Fisica I - Manual de Laboratorio

 

 

VKMTFSQMGIG KIAMLKIN @LSEF CIQIGSF ESLOJIKK DIAVNWIG GF AMFKAMIQ GFXISWIJFKWL IAIGÍJMAL GF DÊQMAI

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

MKGMAF

XSÉAWMAI K¸ 890 JFGMAMLKFQ ............................................................................................................................ ............................................................................................................................ 3 XSÉAWMAI K¸ 830 ESÉDMAIQ ............................................................................................................................... ............................................................................................................................... 96 XSÉAWMAI K¸ 810 JLTMJMFKWL GF VK XSL]FAWMN X SL]FAWMN............................................................ ........................................................................................... ............................... 31 XSÉAWMAI K¸ 870 87 0 ALKGMAMLKFQ GF FYVMNMCSML ............................................................................................... ............................................................................................... 3= XSÉAWMAI K¸ 860 FKFSEÊI XLWFKAMIN0 FNÉQWMAI ] ESITMWIWLSMI ................................................................ 16 XSIAWMAI K¸ 840 JLTMJMFKWL SFAWMNMKFL VKMDLSJF ..................................... .....................................¡Frrlr! ¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 85 - FYVMNMCSML GF DVFSPIQ ] JLJFKWLQ ..................................¡Frrlr! ..................................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 8? - JLTMJMFKWL SFAWMNÊKFL VKMDLSJFJFKWF TISMIGL......... TISMIGL.........¡Frrlr! ¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 8= - JLTMJMFKWL FK GLQ GMJFKQMLKFQ ......................................¡Frrlr! ......................................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 98 - QFEVKGI NF] GF KFUWLK ......................................................¡Frrlr! ......................................................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 99 - ALKQFSTIAMLK GFN JLJFKWL NMKFIN.................................¡Frrlr! .................................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 93 - ALKQFSTIAMÑK GF NI FKFSEÊI JFAÉKMAI ............................¡Frrlr! ............................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl.  XSIAWMAI K¸ 91 - JLTMJMFKWL GF WSIQNIAMÑK ] SLWIAMÑK ...........................¡Frrlr! ...........................¡Frrlr! Jiraiglr kl gfdmkmgl.  gfdmkmgl. 

Jikuin gf Niclritlrml

Xéemki 9

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

XSÉAWMAI K¸ 890 JFGMAMLKFQ Einmnfl Einmnfm Kiamñ fk Xmsi fn 96 gf dfcrfrl gf 9647. Istrñkljl y Dêsmal 9647- 9473. „Kl jf smfktl lcnmeigl i arffr quf uk Gmls quf kls oi gltigl gf mktfnmefkami, sfktmgl aljðk, y riamlamkml, tuvmfri aljl lc`ftmvl prmvirkls gf su usl „  

LC@FWMTLQ Dlrtinfafr nis aljpftfkamis y aipiamgigfs gf nls inujkls ukmvfrsmtirmls gf ni VK@CE slcrf fn usl alrrfatl gf jitfrminfs f mkstrujfktls gf jfgmamñk, jfgmiktf ni ipnmaiamñk gf tíakmais quf nfs pfrjmti auiktmdmair fn erigl gf prfamsmñk fk nls gmvfrsls prlafsls gf jfgmamñk.

M.- JIWFSMINFQ JIWFSMINFQ   9 Cinikzi gf trfs cirris 9 Xmf gf rfy (ainmcriglr Tfrkmfr) 9 Xinjfr (l jmarñjftrl) 3 Wfrjñjftrl 9 Sfeni jítrmai 9 Arlkñjftrl 9 tirrl gf irfki 9 visl gf prfampmtigl Fsdfri jfténmai/vmgrml Néjmki gf vmgrml/jftin/jmai Wiruel gf jigfri

M.  M. 

DVKGIJFKWL WFÑSMAL  Jfgmr , fs aljpirir aiktmgigfs dêsmais oljleíkfis gf ni jmsji gmjfksmñk, uki gf fnnis gf vinlr

gfsalklamgi, y ltri auyi ukmgig gf jfgmgi sfi alklamgi (ukmgig pitrñk).

