Química (by Carrascal). Mis respuestas a problemas de Yahoo Respuestas!

7/23/2019 Química (by Carrascal). Mis respuestas a problemas de Yahoo Respuestas!

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Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac 3 ij ?6

SuímndcMns sh`udnhajs c `hs prho`jmcs ij ^cghh _jspujstcs#

Nócln Dcrrcsdc` Mhzh! bísndcsKycghh!js gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs(

v3!;5 ;6(;?(?;34! Õ`tnmc cdtuc`nzcdnôa5 v3!;5 ;6(;?(?;34

Nócln Dcrrcsdc` Mhzh! Rjrsnôa 3!; — Drjcih j` ;6(;?(?;34! Suímndc dhatnjaj 96 prjfuatcs ja ?6 pãfnacs

Ja`cdj '@nal. ij` ihdumjath gttp5((js!sdrnoi!dhm(N*D4*O3clnDcrrcsdc`

[ujsth 4µ ja ‐@hs mjehrjsij Bísndc”!

>4 * Mjehr _jspujstc!

73 bcas!

Anvj` 6! ?:!27; puaths!

36:> prjfuatcs ';6(;?(?;34.

Nócln Dcrrcsdc` Mhzh v3!;5 ;6(;?(?;34 gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js Nócln Dcrrcsdc`

mailto:[email protected]

http://www.carrascal.net46.net/fisicas/

http://es.scribd.com/I%C3%B1akiCarrascal












Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac ? ij ?6

J` 33 ij hdtuorj ij ?;3? mj gndj mnjmorh ij ^cghh# _jspujstcs y mj pusj c rjsh`vjr

jejrdndnhs quj p`catjcoc `c dhmuanici! Mj fustcoc j` p`catjcmnjath ij quj c`fuac iuic quj tuvnjrc

c`funja puinjrc rjsh`vjr`c uah h vcrnhs dhmpcójrhs c trcvîs ij natjrajt! Ja 'jxcdtcmjatj. ua mjs

c`dcadî j` Anvj` 2 'supjrcaih `hs 3;!;;; puaths.! ^ ja 'eustcmjatj. ihs mjsjs gj supjrcih `hs

36!;;; puaths y mj gj dh`cih gcstc j` 4µ pujsth ij `hs ‐Mjehrjs ij Bísndc”! Ijsij j` ;6 ijbjorjrh ij ?;34 hduph j` Anvj` 6!

Gj snih ‐Dh`cohrcihr ijstcdcih” ja Bísndc, Mctjmãtndcs, Nafjanjríc y Thbtwcrj! Ijsij

j` ?4 ij ahvnjmorj jsthy jatrj `hs 3; prnmjrhs pujsths ij ‐@hs mjehrjs ij Bísndc”, j` ;4 ij

indnjmorj hdupî j` 6µ pujsth, j` 3: ij indnjmorj j` :µ `ufcr y j` ;6 ij bjorjrh ij ?;34, j` tjrdjr

pujsth! Gj c`dcazcih ua >4 * ij Mjehr _jspujstc!

C bjdgc ;6(;?(?;34 ``jvh dhatjstcics 36:> prjfuatcs, dha ?:!27; puaths 'anvj` 6., tjafh ua

>4 * ij Mjehr _jspujstc, hduph `c 4ª phsndnôa ij ‐@hs Mjehrjs ij Bísndc” y tjafh 73 ‐bcas”!

C dhatnaucdnôa prjsjath uacs ducatcs prjfuatcs ij cghh# _jspujstcs quj yh mnsmh

rjsh`ví, dha `c bjdgc ja quj `h gndj! Ja `c mcyhríc ij j``cs gj rjspjtcih `c prjfuatc hrnfnac`! Sunzã

gcyc dhrrjfnih c`fuac bc`tc ij hrthfrcbíc h mjehrcih ua phdh j` jauadncih pcrc gcdjr`h mcs d`crh!

Dha j` tnjmph nrî hrijacaih `hs jejrdndnhs phr hrija ij inbndu`tci drjdnjatj!

Cuaquj mudghs prho`jmcs pujija rjsh`vjrsj ij htrc bhrmc, drjh quj `cs rjspujstcs quj gj

icih sha `c mcajrc mãs cijducic ij gcdjr`h, bruth ij cóhs ij ihdjadnc ij Bísndc y Mctjmãtndcs canvj` uanvjrsntcrnh!

@cs rjspujstcs jstãa tc` y dhmh `cs rjsphaií ja su mhmjath, dha j` 'sjadn``h. jinthr ij

tjxths ij cghh! Gj prhdurcih phajr pcrîatjsns pcrc d`crnbndcr `cs mnsmcs! @cs phtjadncs `cs naindh

dha5 Q ':Q9.< `c rcíz ducircic, dha Q'3(?., dha TS_Y h dha ‐rcíz” 'je! rcíz '?. = ?Q'3(?..< `c natjfrc`

dhmh ‐natjfrc`”! Ah pujih jmp`jcr suoíaindjs 'je! rcinh ij `c Ynjrrc5 _Y< îpsn`ha suo h.!!!

Tn c`fuac ij `cs rjspujstcs js nadhrrjdtc, quj pujij, pujs thihs shmhs gumcahs y ij vjz ja

ducaih ahs dhabuainmhs, phiîns dhmuandãrmj`h phr dhrrjh j`jdtrôandh5 bísndcsKycghh!js !

_jvnscrî mn rjspujstc y `c quj mj nainquîns y `c dhrrjfnrî sn js ajdjscrnh!













J` 37(33(?;3? mj cfrjfuî c` bhrh3;;dnc y j` ;>(3?(?;3? c` Fruph ij Bcdjohhl

Cyuiîmhsahs ja mctjmãtndcs phr `h quj tcmonîa gj nadùnih mns rjspujstcs c jejrdndnhs quj gj

rjsuj`th c trcvîs ij` bhrh h ij Bcdjohhl!

Gj rjuanih thihs `hs 96 prho`jmcs ij Suímndc ja ua sh`h `norh ij ?6 pãfnacs! Ycmonîa `hs

ij Mctjmãtndcs ja ua sh`h tjxth! @hs ij Bísndc, ja ihs5

— Bísndc N, ihaij sj cac`nzca `hs tjmcs ij dnajmãtndc, jstãtndc, inaãmndc, trcoceh y jajrfíc,

snstjmcs ij pcrtídu`cs y dghqujs, inaãmndc ij `c rhtcdnôa, dcmph frcvntcthrnh, bùnihs,

mhvnmnjath crmôandh snmp`j y mhvnmnjath haiu`cthrnh! :74 prjfuatcs, ja ?>2 pãfnacs!— Bísndc NN, ihaij sj cac`nzca `hs tjmcs dhrrjsphainjatjs c `c j`jdtrndnici y mcfajtnsmh,

ôptndc y bísndc mhijrac! J` sjfuaih thmh tnjaj ?;; prjfuatcs ja 3;2 pãfnacs!

C` dhmnjazh ij dcic dcpítu`h, naindh `cs bôrmu`cs mãs usuc`js quj cpcrjdjrãa ja j` mnsmh!

Dha j` tnjmph qunzã jxp`nquj dômh uscr`cs y dômh rjsh`vjr ijtjrmnacihs ‐prho`jmcs mhij`h”! Ah

js ua `norh ij tjhríc, snah ij prho`jmcs! Tô`h cpcrjdjrãa `cs bôrmu`cs y `hs prho`jmcs rjsuj`ths!

Tnjmprj phiîns rjdurrnr c mn pãfnac wjo pcrc dhasu`tcr mcs bôrmu`cs y icths5

gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( y c Vnlnpjinc5 gttp5((js!wnlnpjinc!hrf( !

[hiîns inbuainr jstj ihdumjath jatrj vujstrhs dhmpcójrhs! _jspjtci, jsh sí, j` bhrmcth ij`

mnsmh, su cuthríc y `c mcrdc ij cfuc dha mn bhth! ¸C quj mh`h ij pjqujóh8

Jstj ihdumjath sj jstcrã cdtuc`nzcaih dhatnaucmjatj phr `h quj js rjdhmjaico`j quj

dhasu`tîns `c õ`tnmc vjrsnôa ijsij mn pjrbn` ja Tdrnoi5 gttp5((js!sdrnoi!dhm(N*D4*O3clnDcrrcsdc`

Frcdncs c qunjajs gcoîns prjfuatcih y rjsphainih tcmonîa! Za scùih c thihs y jspjrh quj

jsths prho`jmcs hs pujica sjrvnr ja vujstrhs jstuinhs!

Nócln Dcrrcsdc` Mhzh! Ijsij Dcstrn``h ij Iha Euca, ua pjqujóh pujo`h ij [c`jadnc 'Jspcóc.

Tn qujrîns vnsntcr mn pujo`h, jdgci uac hejcic c mn wjo5 gttp5((www!dcstrn``hijihaeuca!ajtcn!ajt(


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Íaindj ij dcpítu`hs! Suímndc

Yjmc Yítu`h [ãfnac Jejrdndnhs

;3 Dhadjpths prjvnhs ;: ;6

;? Fcsjs nijc`js ;7 37

;4 _jcddnhajs químndcs 36 ;>

;9 Insh`udnhajs ?3 ;6

;: Yjrmhquímndc ?: ;4

;2 Jqun`nornh químndh ?2 ;3

;6 _jcddnhajs ij trcasbjrjadnc ij prhthajs ?6 ;?










Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac : ij ?6

Yjmc ;3! Dhadjpths prjvnhs

W UC , ihaij U js j` aõmjrh ctômndh 'aõmjrh ij prhthajs h ij j`jdtrhajs ja ua ãthmh

j`îdtrndcmjatj ajutrh. y C j` aõmjrh mãsndh 'aõmjrh ij prhthajs aõmjrh ij ajutrhajs.!

