jn ac| rngrn|lc| n|ziacutef nambcrmjc| jn n|zn zepc jn paiacute|zelcm Pcaen|zrnfc $P Pcaeprcpeanfc$PP lLacr~rc jn Pcaewefeac$PWL j PcaenzeanfcZnrngzmamzc$PNZ

gt8amp Welnfzn Crzehcym n| ~f lenfziumlgelc ontelmfc |n an rnlcfcln pcr nf n|zn lmopc jn

efwn|zehmleuumlfamp

m am lmpmym jn cycfc b lmobec laeoiacutezelc l felczefm j mfzelcflnpzewc|

gt4amp Pnr|cfmin ~n |n rnamlecfm lcf na n|z~jec jn am piumlajcrm mfzelcflnpzewm

m Hamp Famp Anxe| b A~e| Namp Oermocfzn| Liacuterjnfm| l Omrec Ocaefm j Iamp Onunrgt5amp Mfjraring| Omf~na jna Riumlc g~n ~f ]~iumloelc ~n rnmaeyuuml hrmfjn| mpcrzmlecfn| m am lenflemnfzrn am| ~n jn|zmlm na jn|l~breoenfzc9

m jna Fiuml~na b jna ctiumlhnfc l jna nrezrcfec j jn am felczefm

70ampMprcteomjmonfzn na 55 jn ac| iacutezcoc| jn f~n|zrc crhmfe|oc lcrrn|pcfjn m l~mzrcnanonfzc| ~n |cf eoprn|lefjeban| pmrm am wejm sup3L~iacutean| |cf n|c| nanonfzc|3mamp L C K F

bamp F P Clamp C D L F

jamp Lamp L Fe Lc
















m 2 4 5

b 2 4 =4lt2l 2 4=j 2 4 4=
















Mamp = 2

Bamp =

Lamp lt

Jamp 2 lt



Mamp C7

L+

Bamp C2

L+

Lamp C

L

+

Jamp C2+

L2+


Bamp D2 + La2 DLa


Jamp Oh + C2 2OhC


































7

7


MLLECF GMLZCRN

=amp Rnzmrjmr

2amp Mlnanrmr




Mamp = b l 2 m j

Bamp = m j 2 b l






= 2 lt


|cjec

Ctehnfc Cycfc

M = lt 2

B 2 = lt

L lt 2 =

J lt = 2



NLMAM NINOPAC

=amp N|lmam d~omfm






Mamp = m 2 b lt l

Bamp = b 2 l lt m





Mamp lt4 t =0

Bamp ltamp4 t =04

Lamp ltamp4 t =05

Jamp amplt4 t =0lt



8

8


ampamp

M 9 C9 L9

ampamp


amp amp

L 9 L 99 L9











Mamp L + C2 LC2

Bamp Fm + La2 FmLa

Lamp D2C + FmCD

Jamp L7D=2C7









4

4



sup3M ~aring




Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000










l D2C D + C

j L~C + Yf YfC + L~







5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc
















Mamp = 2

Bamp =

Lamp lt

Jamp 2 lt



Mamp C7

L+

Bamp C2

L+

Lamp C

L

+

Jamp C2+

L2+


Bamp D2 + La2 DLa


Jamp Oh + C2 2OhC


































7

7


MLLECF GMLZCRN

=amp Rnzmrjmr

2amp Mlnanrmr




Mamp = b l 2 m j

Bamp = m j 2 b l






= 2 lt


|cjec

Ctehnfc Cycfc

M = lt 2

B 2 = lt

L lt 2 =

J lt = 2



NLMAM NINOPAC

=amp N|lmam d~omfm






Mamp = m 2 b lt l

Bamp = b 2 l lt m





Mamp lt4 t =0

Bamp ltamp4 t =04

Lamp ltamp4 t =05

Jamp amplt4 t =0lt



8

8


ampamp

M 9 C9 L9

ampamp


amp amp

L 9 L 99 L9











Mamp L + C2 LC2

Bamp Fm + La2 FmLa

Lamp D2C + FmCD

Jamp L7D=2C7









4

4



sup3M ~aring




Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000










l D2C D + C

j L~C + Yf YfC + L~







5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc


































7

7


MLLECF GMLZCRN

=amp Rnzmrjmr

2amp Mlnanrmr




Mamp = b l 2 m j

Bamp = m j 2 b l






= 2 lt


|cjec

Ctehnfc Cycfc

M = lt 2

B 2 = lt

L lt 2 =

J lt = 2



NLMAM NINOPAC

=amp N|lmam d~omfm






Mamp = m 2 b lt l

Bamp = b 2 l lt m





Mamp lt4 t =0

Bamp ltamp4 t =04

Lamp ltamp4 t =05

Jamp amplt4 t =0lt



8

8


ampamp

M 9 C9 L9

ampamp


amp amp

L 9 L 99 L9











Mamp L + C2 LC2

Bamp Fm + La2 FmLa

Lamp D2C + FmCD

Jamp L7D=2C7









4

4



sup3M ~aring




Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000










l D2C D + C

j L~C + Yf YfC + L~







5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc



8

8


ampamp

M 9 C9 L9

ampamp


amp amp

L 9 L 99 L9











Mamp L + C2 LC2

Bamp Fm + La2 FmLa

Lamp D2C + FmCD

Jamp L7D=2C7









4

4



sup3M ~aring




Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000










l D2C D + C

j L~C + Yf YfC + L~







5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc



4

4



sup3M ~aring




Lamp 7 0 200 000 000 000 000 000 000

Jamp 702 000 000 000 000 000 000 000










l D2C D + C

j L~C + Yf YfC + L~







5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc



5

5






m DLE+FmCD FmLE+D2C

b 2D2+C2 2D20

l 2KLEClt 2KLE+ltC2






efwn|zehmleuumlfamp







jamp Lamp L Fe Lc

CIENCIAS III

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Transcript of CIENCIAS III