Jikuin gf Niclritlrml

Xéemki 3

   

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Fn rfsuntigl gf uki jfgmamñk, fs uki aiktmgig auyi jiekmtug gmaf auiktl jiylr fs ni aiktmgig gfsalklamgi rfspfatl gf ni ukmgig pitrñk alrrfsplkgmfktf, fs ialjpiùigi gf ni ukmgig rfspfatmvi gigi fk uk smstfji gf ukmgigfs. F`fjpnl F`fjpnl.. Qmstfjis0 AEQ, JBI, mkenís, tíakmal, smstfji mktfrkiamlkin (QM). Fk igfniktf fk fn prfsfktf jikuin usirfjls fn QM gf ukmgigfs gf jfgmgi. F`fjpnl00 j (ukmgigfs gf nlkemtug) F`fjpnl s (ukmgigfs gf tmfjpl) be (ukmgigfs gf jisi) B (ukmgigfs gf tfjpfrituri) Auikgl sf rfinmzi uki jfgmamñk gf ni jiekmtug gf uki aiktmgig dêsmai fs mjplsmcnf quf fn rfsuntigl gf fsti jfgmamñk sfi fxiatl, aljl qumsmírijls. Mkanusmvf nls pitrlkfs mktfrkiamlkinfs gf jfgmgi tmfkfk su prlpml frrlr, fvmgfktfjfktf fstf fsté fxtrfjigijfktf jmkmjmzigl. Fk alksfaufkami, i dmk gf irrmcir i alkanusmlkfs smekmdmaitmvis y alkdmicnfs piri mktfrprftir mktfrprftir y fvinuir rfsuntigls, sf gfcf mkanumr fk fn frrlr fstmjigl alrrfsplkgmfktf. Fn vinlr gf uki jfgmamñk gf uki aiktmgig dêsmai sf fxprfsi gf ni smeumfktf jikfri0 _ ᵣ : xᵣ ¹ Η xᵣ  Glkgf, _ᵣ  0 Tinlr rfin (alksmgfrigl fxiatl) xᵣ 

0 Jfgmgi m-ísmji

Η xᵣ 

0 Frrlr l mkafrtmgujcrf fk ni jfgmgi

F`fjpnl0 Jfgmgi gfn nirel gfn airkí ukmvfrsmtirml sikjirqumkl

?7,8

-8,6+8,6 ?

8

9

3

1

7

6

4

5

?

=

98

Fn nirel gfn airkí ukmvfrsmtirml jmgf N: ?7,8 ¹8,6jj

WMXLQ GF JFGMAMLK Qf alksmgfrik gls tmpls gf jfgmamñk0 gmrfati f mkgmrfati. Jfgmamñk gmrfati0 gmrfati0 Fn vinlr gf ni aiktmgig gfsalklamgi fs lctfkmgl vmsuinjfktf plr aljpiriamñk alk uki ukmgig alklamgi (pitrñk). Jikuin gf Niclritlrml

Xéemki 1

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

Jfgmamñk mkgmrfati0 mkgmrfati0 Fn vinlr gf ni aiktmgig fs fn rfsuntigl rfsuntigl lctfkmgl gf ni ipnmaiamñk gf dñrjunis jitfjétmais quf vmkaunik uki l jés jfgmgis gmrfatis. Nls vinlrfs gf nis jfgmamlkfs rfinmzigis fk nis jmjis alkgmamlkfs gufnfk prfsfktir dnuatuiamlkfs fk uk fktlrkl l mktfrvinl gf vinlrfs. Aljl sicfjls, fstis gmdfrfkamis mkgmaik ni mjplsmcmnmgig gf tfkfr uki jfgmgi fxiati. Nis jfgmamlkfs rfinmzigis sufnfk sfr tritigis fstigêstmaijfktf jfgmiktf ni Wflrêi gf ni Jfgmamñk glkgf sf mkanuyf ni tflrêi gf frrlrfs. Nls frrlrfs pufgfk sfr smstfjétmals y infitlrmls. FSSLSFQ QMQWFJÉWMALQ (F s)  Nls frrlrfs smstfjétmals fsték rfniamlkigls alk ni gfstrfzi gfn lpfriglr, ni tíakmai utmnmzigi, ni lpfritmvmgig gfdfatulsi gf uk mkstrujfktl, nls jítlgls gf aénaunl l rfglkgfl. Fstls pufgfk sfr0 gf pirini`f, ijcmfktinfs y dêsmals, gf igqumsmamñk gf gitls, gf aénaunl, fta. Frrlr gf pirini`f (F pirini`f (Fᵯ). Fs uk frrlr smstfjétmal smstfjétmal islamigl alk fn lpfriglr. Fstf frrlr tmfkf quf vfr alk uki plsturi mkigfauigi quf tlji fn lpfriglr in rfinmzir ni nfaturi nfaturi gf ni jfgmamñk. jfgmamñk. Ni plsturi alrrfati gfn lcsfrviglr gfcf sfr tin quf su nêkfi gf vmsmñk sfi  pfrpfkgmaunir i ni supfrdmamf supfrdmamf glkgf sf fkaufktri fn fn puktl  puktl gf jfgmgi‚  jfgmgi‚  