@hs nsôthphs ij ua j`jmjath5 tnjaja j` mnsmh aõmjrh ij prhthajs y j`jdtrhajs pjrh inbnjrja ja j`

aõmjrh ij ajutrhajs! J` pjsh ctômndh ij ua nsôthph js `c mjinc phaijrcic 'tjanjaih ja dujatc su

couaicadnc. ij `hs pjshs ctômndhs ij `hs nsôthphs ij quj dhastc!

[rjfuatc ;3! _jsuj`tc j` 3;(33(?;3?

¸Duãaths mh`js gcy ja 3; dm dõondhs ij cfuc8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

R = 3; dmQ4 = ;,;3 `

Yjanjaih ja dujatc quj `c ijasnici js

i = m ( R

m = i ¶ R = 3 lf(` ¶ ;,;3 ` = ;,;3 lf = 3; f

pujs `c ijasnici ij` cfuc js ij` 3 lf ( `

J` aumjrh ij mh`js js a = m ( M snjaih M j` pjsh mh`jdu`cr ij` cfuc '37 f(mh`.

`ujfh5 a = 3;(37 = ;,:2 mh`js

[rjfuatc ;?! _jsuj`tc j` 3;(33(?;3?

¸Duã` js j` prhiudth ij `c dhmoustnôa ij gnirôfjah8Csí dhmh `c fcsh`nac c` gcdjr dhmoustnôa prhiudj DH?, quî prhiudj j` gnirôfjah purh c`dhmoustnhacrsjNócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Cfuc

G? '3(?. H? ---1 G? H

[rjfuatc ;4! _jsuj`tc j` 33(33(?;3?

Za ãthmh ajutrh dha 3; prhthajs pnjrij ? j`jdtrhajs! ¸Ja quj sj trcasbhrmc8 ¸Tnfuj snjaihj` mnsmh j`jmjath8 ¸mcatnjaj j` mnsmh aõmjrh mãsndh8

Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Ja ua nha ij indgh j`jmjath!

Tí js j` mnsmh j`jmjath 'js ua nha, dha ihs j`jdtrhajs mjahs quj j` cthmh ajutrh.

Tí pujs j` aumjrh mãsndh js j` aumjrh ij prhthajs ajutrhajs 'y jsths snfuja nfuc`.

[rjfuatc ;9! _jsuj`tc j` ?:(33(?;3?

J` nsôthph ij mcfajsnh mãs couaicatj tnjaj ij aõmjrh ctômndh 3? y ij aõmjrh mãsndh ?9!Tn `hs htrhs ihs nsôthphs ij` mcfajsnh tnjaja ij aõmjrhs mãsndhs ?: y ?2, naindcr `cspcrtídu`cs suoctômndcs quj dhastntuyja dcic uah ij `hs trjs nsôthphs ij` mcfajsnh!












































Aõmjrh ctômndh5 3? 5 3? prhthajs y 3? j`jdtrhajs

Aõmjrh mãsndh ?95 aµ ij ajutrhajs5 ?9 - aµ ij prhthajs = ?9 - 3? = 3?

Aõmjrh mãsndh ?:5 aµ ij ajutrhajs5 ?: - aµ ij prhthajs = ?: - 3? = 34

Aõmjrh mãsndh ?25 aµ ij ajutrhajs5 ?2 - aµ ij prhthajs = ?2 - 3? = 39Js ijdnr

Nsôthph ij aõmjrh mãsndh ?95 3? prhthajs, 3? j`jdtrhajs y 3? ajutrhajs

Nsôthph ij aõmjrh mãsndh ?:5 3? prhthajs, 3? j`jdtrhajs y 34 ajutrhajs

Nsôthph ij aõmjrh mãsndh ?25 3? prhthajs, 3? j`jdtrhajs y 39 ajutrhajs

Jspjrh gcojrtj sjrvnih ij cyuic! Tn tnjajs c`fuac pjfc, prjfuatc!

[rjfuatc ;:! _jsuj`tc j` ;6(33(?;3?

Za aõd`nih js `c rjprjsjatcdnôa ij` aõd`jh ctômndh ij ua j`jmjath utn`nzcaih j` símoh`hquímndh ij îstj 'j` duc` sj rjprjsjatc dha `c `jtrc ‐W”., j` aõmjrh ctômndh 'U.< j` aõmjrh ijmcsc 'C.Ja j` dcsh ij` D`hrh sjríc5 C=4: U = 36Aµ ij prhthajs = 36< Aµ ij j`jdtrhajs =36< Aµ ij mcsc = 4:< Aµ ij ajutrhajs = 4: - 36 = 37Cghrc! [rhphaj : j`jmjaths dha jstc mnsmc bhrmc ij rjprjsjatcr y ijbnaj pcrc dcic uah ijj``hs `hs mnsmhs dhadjpths5Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Hxnfjah5 C = 32, U = 7

Ah! ij prhthajs = 7

Ah! ij j`jdtrhajs =7

Ah! ij mcsc = 32

Ah! ij ajutrhajs = 32 - 7 = 7

Dcrohah5 C = 3? , U = 2

Ah! ij prhthajs = 2

Ah! ij j`jdtrhajs = 2

Ah! ij mcsc = 3?

Ah! ij ajutrhajs = 3? - 2 = 2

Cprjaijs mcs sn `h gcdjs tõ mnsmh! Mnrc, cquí tnjajs uac tco`c pjrnôindc5

gttp5((www!pjrnhian!dhm(js(naijx!gtm`

Bíectj ja j` aumjrh ctômndh y ja j` pjsh ctômndc! Js muy bãdn`! Dhmp`jtc tõ `hs htrhs trjs quj

bc`tca, ¸hl8Tn qunjrjs tj infh trjs j`jmjaths! [jrh gcz`h tõ cghrc quj scojs5

Thinh5 U = 33, C = ?4

Dc5 U = ?;, C = 9;

Bj5 U = ?2, C = :2

[rjfuatc ;2! _jsuj`tc j` ?7(33(?;3?

Dômh sj pujij scojr sn ua ãthmh jstc jxdntcih sconjaih sh`cmjatj `c dhabnfurcdnôaj`jdtrôandc y sna scojr quj j`jmjath js8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`







http://www.periodni.com/es/index.html














http://www.periodni.com/es/index.html








[ujijs hosjrvcr `c dhabnfurcdnôa j`jdtrôandc quj tj ija!

-J` hrija ijoj sjr 3s? ?s? ?p2 4s? 4p2 9s? 4i3; 9p2 :s? , jtd! 'tj sujac `c du`jorn``c jstc, ¸ah8.

-_jdujric cijmãs quj ja ua hrontc` s sh`h dcoja ? j`jdtrhajs, ja uah p 2, js uah i 3;, ja uah b

39 j`jdtrhajs!

-Cijmcs `hs hrontc`js p jmpnjzca ja j` anvj` ?< `hs i ja j` 4, `hs b ja j` 9!Jstcs ihs u`tnmcs dhscs tj `cs sjóc`h pcrc vjr sn jstã ja ua jstcih /nmphsno`j/

Yj vhy c phajr uahs jejmp`hs5

Naindcr duã`js ij `cs snfunjatjs dhabnfurcdnhajs sha phsno`js pcrc ua ãthmh ja jstcih ahrmc`5

c. 3s? ?s3 o. 3s4 d. ?s3 i. 3s? 4s3 j. 3s? ?s? p7 4s3 b. 3s? ?s?p2 ?i?

c. ahrmc`

o. nmphsno`j5 ja ua hrontc` s sh`h dcoja ihs j`jdtrhajs

d. jxdntcih 'prnmjrh tjairíc quj gcojr snih 3s3.

i. jxdntcih

j. nmphsno`j 'ja ua hrontc` p sh`h dcoja 2 j`jdtrhajs.

b. nmphsno`j '`hs hrontc`js i jmpnjzca ja j` anvj` 4, ah ?.

¸Duã`js ij `cs snfunjatjs dhabnfurcdnhajs dhrrjsphaija c ãthmhs ja jstcih jxdntcih, ãthmhs ja

jstcih ahrmc` h duc`js sha nadhrrjdtcs8

c. 3s? ?p? o. 3s? ?s? ?p3 d. 3s? ?s? ?i3 i. 3s? ?s4 j. 3s? ?s? 4s3

Natîatc`h tõ!

Th`udnôa5 c. jxdntcih < o. ahrmc` < d. nmphsno`j < i. nmphsno`j < j. jxdntcih

Jspjrh tj snrvc mn rjspujstc y `cs htrcs quj qunzã tj ija mns dhmpcójrhs quj natjatca cyuicrtj

tcmonîa y `cs vc`hrjs, ah ijeãaih`c quj qujij ja /vhtcdnôa/

[rjfuatc ;6! _jsuj`tc j` ?6(3;(?;3?Dhasnijrc ua ãthmh ajutrh dha `c snfunjatj dhabnfurcdnôa j`jdtrôandc5 3s? ?s? ?p2 9s3¸Duã` js su aõmjrh ctômndh8¸Duã` js su dhabnfurcdnôa j`jdtrôandc mãs jstco`j8¸Coshroj h ijsprjaij jajrfíc ducaih pcsc c tjajr indgc dhabnfurcdnôa8 _czhac `csrjspujstcs!Ycmphdh jatnjaih phrquj pcsc ij` anvj` ?p2 c` 9s3 sna pcscr phr `hs catjrnhrjs 4s? 4p2!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Dhrrjsphaijríc c ua ãthmh ja jstcih /jxdntcih/!

J` aumjrh ctômndh js ? ? 2 3 = 33

Tn ah guonjrc jstcih ja jstcih jxdntcih ijojríc gcojr snih 3s? ?s? ?p2 4s3 11 dhabnfurcdnôa mãsjstco`j!

Ijsprjaijríc jajrfíc!

[hrquj dhrrjsphaij c ua jstcih jxdntcih, sj `j gc dhmuandcih jajrfíc y gc pcscih c ua anvj` ij

mcyhr jajrfíc 'phr jsh ijsprjaij jajrfíc c` rjfrjscr c su jstcih ahrmc`.



