„    

Frrlrfs ijcmfktinfs y dêsmals (F dêsmals (F ɜ). Fn aijcml fk nis alkgmamlkfs anmjétmais pufgf idfatir ineukis prlpmfgigfs dêsmais gf nls mkstrujfktls (rfsmstmvmgig, alkguatmvmgig, dfkñjfkls gf gmnitiamñk, fta.) Nls F ɜ  sf jmkmjmzik y sf aljpfksik, imsnikgl fn fxpfrmjfktl, alktrlnikgl nis alkgmamlkfs ijcmfktinfs fk fn nueir gf mktfrís, tljikgl uk tmfjpl igfauigl piri ni fxpfrmjfktiamñk. F`fjpnl. Idfatiamñk gfn anmji. Qf oiafk gls jfgmamlkfs gfn ikaol gfn jmsjl afréjmal alk uk F`fjpnl. Idfatiamñk pmf gf rfy, uki fk mkvmfrkl y ltri fk vfrikl y irrl`ik nls smeumfktfs vinlrfs0 9?,7?3 7 aj i 95¸A, 9?,7?3 4 aj i 3=¸A Gf ltrl nigl, ¼Fstis nfaturis slk cufkis< ¼Qlk igfauigis< Sfinjfktf, kl plgfjls gfamr kigi sm kl ofjls ofaol uki fstmjiamñk gf frrlrfs.   Qm fk aigi jfgmamñk fn frrlr dufri gf 8,888 9 aj sf idmrjiré quf ni jfgmgi fs klkksmekmdmaitmvi. smekmdmaitmvi. kk kksmekmdmaitmvi smekmdmaitmvi,,   Qm fk aigi jfgmamñk fn frrlr dufri gf 8,888 89 aj sf idmrjiré quf ni jfgmgi fs kk pufs fn mktfrvinl gf frrlr fk fstf aisl vi in 6tl. gfamjin. Frrlrfs gf aénaunl. Qlk nls mktrlguamgls plr nls lpfriglrfs ]/l jéqumkis2 gf jikfri ikénlei

quf nls frrlrfs fk ni igqumsmamñk iutljétmai gf gitls.

Jikuin gf Niclritlrml

Xéemki 7

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

Ni jiylrêi gf nls frrlrfs smstfjétmals slk alktrlnicnfs y susafptmcnfs gf sfr jmkmjmzigls. Qf alrrmefk l sf tlnfrik. Fk tlgl aisl su jikf`l gfpfkgf gfn alklamjmfktl y oicmnmgig gfn fxpfrmjfktiglr.

Frrlrfs gfn mkstrujfktl gf jfgmamñk Nls frrlrfs rfniamlkigls alk ni ainmgig gf nls mkstrujfktls gf jfgmamñk slk0 frrlr gf nfaturi jêkmji y frrlr gf afrl. Frrlr gf nfaturi jêkmji ( jêkmji  (F NJ NJ)0 Auikgl ni fxprfsmñk kujírmai gf ni jfgmamñk rfsunti fstir fktrf gls jirais jêkmjis gf ni fsaini gf ni nfaturi gfn mkstrujfktl. Ni mkafrtfzi (mkgftfrjmkiamñk) gfn vinlr sf alrrmef tljikgl ni jmtig gf ni nfaturi jêkmji gfn mkstrujfktl. F`fjpnl0 Ni rfeni jmnmjftrigi, gf jigfri gf uk jftrl, tmfkf plr aigi afktêjftrl 98 gmvmsmlkfs, Nufel, 9/98 aj fk ni jêkmji nfaturi. Xlr nl tiktl,

    Fνᴊ: ( )0Fs fn frrlr: 8,prlpmijfktf 86  : 8,6 gfnmkstrujfktl kl ainmcrigl. Frrlr gf afrl ( afrl Fₓ

F`fjpnl. Auikgl F`fjpnl.  Auikgl nis fsainis gf nfaturi jêkmji y prmkampin kl almkamgfk, sf vf quf ni nfaturi sf fkaufktri gfsvmigi oiami uk nigl gfn afrl gf ni fsaini. Qm fsti gfsvmiamñk dufri jfklr l iprlxmjigijfktf meuin in frrlr gf nfaturi jêkmji, fktlkafs fktlkafs Fₓ fs, Fₓ :

FNJ .

ᵾᵾ::  FνFνᴊ +Fₓ

 

Ineukis vfafs sf rfqumfrf gf juaoi prfamsmñk, fktlkafs ukl gfcf fstmjir ni aiktmgig gf tmpls gf frrlrfs i alksmgfrir piri gir uk cufk rfsuntigl.

  +  +  +  +  +  + ⋬

FSSLSFQ INFIWLSMLQ (F i)

Nls frrlrfs infitlrmls slk lrmemkigls césmaijfktf plr ni mktfriaamñk gfn jfgml ijcmfktf alk fn smstfji fk fstugml, ipirfafk iuk auikgl nls frrlrfs smstfjétmals oiyik smgl sudmamfktfjfktf jmkmjmzigls, cinikafigls l alrrfemgls. Qf auiktmdmaik plr jítlgls fstigêstmals. Auikgl sf jmgfk k vfafs uk lc`ftl (f`fjpnl0 fn ikaol gf uk airkí ukmvfrsmtirml) sf lctmfkfk k vinlrfs, sm nis nfaturis slk0 fn vinlr fstmjigl gf ni jiekmtug gf fsti aiktmgig dêsmai _ sf ainauni tljikgl fn prljfgml gf ni smeumfkt smeumfktff jikfri,

 

Jikuin gf Niclritlrml

  :  + … +  : ∙

Xéemki 6

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

 

Ni gmdfrfkami gf aigi jfgmgi rfspftl gf ni jfgmi   sf gfkljmki gfsvmiamñk. Fn erigl gf gmspfrsmñk gf ni jfgmamñk, fstigêstmaijfktf sf gfkljmki gfsvmiamñk fstékgir , sf ainauni jfgmiktf ni dñrjuni.





(̆ ∓  )   3

 Fn frrlr frrlr infitlrml Fι  sf tlji aljl, Fι :

1 ∓ ∐ ∓

:9

 



 

Dmkinjfktf, fk fn tritijmfktl gf nls frrlrfs fxpfrmjfktinfs sf alksmgfrik gls tmpls gf frrlrfs0 frrl rfs0 Icslnutl, rfnitmvl quf jés alkvmfkfs fxprfsirnl aljl uk frrlr plrafktuin. Frrlr icslnutl. icslnutl. Fs fn rfsuntigl gf ni suji gf nls frrlrfs smstfjétmals y infitlrmls,

∄:   + 

 

Fn vinlr gf ni jfgmamñk sf fxprfsi aljl,

 

  : ̆ ¹ ∄∄:: ̆ ¹  3 + 3

Frrlr rfnitmvl. rfnitmvl. Qf lctmfkf gf fdfatuir ni rizñk gfn frrlr icslnutl fktrf fn vinlr prljfgml gf ni jfgmgi, 

 : ∄̆ % : 988   

Frrlr plrafktuin. plrafktuin. Qf lctmfkf juntmpnmaikgl fn frrlr rfnitmvl plr 988,   Fn vinlr gf uki jfgmgi jfgmgi sf  sf fxprfsi aljl,   Fk dukamñk gfn frrlr rfnitmvl   Fk dukamñk gfn frrlr plrafktuin

  :: ̆ ̆ ¹¹ %

   

In vinlr alksmekigl fk nis ticnis mktfrkiamlkinfs (oikgcllb) sf nf sufnf gfkljmkir vinlr tfñrmal. I pirtmr gfn vinlr fxpfrmjfktin sf lctmfkf ltri dlrji gf fxprfsmñk gfn frrlr gf ni jfgmamñk alklamgl aljl frrlr fxpfrmjfktin rfnitmvl, rfnitmvl, fn frrlr fxpfrmjfktin plrafktuin, plrafktuin,

     ∓ :              % : |  |  989888 

 

Sfaufrgf Qmfjprf Ni jfgmgi gf uki aiktmgig dêsmai alk uk frrlr jin fstmjigl nl nnfviré mkgfdfatmcnfjfktf i alkanusmlkfs kl-smekmdmaitmvis gf kl-smekmdmaitmvis gf nls rfsuntigls fxpfrmjfktinfs.