Yjmc ;?! Fcsjs nijc`js! Jducdnôa ij

jstcih

Jducdnôa ij jstcih ij ua fcs nijc`! [ R =a _Y ihaij

— [ js `c prjsnôa 'mjinic ja ctmôsbjrcs5 3 ctm = 62; mm ij Gf = 3;34;; [c.<

— R js j` vhùmja 'mjinih ja `ntrhs5 3 ` = 3 im4 = 3;;; dm4.

— a js j` aõmjrh ij mh`js 'mcsc ( pjsh mh`jdu`cr.

— _ js `c dhastcatj ij `hs fcsjs nijc`js5 _=;,;7?

ctm¶`

mh`¶L =7,43

E

mh`¶L =3,>72

dc`

mh`¶L — Y js `c tjmpjrcturc 'ja L5 L = µD ?64.

Tn qujrjmhs ‐dhmpcrcr” ihs sntucdnhajs utn`nzcrjmhs5 [ 3 ¶R 3

Y 3=

[ ? ¶R ?

Y ?ihaij `c tjmpjrcturc ijoj

mjinrsj ja Lj`vna y `c prjsnôa y j` vhùmja ja `cs uanicijs quj sj qunjrca 'ij prjsnôa y ij

vhùmja. jmp`jcaih c cmohs `cihs `cs mnsmcs uanicijs!

Ja dhaindnhajs ahrmc`js ij prjsnôa '3 ctm. y tjmpjrcturc '?64 L., ua mh` ij ua fcs hdupc ua

vhùmja ij ??,9 `ntrhs!

@jy ij Ohy`j — Mcrnhttj5 [ R =dtj 'Y =dtj. !

@jy ij Dgcr`js — Fcy — @usscd! R 3

Y 3=R ?

Y ?=…=dtj ' [ =dtj.

[rjfuatc ;3! _jsuj`tc j` ?7(3;(?;3?

@c `jy ij Fcy @usscd h `jy ij `hs vh`õmjajs ij dhmonacdnôa sj dump`j pcrc `íqunihs h sh`hpcrc fcsjs!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

[crc fcsjs 'nijc`js.!

Tj ijiudj ij `c jducdnôa ij jstcih ij ua FCT NIJC@

[ R ( Y = dhastcatj


















Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac > ij ?6

Tn j` vhùmja ij` fcs js dhastcatj, qujic quj [ ( Y = dhastcatj quj js `c `jy ij Fcy-@usscd!

[rjfuatc ;?! _jsuj`tc j` ?9(3;(?;3?

¸Ja quî bhrmc vcrnc `c ijasnici ij ua fcs ducaih dcmonc ij vhùmja phr jbjdths ij

vcrncdnôa ij prjsnôa8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Rjcmhs, ij `c jducdnôa ij jstcih ij ua fcs nijc` [ R = a _ Y, j` aumjrh ij mh`js a js nfuc` c `c

mcsc 'm. jatrj j` pjsh mh`jdu`cr 'M.

[ R = 'm ( M. _ Y

[ R M = m _ Y

ij ihaij m ( R 'js ijdnr `c ijasnici. = [ M ( '_ Y.

jsth js `h quj ajdjsntcs5 i = [ M ( '_ Y.

sn `c prjsnôa cumjatc 'mcatjanjaih `c Y dtj., `c ijasnici cumjatc< y sn insmnauyj [, insmnaunrã i

[rjfuatc ;4! _jsuj`tc ja hdtuorj ij ?;3?

Ja ua rjdnpnjatj ij 33 @ dhatnjaj ?; f ij fcs ajôa y uac dnjrtc mcsc ij fcs gnirôfjah!Tconjaih ij `c ijasnici ij `c mjzd`c js ij ? f(@ c ;µD, dc`du`c `c prjsnôa thtc`!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

[ R = a _ Y

Ajôa5 [ 'Aj. ¶ 33 = ?; ( ?; ¶ ;,;7? ¶ ?64

[ 'Aj. = ?,;9 ctm

mjzd`c5 ijasnici = m ( R < ij ihaij m = i R = ? ¶ 33 = ?? f ij Ajôa j gnirôfjah

dhmh tjaícmhs ?? f ij ajôa, ij G? gcorã ? f quj jejrdjrãa uac prjsnôa ij

[ R = a _ Y[ 'G?. 33 = ?(? ¶ ;,;7? ¶ ?64, ij ihaij ['G?. = ?,;9 ctm

`c prjsnôa thtc`, js `c sumc ij cmocs5 ?,;9 ?,;9 = 9,;7 ctm

[rjfuatc ;9! _jsuj`tc j` ;3(33(?;3?

Zac mujstrc ij ? ` ij fcs tnjaj uac prjsnôa coshùtc ij 4;; lpc c 4;; l sn tcath `c prjsnôadhmh js vhùmja sj iup`ndca ¸duc` js `c tjmpjrcturc bnac`8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`

[3 ¶ R3!!!!![? ¶ R?----------- = -------------

!!!!Y3!!!!!!!!!!!!Y?

Rjmhs d`crcmjatj quj sn [? = ?[3 y R? = ?R3

[3 ¶ R3!!!!!?¶[3 ¶ ?¶R3

----------- = ------------------

!!!!Y3!!!!!!!!!!!!!!!Y?

Y? = 9 Y3

`c tjmpjrcturc 'ja Lj`vna. sj mu`tnp`ndc phr ductrh5 Y? = 3?;; L

[rjfuatc ;:! _jsuj`tc j` ;3(33(?;3?



































Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac 3; ij ?6

¸Ducaths Ln`hfrcmhs ij antrôfjah fcsjhsh 'M = ?7 f(mh`. ``jacrca ua vhùmja ij ?;;; @ cuac prjsnôa coshùtc ij ?;? l[c y uac tjmpjrcturc ij 7;»D8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`5

[ ¶ R = a ¶ _ ¶ Y

ihaij [ js `c prjsnôa ja ctmôsbjrcs

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!… ctm

?;? l[c = ?;?;;; [c = ?;?;;; [c ! ----------------- = 3,>> ctm

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!… [c

R js j` vhùmja ja `ntrhs5 R = ?;;; `

a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr '?7.

_ js `c dhastcatj ij `hs fcsjs nijc`js5 ;,;7? ctm ¶ ` ( 'mh` ¶ L.

Y `c tjmpjrcturc ja L5 Y = 7; ?64 = 4:4 L

ùjfh3,>> ¶ ?;;; = a ¶ ;,;7? ¶ 4:4

ij ihaij a = 346,:; mh`js

dhmh a = m ( M

m = a ¶ M = 346,:; ¶ ?7 = 479>,>4 f = 4,7: lf


¸Duc` js j` vhùmja hdupcih phr 7 f ij fcs antrôfjah 'M = ?7 f(mh`. c tjmpjrcturc yprjsnôa jstãaicr '[ts.8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`5[ ¶ R = a ¶ _ ¶ Y


R js j` vhùmja ja `ntrhs



Y `c tjmpjrcturc ja L

Dhaindnhajs jstãaicr 'sjfõa `c NZ[CD.5 [ = 3 ctm y Y = ?64 L

ùjfh5

3 ¶ R = '7 ( ?7. ¶ ;,;7? ¶ ?64

ij ihaij R = 2,9 `


Za ijphsnth ij ? m dõondhs dhatnjaj fcs antrôfjah 'M = ?7 f(mh`. oceh uac prjsnôamcahmîtrndc ij :;; l[c! Tn `c tjmpjrcturc js ij ?6» D ¸Duã` js `c mcsc ij` fcs dhatjanihja j` ijphsnth8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Rjh quj tus prjfuatcs snjmprj gcdja rjbjrjadnc c `c mnsmc jducdnôa!


[ ¶ R = a ¶ _ ¶ Y

ihaij [ js `c prjsnôa ja ctmôsbjrcs, 3 ctm = 3;34;; [c



































R js j` vh`umja ja `ntrhs, 3 mQ4 = 3;;; `




':;;¶3;Q4 ( 3;34;;. ¶ ?;;; = 'm ( ?7. ¶ ;,;7? ¶ '?6 ?64.ij ihaij m = 33?42 f = 33,?9 lf


Zac dcatnici ij fcs A? hrnfnacrncmjatj dhatjanih ja 9,6: ctm ij prjsnôa ijatrh ij uarjdnpnjatj ij 3 @ c ?>> L sj trcasbnjrj c ua rjdnpnjatj ij 3; @ c ?>4 L! Zac dcatnici ij fcsH? dhatjanic ja ua rjdnpnjatj ij : @ c :,?: ctm y ?>> L sj trcasbnjrj c jstj mnsmh rjdnpnjatj!¸Duc` js `c prjsnôa thtc` ja j` aujvh rjdnpnjatj8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Dcatnici ij fcs A? hrnfnacrncmjatj dhatjanih ja 9,6: ctm ij prjsnôa ijatrh ij ua rjdnpnjatj ij3@ c ?>>L

Dc`du`cmhs indgc dcatnici ij fcs!

c pcrtnr ij `c jducdnôa ij jstcih ij ua fcs nijc`5 [ ¶ R = a ¶ _ ¶ Y






9,6: ¶ 3 = a ¶ ;,;7? ¶ ?>> < a 'A?. = ;,3> mh`js

Dcatnici ij fcs H? dhatjanic ja ua rjdnpnjatj ij :@ c :,?: ctm y ?>>L sj trcasbnjrj c jstj

mnsmh rjdnpnjatj:,?: ¶ : = a ¶ ;,;7? ¶ ?>> < a 'H?. = 3,;6 mh`js

% Aõmjrh thtc` ij mh`js5 ;,3> 3,;6 = 3,?2 mh`js

% Aujvh rjdnpnjatj5 R = 3; ` , Y = ?>4 L

[ ¶ 3; = 3,?2 ¶ ;,;7? ¶ ?>4 , ij ihaij [ = 4,;9 ctm! Dhrrjdth!