Jikuin gf Niclritlrml

Xéemki 4

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

XSLXIEIAMÑK GF FSSLSFQ Ni jiylrêi gf nls fxpfrmjfktls mkvlnuarik jfgmamlkfs gf virmis aiktmgig fs dêsmais, aljl ni jisi, nlkemtug, tmfjpl, tfjpfrituri, fta. Fn rfsuntigl dmkin gf uk fxpfrmjfktl klrjinjfktf sf fxprfsi fk fauiamlkfs quf airiatfrmzik y prfgmafk fn aljplrtijmfktl gfn smstfji l fn dfkñjfkl fstugmigl. Gmaols rfsuntigls vik ialjpiùigls gf vinlrfs quf gik su alkdmicmnmgig, in auin nnijijls frrlrfs. ¼Añjl sf ainauni fn frrlr frrlr i pirtmr gf nls frrlrfs gf nis aiktmgigfs aiktmgigfs dêsmais jfgmgis<

  ¹ ∄ ,  ¹ ∄ .

Fk prmjfr nueir fstugmfjls fn aisl gf ni jfgmgi gf gls aiktmgigfs dêsmais I y C alksmgfrikgl sus

 

frrlrfs alrrfsplkgmfktfs0

¼Añjl sfré fn frrlr fk ni suji, rfsti, juntmpnmaiamñk, gmvmsmñk y pltfkamiamñk gf fstis aiktmgigfs< Xufs, auikgl sf jmgf ni aiktmgig a iktmgig dêsmai gf gls lc`ftls, nis nfaturis vmfkfk gigis plr nls vinlrfs, ,  

  :   ¹∄

 :  ¹ ∄ .

Xrlpieiamñk gf frrlrfs fk ni suji y ni rfsti. Ni rfspufsti i nis lpfriamlkfs gf suji y rfsti gf nis aiktmgigfs dêsmais  I  y C  sf gi plr uki fxprfsmñk gf ni dlrji,

Glkgf,

∄

 :   ̆  ¹   ¹ ∄

 

 sf ainauni plr suji gf auigrituris alk ni smeumfktf fxprfsmñk,

∄:  ∄ ∄ + ∄ 

Xrlpieiamñk gf frrlrfs fk ni juntmpnmaiamñk/gmvmsmñk. Ni rfspufsti i nis lpfriamlkfs gf juntmpnmaiamñk y gmvmsmñk gf nis aiktmgigfs dêsmais I y C sf gik jfgmiktf fxprfsmlkfs gf ni dlrji,

Glkgf,

 :     ̆ .   ¹ ∄

 

 :    ̆ ¹ ∄   ∄ ∄ ∄ :    ̆ (     ̆ ) + (  )  

Xrlpieiamñk gf frrlrfs fk pltfkamiamñk. Fn rfsuntigl gf ni lpfriamñk gf pltfkamiamñk gf uki aiktmgig dêsmai fxpfrmjfktin, aljl gi jfgmiktf uki fxprfsmñk gf ni dlrji,

Glkgf,

Jikuin gf Niclritlrml

 :  ¹ ∄ ∄ :  ∄  ̆    ̆

 

 , sf

 

 

Xéemki 5

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

SFALJFKGIAMLKFQ  

Qm in jfgmr nls prmjfrls vinlrfs (inrfgfglr gf plr f`fjpnl 6 jfgmamlkfs) gf uki aiktmgig dêsmai sf lcsfrvi quf ni gfsvmiamñk fstékgir fs pfqufùi

aljpirigi alk fn frrlr gfn mkstrujfktl, kl oicré kfafsmgig gf tljir uki erik aiktmgig gf gitls piri fkalktrir fn vinlr prljfgml.   Nis jfgmgis quf tfkeik uki gfsvmiamñk jiylr quf trfs vfafs ni gfsvmiamñk fstékgir, sf rfaljmfkgi gfsairtirnis.

LCQFSTIAMÓK Gfcf gfsirrlnnir ni prfsfktf préatmai gf niclritlrml fk slnl 988 jmkutls. Alktrlnf su tmfjpl y kl nl gfspfrgmamf.

MM. 

XSLAFGMJMFKWL 9.  9.  Lcsfrvf y fstugmf gftfkmgijfktf aigi mkstrujfktl gigl. Gftfrjmkf ni nfaturi gf ni fsaini gf aigi ukl gf fnnls. Tfrmdmquf sm nls mkgmaiglrfs fsték gfsvmigls gfn afrl.

jêkmji

KLWI 90 Wlgls nls jmfjcrls gfn erupl gfcfk rfinmzir nis jfgmamlkfs piri aigi jitfrmin. KLWI 30 Kl lnvmgf gf ainmcrir  ni  ni cinikzi iktfs gf aigi jfgmamñk, l vlnvfr i afrl. KLWI 10 Writf nls mkstrujfktls alk sujl aumgigl. Qm plr kfenmefkami l gfsaumgl rfsuntiri giùigl ineðk mkstrujfk mkstrujfktl, tl, fn erupl mkdlrjiré mkjfgmitijfktf in Xrldfslr Mkstruatlr. Fn Sfenijfktl gfn Niclritlrml sfùin0 „Wlgl fn erupl fs rfsplksicnf slnmgirml y sucsikiré fn giùl‚  Fsti klrji rmef piri tlgis nis fxpfrmfkamis gf niclritlrml.

3.  3.  Wljf jfgmgis gf nis gmjfksmlkfs gmjfksmlkfs y jisis gf nls lc`ftls quf sf nf fktrfeiré fktrfeiré fk anisf. Wljf ni néjmki gf vmgrml. Jmgi sus gmjfksmlkfs. Sfinmaf amkal jfgmamlkfs gf gf aigi ukl. ¼Añjl slk nis jfgmgis fktrf sê< ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………  ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………  ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………  ¼Qfré kfafsirml gf uki slni jfgmgi< ¼Fk quí aisls< ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………  ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………  ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………… …………………………

1.  1.  Ainaunf nls frrlrfs icslnutl, infitlrml y plrafktuin fk aigi aisl0         %  : \\\\\\\\\\\\  : \\\\\\\\\\\\  : \\\\\\\\\\\\ Jikuin gf Niclritlrml

Xéemki ?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

I. WISVEL, FQDFSI ] XNIAI 9. Jmgi nis jisis y nis gmjfksmlkfs gfn tiruel, gf ni fsdfri y gf ni pniai, tljir fk aufkti nls smeumfktfs mkstrujfktls gf iaufrgl in lc`ftl0 Wiruel0 ainmcriglr pmf gf rfy Fsdfri0 Jmarñjftrl Xniai0 Ainmcriglr pmf gf rfy y jmarñjftrl Sfinmaf amkal jfgmamlkfs gf aigi aisl0 Oinnf nls frrlrfs icslnutl, infitlrml y plrafktuin fk aigi aisl0 Wiruel0 Fsdfri0 Xniai0

 : \\\\\\\\\\\\  : \\\\\\\\\\\\ % : \\\\\\\\\\\\  :: \\\\\\\\\\\\ \\\\\\\\\\\\  :: \\\\\\\\\\\\ \\\\\\\\\\\\ %% :: \\\\\\\\\\\\ \\\\\\\\\\\\  

 

 

   

   

   

WISVEL

Jfgmgi

 

(jj)



89 83

  (jj)



FQDFSI

 

 

 

(e)



(jj)





Jisi jn (e) (e)  

Tlnujfk (aj1) 

Jisi

(e)

XNIAI

n

i

(jj)   (jj)

(jj)   (jj)

 

(jj)   (jj)

ℋ

 

(e) (e)  



81 87 86 Xrljfgml

 : / 3 ∄:   +   ̆ ¹ ∄   

 

Jfgmgi

 

(jj)   (jj)

Tlnujfk Tt (aj1)

̆ ¹ ∄  ̆ ¹ ∄ 

jf

(e) (e)  

Tlnujfk Tp (aj1) 

Jisi j p

Jfgmgi

 

Jfgmgi

 

1

(e/aj )

WICNI K°90 WISVEL ‑ FQDFSI - XNIAI Jikuin gf Niclritlrml

Xéemki =

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

C.AVAOISI GF ISFKI 9. Jmgi ni jisi gf uki auaoirigi gf irfki. Sfpmti ni jfgmamñk 6 vfafs. 3. Oinnf nls frrlrfs icslnutl, infitlrml y plrafktuin gf nis jfgmgis rfspfatmvis.         %  : \\\\\\\\\  : \\\\\\\\\\\  : \\\\\\\\\\\ MJXLSWIKWF