[rjfuatc ;>! _jsuj`tc j` 34(33(?;3?

Za rjdnpnjatj ij :; `t dhatnjaj cnrj dhmprnmnih c 3; ctm c uac tjmpjrcturc ij ; frcihsdjatífrcihs! Tj corj ja ua cmonjatj c ? frcihs djatífrcihs y dha uac prjsnôa ij 3 ctm!Dc`du`cr j` pjsh ij` cnrj quj sj jsdcpc !Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Dc`du`jmhs `c mcsc 'mh`js. ij cnrj quj gcy nandnc`mjatj!

R = :; ` < [ = 3; ctm < Y = ?64 L

[ ¶ R = a ¶ _ ¶ Y

3; ¶ :; = a ¶ ;,;7? ¶ ?64

a 'catjs. = ??,49 mh`js!

Ja `c sntucdnôa bnac`, c` cornr `c ``cvj, j` rjdnpnjatj sj qujicrã dha `cs dhaindnhajs ij` jxtjrnhr5

Y = ?6: L y [ = 3 ctm! J` vh`umja sjrc j` mnsmh

3 ¶ :; = a ¶ ;,;7? ¶ ?6:

a 'ijspuîs. = ?,?? mh`js

Tj gcorã jsdcpcih jathadjs5 a'catjs. - a'ijspuîs. = ??,49 - ?,?? = ?;,3? mh`js ij cnrj!


























Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac 3? ij ?6

Dhmh j` pjsh mh`jdu`cr cprhxnmcih ij` cnrj js ij ?> f(mh`

@c mcsc quj sj gc jsdcpcih sjrã5 ?;,3? ¶ ?> = :74,97 f

[rjfuatc 3;! _jsuj`tc j` 36(33(?;3?

@c ijasnici ij` hxífjah 'H?. c ; µD y 3 ctm ij prjsnôa 'D!A!., js ij 3,9?> f(`! ¸Duã` sjríc `cmcsc mh`cr ij` cmhancdh 'A G4 . ja `cs mnsmcs dhaindnhajs sn, ja `cs mnsmcs dhaindnhajs suijasnici js ij ;,6:> f(`8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`



[ R = 'm ( M. _ Y

[ R M = m _ Y


jsth js `h quj ajdjsntcs5 i = [ M ( '_ Y.c. Tí, ja jbjdth5 i = 3 ¶ 4? ( ';,;7? ¶ ?64. = 3,9?> f ( `

o. Tn ijspjecmhs j` pjsh mh`jdu`cr M5

M = i ¶ _ ¶ Y ( [ = ;,6:> ¶ ;,;7? ¶ ?64 ( 3 = 36 f ( mh`

[rjfuatc 33! _jsuj`tc j` ?2(33(?;3?

Za ouzh suj`tc uac ourouec ij cnrj dha ua vhùmja ij ?!; dm4 ijsij uac prhbuainici ij 3:m oceh `c supjrbndnj ij ua c`cfh, ihaij `c tjmpjrcturc js ij 6!; µD! ¸Suî vhùmja tjairã `courouec ducaih ``jfuj eusth ijoceh ij `c supjrbndnj ij` `cfh ihaij `c tjmpjrcturc js ij ?;µDNócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Ja `c supjrbndnj `c prjsnôa quj tnjajs js `c ctmhsbîrndc [? = 3 ctm = 3;34;; A(mQ?C uac prhbuainici g, `c prjsnôa js5

[3 = [c rh ¶ f ¶ g

snjaih rh `c ijasnici ij` cfuc ja jstj dcsh y g `c prhbuainici,

ùjfh

[3 = 3;34;; 3;;; ¶ 3; ¶ 3: = ?:34;; A(mQ? = ?,97 ctm

pujs dhmh tj gj sjóc`cih 3 ctm = 3;34;; A(mQ?

Cghrc cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`

[3 ¶ R3!!!!!!!!!![? ¶ R?

----------- = -------------

!!!!Y3!!!!!!!!!!!!!!!!Y?

?,97 ¶ ? dmQ4!!!!!!!!!!!3 ¶ R?

-------------------- = -----------

…!!!6 ?64!!!!!!!!!!!!!!?;?64

ij ihaij R? = :,3> dmQ4

Jspjrh gcojrtj cyuicih!

[rjfuatc 3?! _jsuj`tc j` ?7(33(?;3?

¸Duã` js `c ijasnici ij 3 m4 ij cnrj c ; »D y 6?; mm ij Gf8! Ja dhaindnhajs ahrmc`js 3 m4ij cnrj tnjaj uac mcsc ij 3!?>4 LfNócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`






































a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr

_ js `c dhastcatj ij `hs fcsjs nijc`js5 ;,;7? ctm ¶ ` ( 'mh` ¶ L.Y `c tjmpjrcturc ja L

[ R = 'm ( M. _ Y

[ R M = m _ Y


jsth js `h quj ajdjsntcs5 i = [ M ( '_ Y.

j` pjsh mh`jdu`cr `h ijiudjs c pcrtnr ij` icths ij quj 3 mQ4 = 3;;; ` = 3?>4 lf< ùjfh ??,9 `

sjrãa x = ??,9 ¶ 3?>4 ( 3;;; = ?7,>2 f (mh`

…!!'6?; ( 62;. ¶ ?7,>2

i= ----------------------- = 3,?? f ( `

!!!!!!!!!!!!!;,;7?¶ ?64

[rjfuatc 34! _jsuj`tc j` ;?(3?(?;3?

3! Dc`du`cr j` vhùmja hdupcih phr uac dcatnici ij fcs c 7; frcihs y 2;; mm Gf , snc : frcihs y 7;; mm Gf hdupc ?:; m@!

?! ¸Duc` js `c ijasnici ij 2; f ij Antrôfjah ja dhaindnhajs ahrmc`js sn ja uarjdnpnjatj ij 9; @ c :; frcihs jejrdj uac prjsnôa ij 3,9? ctm8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

3. Cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`

[3 ¶ R3!!!!!!!!!![? ¶ R?

----------- = -------------!!!!Y3!!!!!!!!!!!!!!!!!!Y?

7;; ¶ ?:;!!!!!!!!!!2;; ¶ R?

-------------- = --------------

!: ?64!!!!!!!!!!!!7; ?64

ij ihaij R? = 94?,?2 m@

?. Ja dhaindnhajs ahrmc`js ij [ y Y ua mh` ij uac fcs '?7 f, pcrc j` dcsh ij` A?. hdupc ua

vhùmja ij ??,9 `!

Csí quj

i = ?7 f ( ??,9 ` = 3,?: f(`

@c nabhrmcdnôa quj tj ica ja j` jauadncih js /pcec/! Ja dhaindnhajs ahrmc`js ij prjsnôa ytjmpjrcturc ua mh` ij ua fcs hdupc ua vhùmja ij ??,9 `!

[rjfuatc 39! _jsuj`tc j` ??(3?(?;3?

Dc`du`cr `c mcsc ij 3 `ntrh ij cnrj scturcih ij gumjici c ?:µD y prjsnôa c 66; mmGf! @cprjsnôa ij vcphr c ?:µD ?4,7 mm Gf! Mr 3(?=?7,>2 fr(mh`!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`


[ ¶ R = a ¶ _ ¶ Y





























a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr '?7,>2.



Ijojs tjajr ja dujatc quj ja `c prjsnôa tnjajs quj rjstcr c `hs 66; mm , `c prjsnôa ij vcphr ij`cfuc, ?4,7 mm

Js ijdnr, tj qujicrã5

\'66; - ?4,7. ( 62;] ¶ 3 = \ m ( ?7,>2 ] ¶ ;,;7? ¶ '?: ?64.

ij ihaij m = 3,32 f

[rjfuatc 3:! _jsuj`tc j` ;6(;3(?;34! _jspujstc aõmjrh 399>

3! C uac tjmpjrcturc ij >: µD y c uac prjsnôa ij 67? mm ij Gf ua fcs hdupc ua vhùmjaij ?;; Dc`du`cr j` vhùmja quj hdupcrc indgh fcs c `c tjmpjrcturc ij 2: µD y c 73: mm ijGf prjsnôa?! Tn :!6: f ij ua fcs hdupca ua vhùmja ij 4!93 c ua tjmpjrcturc ij :; µD y c uac prjsnôaij ;!>9 ctm ¸Duc` js su pjsh mh`jdu`cr8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

[_HO@JMC 3!

Cp`ndc `c jducdnôa ij jstcih ij ua fcs nijc`

[3 ¶ R3!!!!![? ¶ R?

----------- = -------------

!!!!Y3!!!!!!!!!!!!Y?

67? ¶ ?;; ( '>: ?64. = 73: ¶ R? ( '2: ?64.

ij ihaij R? = 362,?2 suphafh quj dmQ4 'phrquj ah pusnstj `cs uanicijs ij` vhùmja.!

Tn qunjrjs `c jxp`ndcdnôa y j` ijscrrh``h ij `cs bhrmu`cs, `cs dhastcatjs jmp`jcics, jdgc uachejcic c jstj ihdumjath dha prho`jmcs quj yh mnsmh rjsh`ví ij cghh# _jspujstcs! Jstc thih

jxp`ndcih5

gttp5((www!sdrnoi!dhm(ihd(339??3499(Sunm…

@h õandh quj ijojs tjajr muy ja dujatc ja quj `c tjmpjrcturc ijojs jxprjscr`c ja Lj`vna '`c

prjsnôa y j` vhùmja ic nfuc` snjmprj y ducaih phafcs `cs mnsmcs uanicijs c cmohs `cihs.

[_HO@JMC ?!

Ij aujvh cp`ndcs `c jducdnôa ij jstcih ij ua fcs nijc`, jstc vjz jsdrntc dhmhX

[ ¶ R = a ¶ _ ¶ Y

ihaij [ js `c prjsnôa ja ctmôsbjrcs,

R js j` vhùmja ja `ntrhs,a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr



vhy c jatjaijr quj 4,93 sha `ntrhs 'pha uanicijs.

Ja aujstrh dcsh5 ;,>9 ¶ 4,93 = ':,6: ( M. ¶ ;,;7? ¶':; ?64.

ij ihaij M = 96,: f ( mh`

Yj rjmnth c` ja`cdj catjrnhr pcrc quj jdgjs ua vnstczh c mcs prho`jmcs ij fcsjs nijc`js rjsuj`ths

y csí prcdtnqujs!

[rjfuatc 32! _jsuj`tc j` 3>(;3(?;34 c cs 36593 g 'ghrc jspcóh`c.!! _jspujstc aõmjrh 3:?6


















Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac 3: ij ?6

¸Dômh scojr `c mcsc ij uac sustcadnc sconjaih su vhùmja, prjsnôa y tjmpjrcturc8¸Duã` js `c mcsc ij 9>!9 `ntrhs ij D`? c ?6 »D y 2;7 mm ij Gf8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`


[ ¶ R = a ¶ _ ¶ Y

ihaij [ js `c prjsnôa ja ctmôsbjrcs, 3 ctm = 62; mm Gf


a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr '4:,: ¶ ? pcrc j` D`?.



'2;7 ( 62;. ¶ 9>,9 = \m ( '4:,:¶?.] ¶ ;,;7? ¶ '?6 ?64.

ij ihaij m = 33?,92 f

[rjfuatc 36! _jsuj`tc j` ?;(;3(?;34 c `cs 335?2 g 'ghrc jspcóh`c.! _jspujstc aõmjrh 3:4?Ijtjrmnaj j` vhùmja ij 7 f ij gj`nh c 3: »D y 97; mm Gf 'M = 9 lf ( lmh`.Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`


[ ¶ R = a ¶ _ ¶ Y

ihaij [ js `c prjsnôa ja ctmôsbjrcs, 3 ctm = 62; mm Gf


a js j` aõmjrh ij mh`js a = m ( M snjaih M j` pjsh mh`jdu`cr '7 f(mh`.



'97; ( 62;. ¶ R = '7 ( 9. ¶ ;,;7? ¶ '3: ?64.ij ihaij 5 R = 69,67 `

[rjfuatc 37! _jsuj`tc j` ?;(;3(?;34 c cs 3754; g 'ghrc jspcóh`c.! _jspujstc aõmjrh 3:93

Ja j` supujsth ij quj `c `jy fjajrc` ij `hs fcsjs bujrc [ R? = a? _ Y, ¸duã` sjríc j` vc`hr ij_ y sus uanicijs, sn [ jstã icic ja ctmôsbjrcs, a ja mh`js, Y ja lj`vnas y R ja `ntrhs8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Tn tjajmhs ja dujatc quj 3 mh` ij ua fcs nijc` hdupc ua vhùmja ij ??,9 ` c 3 ctm y ; µD '?64

L.

[¶RQ? = aQ? ¶ _ ¶ Y3 ctm ¶ '??,9 `.Q? = '3 mh`.Q? ¶ _ ¶ ?64 L

ij ihaij _ = 3,747 ctm ¶ `Q? ( 'mh`Q? ¶ L.



































Yjmc ;4! _jcddnhajs químndcs

[rjfuatc ;3! _jsuj`tc j` ?7(3;(?;3?¸Mj pujija cyuicr indnîaihmj duc`js ij jstcs jducdnhajs ah sha dhrrjdtcs8

B Oj --1 Bj ODH H --1 DH?? C` 's. Bj?H4 's. --1 ? C`H's. ? Bj G?H? L? H? --1 ? L?HBj? 4 H? --1 Bj?H4


3. b oj -bj o 5 mc` ! c `c nzqunjric tnjajs b`õhr y ojrn`nh y c `c ijrjdgc tnjajs quj tjajr

dhmpujsths dha jsths j`jmjaths 'ah snrvj dcmoncr `cs `jtrcs.?. mc`, j` hxífjah ijoj cpcrjdjr dhmh H? 'ah dhmh H.

4. mc` C` H ¸ijsij ducaih j` c`umnanh tnjaj vc`jadnc ? h j` hxnfjah vc`jadnc 48

9. mc` ! ah jxnstj j` L?, jxnstj j` phtcsnh L, pjrh ah L?

:. mc` ! J` gnjrrh js Bj, ah Bj?, ja thih dcsh phirícs jsdrnonr5 ? Bj 4 H? --1 Bj? H4 , jsth sí

jstc onja!

Frcdncs phr puatucr

[rjfuatc ;?! _jsuj`tc j` 33(33(?;3?

Ceustcr cs snfunjatjs rjcddnhajs5Dr H? =

DrH4 =D4G7 H? =DH? G?H =Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Tuphafh quj sha IHT `cs rjcddnhajs quj qunjrjs ceustcr5

Dr H? --1 DrH4

Dr '4(?. H? --1 DrH4

y

D4G7 H? --1 DH? G?H

D4G7 : H? --1 4 DH? 9 G?HFrcdncs phr dc`nbndcr <-.

[rjfuatc ;4! _jsuj`tc j` ?4(;3(?;34 c cs 395:9 g 'ghrc jspcóh`c.! _jspujstc aõmjrh 3:2>

Yjafh quj ijdnr duc`js sha `hs rjcdtnvhs y duc`js sha `hs prhiudths ij` snfunjatj prhdjshquímndh! [rnmjr prhdjsh químndh js5 D;?,G?;,'D9G3;.';?.y j` snfunjatj prhdjsh químndh js5?Mf;?--------------?Mf;Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Mj nmcfnah quj j` prnmjr prhdjsh quj naindcs js `c dhmoustnôa ij` outcah

D9 G3; H? --1 DH? G?H 'dhihs mhecihs.

`hs rjcdtnvhs sha j` outcah D9G3; y j` hxífjah H? y `hs prhiudthr j` inôxnih ij dcrohah DH? y



































j` cfuc G?H

[crc `c sjfuaic rjcddnôa5 ?Mf;?--------------?Mf;

`hs rjcdtnvhs sha j` mcfajsnh Mf y j` hxífjah H? y j` prhiudth j` hxnih ij mcfajsnh Mf H

`hs rjcdtnvhs cpcrjdj c `c nzqunjric ij `c jducdnôa y `hs prhiudths c `c ijrjdgc!


¸Ducatcs thaj`cics ij gnjrrh pujija hotjajrsj ja `c rjiuddnôa ij : thaj`cics ij mnajrc`gjmctntha 'ôxnih bîrrndh.8J` mjrdurnh gnjrvj c 2:»B y sj sh`ninbndc c -47»B c `c prjsnôa ij uac ctmôsbjrc! Jxprjscrîstcs tjmpjrcturcs c frcihs lj`vna '»L.Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Bj? H4 --1 ? Bj '4(?. H?

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3 mh` Bj? H4!!!!!!!!!!!!!!!!!!? mh`js Bj!!!!!!!!!!!!!:2 f Bj

: Ym Bj? H4 ! ------------------------------- ¶ ------------------- ¶ -------------- = 4,: Ym Bj!!!!!!!!!!!!!!!!!!!!!!!!!!!?¶:2 4¶32 f Bj? H4!!!!!!!3 mh` Bj? H4!!!!!!!!!3 mh` Bj

O. 2:µB

D!!!!B - 4?

-- = ---------

:!!!!!!!!>

D(: = '2: - 4?. ( >, ij ihaij D = 37,4 µD

L = µD ?64 = ?>3,4 L

ij` mnsmh mhih5

D(: = '-47 - 4?. ( >, ij ihaij D = -47,> µD

L = µD ?64 = ?49,3 L Ahtc5 sj `jj ?49,3 Lj`vna 'ah frcihs Lj`vna.

[rjfuatc ;:! _jsuj`tc j` ?7(33(?;3?

Ja uac ohmohac dha 3; lf ij outcah 'D9 G3;., ¸ducaths `ntrhs 'ja dhaindnhajs ahrmc`js. ijDH? sj jmntja8 y, ¸ducaths `ntrhs ij cfuc 'jstcih `nqunih. sj jmntja8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Ja `c rjcddnôa ij dhmoustnôa ij ua gnirhdcrourh 'dha H?. sj bhrmca /dhihs mhecihs/5 D H? y

G? H

D9 G3; '34(?. H? --1 9 D H? : G? H

!!!!!!!!!!!!!!!!!!!!!!!!3 mh` D9G3;!!!!9 mh`js DH?!!!!??,9 ` DH?

3;;;; f D9G3; !------------------- ! -------------------- !----------------- = 3:997,4 ` DH?

!!!!!!!!!!!!!!!!!!!!!!!!!:7 f D9 G3;!!!3 mh` D9G3;!!!!3 mh` DH?

!!!!!!!!!!!!!!!!!!!!!!!!!!!3 mh` D9G3;!!!!!!!!: mh`js GH?!!!!!!!!!!37 f GH?

3;;;; f D9G3; !------------------- ! -------------------- ! --------------- = 3::36,? f G?H

!!!!!!!!!!!!!!!!!!!!!!!!!!!!:7 f D9 G3;!!!!!!!!3 mh` D9G3;!!!!!!!!3 mh` GH?

js ijdnr 3:,:? lf!