Kl gfrrijf irfki fk ni jfsi y jfkls fk ni cinikzi pufs giùirêi sus i`ustfs y fn ipiritl

WICNI K¸ 30 JIQI GF VKI AVAOISIGI GF ISFKI K° Jfgmgi

Cinikzi gf trfs cirris (e)

9 3 1 7 6



 

Frrlr Wltin



 



 

∄:   +  

A. WFJXFSIWVSI GFN IEVI 9. Jmgi ni tfjpfrituri gfn ieui alktfkmgi fk uk visl gf prfampmtigls utmnmzikgl fn tfrjñjftrl.

WICNI K¸ 10 WFJXFSIWVSI GFN IEVI K° Jfgmgi

Wfrjñjftrl (°A)

  

9 3 1 7 6



Frrlr Wltin

 

F_XFSMJFKWL K° 9 JFGMAMLKFQ 

INVJKL0 JIWSMAVNI0 T.

   ∄:   +  

DFAOI0

T° C° gfn Xrldfslr

FTINVIAMÑK  (Gf sfr kfafsirml igmamlkf ol`is piri aljpnftir sus rfspufstis)

Jikuin gf Niclritlrml

Xéemki 98

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

9. Alk iyugi gf Wicnis (Oikgcllbs y fk tfxtls gf Dêsmai), mgfktmdmquf gf quf jitfrminfs slk nls lc`ftls usigls fk fn fxpfrmjfktl. Lc`ftl Xniai gf vmgrml



 (e/aj1)

ó

 (e/aj1) 

Qustikami mgfktmdmaigi

Wiruel Fsdfri jfténmai

3. Ainaunf nls frrlrfs fxpfrmjfktinfs fxpfrmjfktinfs plrafktuinfs gf nis jfgmgis jfgmgis.. (Alksmgfrf nls vinlrfs gf nis ticnis aljl vinlrfs tfñrmals) Xniai

Wiruel

Fsdfri

Frrlr Fxpfrmjfktin plrafktuin   plrafktuin

1.  1.  I su alksmgfriamñk ¼Auénfs slk nls frrlrfs smstfjétmals aljftmgls fk fsti fxpfrmfkami y i quf nl itrmcuyf<

…………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… ……

……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………..…….. ………………………..…….. 

7.  7.  I su alksmgfriamñk, ¼quí aumgigls sf gfcf tfkfr fk aufkti piri lctfkfr rfsuntigls jés alkdmicnfs< …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… ……………………………………………..………………………….. …………..………………………….. 

¼Yuí fs uki virmicnf mkgfpfkgmfktf y quí uki gfpfkgmfktf< ¼Fk quí sf gmdfrfkamik< Gf trfs f`fjpnls.

…………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………….…………………………….. ….…………………………….. 

6.  6.  Nnfkir ni smeumfktf ticni utmnmzikgl prlpieiamñk gf frrlrfs auikgl sfi kfafsirml, sm nis jfgmgis gfn amnmkgrl dufrlk tljigis alk uk pmf gf rfy auyi nfaturi jêkmji fs 8.86jj y ni jisi gfn amnmkgrl duf tljigi plr uki cinikzi jfaékmai gf 1 crizls auyi nfaturi jêkmji fs  aljl F smstfjétmal tltin. gf 8.9 erijl. Vsf fn frrlr gf ni nfaturi jêkmji

F

Jikuin gf Niclritlrml

Xéemki 99

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

AMNMKGSLM AMNMKGSLM

Wicni0 JFGMGIQ XISI FN AMNMKGSL (Ainmcriglr pmf gf rfy) Amnmkgrl Aljpnftl

Lrmdmaml Amnêkgrmal

G (jj)

O (jj)



  (jj)

ℋ

  (jj)

n

i

(jj)

(jj)   (jj)

89 83 81

69.96 69.86 69.96

19.98 19.98 19.86

98.96 98.38 98.38

93.68 93.76 93.68

3?.68 3?.76 3?.78

1.76 1.76 1.68

87 86

69.86 69.98

19.86 19.96

98.86 98.98

93.78 93.76

3?.76 3?.76

1.76 1.78

Tlnujfk (aj1)

(Ta)

Tlnujfk (aj1)

(Tl)

  7=1.?