Yjanjaih ja dujatc `c ijasnici ij` cfuc 3;;; lf(mQ4

i = m ( R

R = m ( i = 3:,:? ( 3;;; = ;,;3::? mQ4 ij cfuc = 3:,:? ` ij G?H



























[rjfuatc ;2! _jsuj`tc j` ;:(;?(?;34 c `cs ?;597 'ghrc jspcóh`c.! _jspujstc aõmjrh 3647

Za ghrah ij dc` utn`nzc dhmh mctjrnc prnmc uac pnjirc dc`nzc, DcDH4, dha ua 3:* ijnmpurjzc sn`ídndc! Dc`du`c `hs mjtrhs dõondhs ij DH? quj sj ijsprjaija phr thaj`cic ijpnjirc dc`nzc!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Tuphafh quj `c rjcddnôa js5

Dc D H4 ---1 D H? Dc H

[crtnmhs ij 3;Q2 f ij dc`nzc /nmpurc/

!!!!!!!!!!!!!!!!!!!!!!3: f ij Dc DH4

3;Q2 f dc`nzc !-------------------------- = 3,:¶3;Q: f Dc DH4

!!!!!!!!!!!!!!!!!!!!!!!!3;; f dc`nzc

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3 mh` DcDH4!!!!3 mh` DH?!!!!!!!??,9 DH?

3,:¶3;Q: f Dc DH4 ! -------------------- ! --------------------- ! ---------------

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3;; f DcDH4!!!!!3 mh` DcDH4!!!3 mh` DH?hotjanjaih 442;; ` DH? = 44,2 mQ?

Tuphanjaih quj jstcmhs ja dhaindnhajs ahrmc`js ij prjsnôa y tjmpjrcturc!

[rjfuatc ;6! _jsuj`tc j` ?7(33(?;3?

J` d`hrurh ij gnjrrh 'NN., BjD`?, rjcddnhac dha cmhancdh, AG4, y cfuc, pcrc prhiudnrgnirôxnih ij gnjrrh 'NN., Bj'HG.? y d`hrurh ij Cmhanh, AG9D`!

c. Jsdrnoc uac jducdnôa oc`cadjcic pcrc jstc rjcddnôa! Tn mjzd`cmhs 67,: f ij BjD`?<?: f ij AG4 y ?: f ij cfuc, quj rjcddnhaca tca dhmp`jtcmjatj dhmh js phsno`j!

o. Dc`du`j `hs frcmhs ij Bj'HG.? y AG9D` bhrmcihs!d. Dc`du`j `hs frcmhs ij dcic uah ij `hs rjcdtcatjs quj qujicrha ja jxdjsh c`

dhmp`jtcrsj `c rjcddnôa!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

@c rjcddnôa ceustcic js

Bj D`? ? AG4 ? G?H --1 Bj 'HG.? ? AG9D`

`c gj ceustcih c heh

c. Yjajmhs ua prho`jmc ij rjcdtnvh `ímntj 'dha trjs sustcadncs, ¡mh`c#, `c prnmjrc vjz quj `h

vjh.! Tuphafcmhs quj j` j` BjD`?

Rcmhs c pcrtnr ij jstj y dc`du`cr `c dcatnici ij `hs htrhs quj ajdjsntcmhs y vjrjmhs sn

insphajmhs h ah ij tc`js dcatnicijs!

!!!!!!!!!!!!!!!!!!!!!!!!3 mh` BjD`?!!!!!!!!? mh`js AG4!!!!!!!!36 f AG4

67,: f BjD`? ! ------------------ ! ------------------- ! ---------------- = ?3,;? f AG4

!!!!!!!!!!!!!!!!!!!!!!!!3?6 f BjD`?!!!!!!!!3 mh`j BjD`?!!!!!!!!3 mh` AG4

!!!!!!!!!!!!!!!!!!!!!!!!!3 mh` BjD`?!!!!!!? mh`js G?H!!!!!!!!!37 f G?H

67,: f BjD`? ! ------------------ !------------------- ! --------------- = ??,?: f G?;

!!!!!!!!!!!!!!!!!!!!!!!!3?6 f BjD`?!!!!!!!3 mh` BjD`?!!!!!!!!!3 mh` G?H

d. ¡quî sujrtj# c `c prnmjrc! J` rjcdtnvh `ímntj js j` BjD`? y ja jxdjsh jstãa j` AG4 'shorcrãa ?:

- ?3,;? = 4,>7 f. y j` G?H 'quj shorcrãa ?: - ??,?: = ?,6: f.

o.

!!!!!!!!!!!!!!!!!!!!!!!!3 mh` BjD`?!!!!!!!3 mh`js Bj'HG.?!!!!!!!>; f Bj'HG.?

67,: f BjD`? ! ------------------ !----------------------- ! --------------------- = ::,24 f Bj'HG.?


























Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac 3> ij ?6

!!!!!!!!!!!!!!!!!!!!!!!!3?6 f BjD`?!!!!!!!3 mh` BjD`?!!!!!!!!!!!!!!3 mh` Bj'HG.?

!!!!!!!!!!!!!!!!!!!!!!!!!3 mh` BjD`?!!!!!!? mh`js AG9D`!!!!!!!!:4,: f AG9D`

67,: f BjD`? ! ------------------ !----------------------- !-------------------- = 22,39 f AG9D`

!!!!!!!!!!!!!!!!!!!!!!!!!!3?6 f BjD`?!!!!!!3 mh` BjD`?!!!!!!!!!!!!!3 mh` AG9D`

[rjfuatc ;7! _jsuj`tc j` ;?(;?(?;34 c `cs 3?5;; 'ghrc jspcóh`c.! _jspujstc aõmjrh 329:

¸Tn 3 tcaquj a 3 dhgjtj dhatnjaj 3?2 f i O:G> y htrh tcaquj dhatnjaj 3>?f i H?, ijtjrmnacr`c mcsc i cfuc q puji sjr8Za dhmoustno`j phtjadnc` pcrc `hs dhgjtjs jspcdnc`js js uac dhmonacdnôa ij` O:G> y j`H?!Cmohs rjcddnhaca ij cdujrih c c snfunjatj jducdnôa oc`cadjcic5?O:G>'`. 3?H?'f. ↟ :O?H4's. >G?H'f.Tn ua tcaquj ja ua dhgjtj dhatnjaj 3?2 f ij O:G> y htrh tcaquj dhatnjaj 3>? f ij H?,ijtjrmnaj `c mcsc ij cfuc quj pujij sjr prhiudnic ducaih j` dhatjanih thtc` ij cmohstcaqujs rjcddnhac jatrj sí Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Js ua prho`jmc ij rjcdtnvh `ímntj!

Tuphafcmhs quj îstj sjc j` O:G>, vcmhs c vjr `c dcatnici ij H? quj ajdjsntcmhs y vjr sn

insphajmhs h ah ij `c mnsmc5

!!!!!!!!!!!!!!!!!!!!24 f O:G>!!!!!? mh` O:G;!!!!!3 mh` H?

3?2 f O:G> !------------------- !-------------------- !-------------- = 93,49 f H?

!!!!!!!!!!!!!!!!!!!!3 mh` O:G>!!!!3? mh`js H?!!!!!4? f H?

tjajmhs ij shorc, `ujfh j` O:G> js j` rjcdtnvh `nmntj y j` H? j` rjcdtnvh ja jxdjsh!

Dc`du`jmhs `c mcsc ij cfuc bhrmcic! Ij` mnsmh mhih5

!!!!!!!!!!!!!!!!!!!!24 f O:G>!!!!!? mh` O:G;!!!!!3 mh` G?H3?2 f O:G> !------------------- !-------------------- !----------------- = >7 f G?H

!!!!!!!!!!!!!!!!!!!!3 mh` O:G>!!!!> mh`js G?H!!!37 f G?H

Bujatj's.5

_jsuj`tc j` ;?(;?(?;34

Jspjrh tj cyuij mn rjspujstc y `c vc`hrjs ah ijecaih`c quj qujij ja vhtcdnôa!

[rjfuatc ;>! _jsuj`tc j` ;?(;?(?;34 c cs 3>543 'ghrc jspcóh`c.! _jspujstc aõmjrh 3224

3! ¸Duãaths mh`js ij H? sj ajdjsntca pcrc bhrmcr 37 frcmhs ij G?H8?! ¸Duãaths frcmhs ij D?G2 sj ajdjsntca pcrc bhrmcr 4 mh`js ij G?H8_jsuj`vj hs snfunjatjs prho`jmcs rj`cdnhacihs c` tjmc ij rjcdtnvh nmntcatj5

4! Naindc duã` js j` rjcdtnvh `nmntcatj ja `c snfunjatj rjcddnôa oc`cadjcic dhasnijrcaih qujrjcddnhaca 3:f ij Mf y 3:f ij Gd`5 Mf ? GD` ----------1 MfD`? G?Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

3! Ajdjsntcrícmhs `c rjcddnôa! Tuphafh quj sn qujrjmhs hotjajr G?H js c pcrtnr ij G? y H?,

ij cdujrih dha `c rjcddnôa ?G? H? ---1 ?G?H

!!!!!!!!!!!!!!!3 mh` G?H!!!!3 mh` H?

37 f G?; !---------------- !-------------------- = ;,: mh`js H?

!!!!!!!!!!!!!!!!!37 f G?H!!!? mh`js G?H

?! Tuphafcmhs quj tjajmhs `c rjcddnôa ij dhmoustnôa ij` jtcah


























Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac ?; ij ?6

D?G2 '6(?. H? ---1 ?DH? 4G?H '/dhihs mhecihs/.

!!!!!!!!!!!!!!!!!!!!!3 mh` D?G2!!!!!!!4; f D?G2

4 mh`js G?H !------------------- ! ----------------- = 4; f D?G2

!!!!!!!!!!!!!!!!!!!!!4 mh`js G?H!!!3 mh` D?G2

4! Mf ? GD` ----------1 MfD`? G?

Tuphafcmhs quj js j` Mf, vjcmhs `c dcatnici ij GD` ajdjscrnc5

!!!!!!!!!!!!!3 mh` Mf!!!? mh`js GD`!!!42,: f GD`

3: f Mf !------------- !------------------- !---------------- = 9:,2?: f GD`

!!!!!!!!!!!!!!?9 f Mf!!!!!!3 mh` Mf!!!!!3 mh` GD`

`ujfh j` rjcdtnvh `ímntj js j` GD`











Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac ?3 ij ?6

Yjmc ;9! Inshùdnhajs

Bhrmcs ij jxprjscr `c dhadjatrcdnôa ij uac inshùdnôa!

Dhadjatrcdnôa djatjsnmc` h tcath phr dnjath ja pjsh! Tha `hs frcmhs ij shùth quj gcy ja 3;; f

ij inshùdnôa!

Mh`crnici! Tha `hs mh`js ij shùth dhatjanihs ja ua `ntrh ij inshùdnôa!

Ahrmc`nici! Js j` aõmjrh ij jqunvc`jatjs frcmh ij shùth phr dcic `ntrh ij inshùdnôa!

Mh`c`nici! Tha `hs mh`js ij shùth phr dcic ln`hfrcmh ij insh`vjatj!

* ja mcsc

[rjfuatc ;3! _jsuj`tc j` ?:(3;(?;3?

C`funja mj pujij jxp`ndcr onja `h quj js `c DHADJAY_CDNHA JA MCTC, c sjr phsno`jdha ua jejmp`h!Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Ja uac inshùdnôa 'quj dhastc ij shùth y insh`vjatj., j` * ja mcsc sha `hs frcmhs ij shùth quj

gcy ja 3;; f ij inshùdnôa! [ujijs gcdjr`h dha uac sjadn``c rjf`c ij trjs!

Za jejmp`h5

Tj insuj`vja ? f ij gnirôxnih sôindh 'Ac H G. ja 3; f ij cfuc! ¸Duã` js `c dhadjatrcdnôa

djatjsnmc`8

Thùdnôa5Thùth5 gnirôxnih ij shinh

Insh`vjatj5 cfuc

Tn ja ? 3; frcmhs ij inshùdnôa tjajmhs ? frcmhs ij shùth

ja 3;; frcmhs ij inshùdnôa gcorã !!!!!!!!!!! x frcmhs ij shùth

ij ihaij x = ?¶3;; ( 3? = 32,26 *

[rjfuatc ;?! _jsuj`tc j` 43(;3(?;34 c cs ?3533 g 'ghrc jspcóh`c.! _jspujstc aõmjrh 32?>

Tj insuj`vja 3; f ij scdcrhsc ja ?:; f ij cfuc! Naindc `c dhadjatrcdnôa ij `c inshùdnôa japhrdjatcej ja mcsc!



























Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac ?? ij ?6

@c dhadjatrcdnôa djatjsnmc` h * ja mcsc sha `hs frcmhs ij shùth 'ja tu dcsh, `c scdcrhsc. phr

dcic 3;; frcmhs ij inshùdnôa 'ja tu dcsh scdcrhsc cfuc.! [ujijs gcdjr uac sjadn``c rjf`c ij trjs5

Tn ja ?:; 3; frcmhs ij inshùdnôa gcy 3; f ij scdcrhsc

!!!!!!!!!!!ja 3;; frcmhs ij inshùdnôa gcorã !!!!! x f ij scdcrhscij ihaij x = 3;; ¶ 3; ( '?:; 3;. = 4,79 * js j` phrdjatcej ja mcsc ij shùth!

Tn qunsnjrcs dc`du`cr j` * ja mcsc ij insh`vjatj, bãdn`, c pcrtnr ij` catjrnhr5 3;; - 4,79 = >2,3: *

Bnectj quj gjmhs pujsth ?:; f ij insh`vjatj 3; f ij shùth = ?2; f ij inshùdnôa!

Mh`crnici

[rjfuatc ;?! _jsuj`tc j` 39(33(?;3?

¸Ducaths frcmhs, sj rjqunjrja pcrc prjpcrcr :;; m`s ij uac shùdnôa ? M i DcDH48Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

@c mh`crnici ij uac inshùdnôa js j` aumjrh ij mh`js ij shùth pcrtnih ij` vhùmja 'ja `ntrhs.

ij `c inshùdnôa5

M = a ( R

? = a ( ;,:

ij ihaij a = 3 mh`

J` aumjrh ij mh`js a = m ( M 'mcsc ( pjsh mh`jdu`cr.

m = a ¶ M = 3 mh` ¶ '9; 3? 4¶32. f(mh` = 3;; f 111 Thùdnôa


¸Duã` js `c mh`crnici ij uac shùdnôa quj dhatnjaj 3; m@ ij G?TH9 ja ?;; m@ ij shùdnôa8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

@c mh`crnici ij uac inshùdnôa js j` aõmjrh ij mh`js ij shùth pcrtnih ij` vhùmja 'ja `ntrhs.

ij `c inshùdnôa!

Ajdjsnth `c ijasnici ij` ãdnih su`bõrndh pcrc dc`du`cr `c mcsc y `hs frcmhs!

Ousdh ja Vnlnpjinc y hotjafh quj `c ijasnici js5 3,7 f(dmQ4

ijasnici = mcsc ( vhùmja

mcsc = ijasnici ¶ vhùmja = 3,7 f(dmQ4 ¶ 3; dmQ4 = 37 f

j` aumjrh ij mh`js js a = m ( M 'mcsc ( pjsh mh`jdu`cr.

a = 37 ( '?¶3 4? 9¶32. = 37 ( >7 = ;,37 mh`js

@c mh`crnici js5 M = a ( R = ;,37 ( ;,? = ;,>? mh`js ( Àhtc5 gj dhasnijrcih quj `hs ?;; m` sha ij inshùdnôa 'shùth insh`vjatj.

Tn `hs ?;; m` sô`h bujrca ij insh`vjatj, ij inshùdnôa tjairícmhs `c sumc5 ?;;3; = ?3; m` y js

jstj dcsh M = ;,37 ( ;,?3 = ;,76 mh`js (`

Jspjrh gcojrtj cyuicih

Ahrmc`nici


¸Ducaths m`s sj ajdjsntca pcrc prjpcrcr :;; frs ij G?T 'ãdnih su`bõrndh. ij uac shùdnôa

;,?: A8




























J` ãdnih su`bõrndh js G? T H9

G? T js j` su`burh ij gnirôfjah

¸c duã` ij `hs ihs tj rjbnjrjs8

Rhy c suphajr quj c` ãdnih su`bõrndh G? T H9

@c ahrmc`nici ij uac inshùdnôa js j` aõmjrh ij jqunvc`jatjs ij shùth ( vhùmja ij `c

inshùdnôa 'ja `ntrhs.

Dc`du`cmhs `hs mh`js5 a = m ( M 'mcsc ( pjsh mh`jdu`cr.

a = :;; ( '?¶3 4? 9¶32. = :;; ( >7 = :,3; mh`js

Cghrc onja ua mh` ij G?TH9 sha ? jqunvc`jatjs 'pujs js ua ãdnih quj tnjaj ? gnirôfjahs.

ùjfh j` aõmjrh ij jqunvc`js sjrã5 ?¶:,3; = 3;,?; jqunvc`jatjs

A = a jq ( R

ij ihaij R = a jq ( A = 3;,?; ( ;,?: = 9;,7? `

Mh`c`nici

[rjfuatc ;:! _jsuj`tc j` ?6(3;(?;3?

Dc`du`cr `c mh`c`nici ij uac inshùdnôa ij GD` quj dhatnjaj 3?: f ij shùth ja 7;; m` ijinshùdnôa!


@c mh`c`nici ij uac inshùdnôa sha `hs mh`js ij shùth phr dcic ln`hfrcmh ij insh`vjatj!

Tuphafh quj sj trctc ij uac inshùdnôa ja CFZC!

7;; m` = ;,7 lfJ` pjsh mh`jdu`cr ij` G D` js 42,: f, ùjfh tjajmhs 3?: ( 42,: = 4,9? mh`js

ùjfh `c mh`c`nici js 5 4,9? mh`js ( ;,7 lf = 9,?7 mh`js(lf ô /mh`c`/

[rjfuatc ;2! _jsuj`tc j` ?6(3;(?;3?

Duãaths frcmhs ij antrcth ij p`ctc sj ajdjsntca pcrc prjpcrcr ?;; m` ij shùdnôa ;!? mh`c`Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Jatnjaih quj sj trctc ij uac inshùdnôa cduhsc!

@c mh`c`nici ij uac inshùdnôa sha `hs mh`js ij shùth phr dcic ln`hfrcmh ij insh`vjatj!

;,? mh`js(lf = a ( ;,? lf

ij ihaij j` aumjrh ij mh`js js a = ;,;9

J` antrcth ij p`ctc Cf A H4 tnjaj ua pjsh mh`jdu`cr ij 5 3;7 39 97 = 36;,

ùjfh `c mcsc rjqujrnic sjrc m = ;,;9 mh`js ¶ 36; f(mh` = 2,7 f


c. Dc`du`j `c mh`c`nici ij 3;; fr ij LMaH9 ja 4 l` ij cfuco. ;!3 mh` ij G4[H9 ja ?,;;; fr ij cfucd. ;!? fr ij MfD`? ja 7;; fr ij cfuc


@c mh`c`nici sha `hs mh`js ij shùth phr dcic ln`hfrcmh ij insh`vjatj!











































3. shùth5 LMaH9< pjsh mh`jdu`cr5 4> :: 32¶9 = 3:7 f(mh`

mh`js ij shùth a = m ( M = 3;; ( 3:7 = ;,24 mh`js

insh`vjatj 4 l` = ¸l`8 -drjh quj gcs qujrnih ijdnr `ntrhs, `c l y `c ` jstca euatcs ja j` tjd`cih-

vhy c suphajr quj sha 4 ` = 4 lf

mh`c`nici = ;,24 ( 4 = ;,?3 mh`js ( lfTn bujrca l` ' ln`h `ntrhs ., sjrnca 4;;; ` = 4;;; lf y ja jstj dcsh mh`c`nici = ;,24 ( 4;;; =

;,;;;? mh`c`

o. shùth5 ;,3 mh`js < insh`vjatj5 ? lf

ah sî sn dha ?,;;; qunjrjs ijdnr ?;;; f h ? f! Rhy c natjrprjtcr quj sha ?;;; f = ? lf 'sn bujrca ?

f, sjrnca ;,;;? lf.! Mudgcs dc`du`cihrcs jmp`jca `c dhmc , pcrc sjpcrcr uanicijs ij mn``cr, ij cgn

mn natjrprjtcdnôa!

mh`c`nici = ;,3 ( ? = ;,;: mh`js(lf

d. shùth5 MfD`?5 [jsh mh`jdu`cr5 ?9 4:,:¶? = >: f(mh`

aumjrh ij mh`js5 ;,? ( >: = ;,;;? mh`js

insh`vjatj5 7;; f = ;,7 lf

mh`c`nici = ;,;;?3 ( ;,7 = ;,;;?2 /mh`c`/ h mh`js(lf











Nócln Dcrrcsdc` Mhzh! Suímndc! Mns rjspujstcs c prho`jmcs ij cghh _jspujstcs# 3!; ;6(;?(?;34! [ãfnac ?: ij ?6

Yjmc ;:! Yjrmhquímndc

[rjfuatc ;3! _jsuj`tc j` ;3(3?(?;3?Tjfõa jstc nabhrmcdnôa `cs snfunjatjs jducdnhajs tjrmhquímndcs, ¸ij quî tnph sha8

c. Mf 's. DN? 'f. -6 MfDN? 's. 293,7 lEo. o` DcDH ':. 367 lE -6 DcH 's. DH? 'f.d. 4 3 j. DuH ':. -6 Du 's. ?/ H? 'f. - >6,3 lE i.i. D':. H? 'f. - 462,? lE -6 DH? 'f.


c. Jxhtîrmndc pujs ijsprjaij dc`hr 'phrquj sumcr 293,7 LE c `c ijrjdgc.

o. Jaihtîrmndc pujs coshroj dc`hr

d. 4 3 j. ¸8! Jaihtîrmndc 'pcsctj `hs ->6,3 c `c nzqunjric dhmh >6,3.i. Jxhtîrmndc 'pcsctj `hs -462,? c `c ijrjdgc sumcaih.

[rjfuatc ;?! _jsuj`tc j` ?7(33(?;3?

J` antrcth ij cmhanh ij ijsdhmphaj ij cdujrih c `c snfunjatj rjcddnôa tjrmhquímndc5AG9AH4----------1A?H ?G?H IG= -42Lesn `c MM ij` AG9AH4 js ij 7; f(mh` y sj ijsdhmphaj 3 frs ij sc` sj ijsprjaija5 8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

[ujijs gcdjr uac sjadn``c rjf`c ij trjs!

Tn 3 mh` '7; f. ijsprjaija 42 LE

3 f ijsprjaijrã!!!!!!!!!!!!!!!!x, ij ihaij x = 42 ( 7; Le = ;,9: LE

h ij uac bhrmc mcs j`jfcatj

!!!!!!!!!42 LE!!!!!!!!3 mh`

3 f !-------------! --------- = 42 LE ( 7; = ;,9: LE

!!!!!!!!3 mh`!!!!!!!!!!!7; f


Icic `c jatc`píc ij rjcddnôa jstãaicr, utn`ndj `cs jatc`pícs jstãaicr ij bhrmcdnôa ij `c tco`cpcrc dc`du`cr `c jatc`píc jstãaicr ij bhrmcdnôa ij` DuH 's.!DuH 's. G? 'f. ----1 Du 's. G?H 'N. CG= -3?>,6 lE


Bãdn`! Ztn`nzc `c `jy ij Gjss, pjrh ¸y `c tco`c8

Ajdjsnth `c jatc`píc jstãaicr ij bhrmcdnôa ij` cfuc5 - ?7:,7 lE(mh` 'ij mns cpuatjs ij químndc

ij DHZ.

ij`tc G = ' sumcthrnh ij ij`tc ij G ij bhrmcdnôa ij prhiudths . - ' sumcthrnh ij ij`tc ij G ij

bhrmcdnôa ij rjcdtnvhs .

-3?>,6 = '-?7:, 7 ;. - 'x ;., ij ihaij x = -3:2,3 lE(mh`

phrquj `cs jatc`pícs jstãaicr ij bhrmcdnôa ij G? y ij` Du sha djrh '¡ yc jstãa bhrmcihs#.

Ycmonîa `h pujijs gcdjr dhmonacaih rjcddnhajs químndcs! [jrh dhmh tj `h gj rjsuj`th js `c

mcajrc mãs rãpnic!



































Yjmc ;2! Jqun`nornh químndh

[rjfuatc ;3! _jsuj`tc j` ;7(33(?;3?@c dhastcatj ij jqun`nornh 'l. js 3,2>x3;Q'-4. c ?4;; lj`vna, sj dc`njatc uac mjzd`c ij : f ijantrôfjah y ? f ij hxnfjah ja ua rjdnpnjatj ij 3 @ c ?4;; lj`vna y sj ijec quj c`dcadj j`jqun`nornh! Dc`du`j `c W 'brcddnôa mh`cr. ij AH ja j` jqun`nornh!A? 'f. mcs H? 'f. !!!!!! ?AH'f.Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Rjcmhs! Js sjadn``h! Rcmhs c dhastrunr uac tco`c

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A? !!!!! !!!!!H? -----1 ? AH

mh`js nandnc`js!!!!!!!:(?7!!!!!!!!!!!?(4?!!!!!!!!!!! ---

mh`js rjcddnhaca!!!!!x!!!!!!!!!!!!!!!!x!!!!!!…!!!! ---mh`js bhrmcihs!!!!!!---!!!!!!!!!!!!!!!!---!!!!!!!… ? x

mh`js jqun`nornh !!!:(?7 — x!!!!!?(4? — x!!!!!!? x

\] ja jq!!!!!!!!!!!!':(?7 — x.(R!!!'?(4?-x.(R!!!!!'? x. ( R

dhastcatj ij jqun`nornh

…!!!!!!!!!!!\AH]Q?!!!!!!!!!!!!!!!!!!!!!\ '? x. ( R]Q?

Ld = ----------------- = -----------------------------------

!!!!!!!!!!\A?] ¶ \H?]!!!!!!!!!\':(?7 - x.(R] ¶ \'?(4?-x.(R]

R sj ahs vc

Ld = 3,2>¶3;Q'-4. = '9 xQ?. ( \':(?7 - x. ¶ '?(4?-x.]

rjsuj`vjs `c jducdnôa ij sjfuaih frcih y hotnjajs, sn ah mj gj dh`cih5

x = ;,;;79 mh`jsmh`js ij AH ja jq5 ? x = ;,;;?3 mh`js

mh`js thtc`js ja jq5 :(?7 - x ?(4? - x ? x = ;,?933

ij ihaij `c brcddnôa mh`cr ij Ah js 5 ;,;;?3 ( ;,?933 = ;,;;77

_jpcsc phr sn cdcsh `cs hpjrcdnhajs!



















Yjmc ;6! _jcddnhajs ij trcasbjrjadnc

ij prhthajs [rjfuatc ;3! 33(33(?;3?

¸J` ãdnih cdîtndh js ua ãdnih bujrtj8Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

Ah! Js j` jejmp`h d`ãsndh ij ãdnih iîon`, duyc dhastcatj ij jqun`nornh js Lc = 3,7¶3;Q'-:.

Tj inshdnc dhmh

G Cd 0===1 G Cd-

J` /0===1/ sjóc`c jqun`nornh

[rjfuatc ;?! _jsuj`tc j` ?>(3?(?;3?

Zac sh`udnôa ij ãdnih cdîtndh ;,9 M tnjaj uac dhadjatrcdnôa ij nhajs gnirôfjah nfuc` c4,67x3;Q'-4. mh`js phr `ntrh! Tj ajdjsntc dc`du`cr `c dhadjatrcdnôa ij ãdnih cdîtndh y j` vc`hrij `c dhastcatj ij nhanzcdnôa! Dhadjatrcdnôa ij ãdnih cdîtndh = ;,4>< Lc = 4,6 x 3;Q'-:.Nócln gttp5((www!dcrrcsdc`!ajt92!ajt(bísndcs( bísndcsKycghh!js gttp5((js!sdrnoi!dhm(NóclnDcrrcsdc`

@c rjcddnôa ij jqun`nornh js

Cd G 0==1 Cd- G

Ahtc5 shy ij `c jsduj`c catnfuc y phafh Cd G

Cghrc onja, \G] = d ¶ c`bc4,67¶3;Q'-4. = ;,9 ¶ c`bc

ij ihaij j` dhjbndnjatj ij inshdncdnôa js5 ;,;;>9: = ;,>9: *

@c dhastcatj ij` ãdnih js

Lc = \Cd-] ¶ \G] ( \Cd G] = d ¶ c`bc ¶ d c`bc ( \d '3 - c`bc.] = d ¶ c`bcQ?

ihaij gjmhs gjdgh `c cprhxnmcdnôa ij 3 - c`bc = 3 'rjdujric quj c`bc = ;,;;>9:.

`ujfh Lc = ;,9 ¶ ;,;;>9:Q? = 4,:6¶3;Q'-:.

@c dhadjatrcdnôa ij ãdnih cdîtndh ja jqun`nornh sjrc

\Cd G] = d '3 - c`bc. quj dha `c cprhxnmcdnôa qujic prjdnscmjatj d = ;,9 M

sn ah gcdjmhs `c cprhxnmcdnôa sj hotnjaj

pcrc `c dhastcatj ij jqun`nornh5 4,2¶3;Q'-:.

y pcrc `c dhadjatrcdnôa ij CdG5 ;,9¶'3-;,;;>9:. = ;,4>2



















Química (by Carrascal). Mis respuestas a problemas de Yahoo Respuestas!

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