  7=7.9

  7=1.=

  =7=.8

Jfgmgi

∄:   +  

Sikuri pirinfnfpêpfgl

ℋ∕

  (jj)

Jfgmgi

̆ ¹ ∄ 

  Tlnujfk (aj1)

(Tp)

Jfgmgi  

̆ ¹ ∄  ¹∄

Jisi (e)  

Tlnujfk Sfin Amnmkgrl





1



Gfksmgig fxpfrmj. amnmkgrl

  7=7.8



 

 ∄

 

(*) Ni jfgmgi „oϚ‚ fsté rfdfrmgi i ni n i inturi gfn pirinfnfpêpfgl quf i su vfz fs ni inturi gfn amnmkgrl, plr nl quf sf alksmgfrirék nls gitls gf ni alnujki „O‚ 

Jikuin gf Niclritlrml

Xéemki 93

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

4.  4.  Vstfg, iolri cufk fxpfrmjfktiglr, oiei nis nfaturis gf nls ainmcriglrfs Tfrkmfr y jmarñjftrl mkgmaigls fk nis dmeuris.

5.  5.  Jfgmgi gfn gméjftrl gf uki fsdfri alk uk jmarñjftrl. Vk jmarñjftrl fsté tltinjfktf afrrigl y smk fjcirel sf nff 8,8?5. In alnlair uki fsdfri sf nff uk gméjftrl gf 36,716 jj. Alk fstls vinlrfs ainaunf fn vlnujfk gf ni fsdfri y su mkgftfrjmkiamñk. …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..…….. ……………………………..…….. 

?.  ?.  Ni prfsmñk gf uk eis sf gftfrjmki jfgmiktf ni dufrzi quf f`fraf slcrf uki supfrdmamf gigi. Qm ni jiekmtug gf ni dufrzi fs 38,8 8,6K y fn fn érfi fs rfatikeunir gf nigls 6,8 8,3jj y 98,8 8,6 jj. Ainaunf0   Fn frrlr icslnutl0   Fn frrlr rfnitmvl0    Fn frrlr plrafktuin0

………………………………….…  …………………………………….  ……………………………………. 

=.  =.  ¼Xlr quí sf gfcfk rfinmzir virmis jfgmamlkfs fk uk fxpfrmjfktl< ¼Yuí alkgmamlkfs sf gfcfk tfkfr fk aufkti piri gir fn vinlr gf uki rfspufsti gftfrjmkigi< @ustmdmquf su rfspufsti. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..…….. ……………………………..…….. 

98.   Gfdmki nls tírjmkls „prfamsmñk‚ y „fxiatmtug‚. Anismdêqufnls sfeðk fn tmpl gf mkgftfrjmkiamñk y 98. sfùinf sus gmdfrfkamis. Gf amkal f`fjpnls. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………………… ……………………………………… Jikuin gf Niclritlrml

Xéemki 91

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

…………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..…….. ……………………………..…….. 

99.   Ci`l alkgmamlkfs mgíktmais, sf rfinmzik virmis jfgmgis gf uk piréjftrl dêsmal gigl. Qf 99. lctmfkfk nufel uki gmstrmcuamñk gf drfaufkamis y sf eridmai lctfkmíkglsf uki aurvi gf Eiuss. ¼Yuí rfprfsfkti ni aijpiki< ¼Qfré mjplrtiktf alklafr fn ikaol gf ni aurvi< ¼Xlr quí< Gf gls f`fjpnls. …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..…….. ……………………………..…….. 

93.   ¼Yuí jfgmgi sfré jf`lr, ni gf uk tfkgfrl quf gftfrjmki 9 be gf izðair alk uki prfamsmñk gf 93. uk erijl l ni gf uk dêsmal quf jmgf 98 ae gf uki sustikami fk plnvl fk uki cinikzi alk uki prfamsmñk fk jmnmerijls< Xiri dukgijfktir jf`lr su rfspufsti, prmjfrl alktfstf sm fs jés smekmdmaitmvl rfaurrmr in frrlr icslnutl l in frrlr rfnitmvl. …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..…….. ……………………………..…….. 

TM.

ALKANVQMLKFQ …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……..… ……………………………..……..… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ……………………………………………………………..…….. …………………………..…….. 

TMM.

LCQFSTIAMLKFQ ] SFALJFKGIAMLKFQ  …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……..… ……………………………..……..… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ……………………………………………………………..…….. …………………………..…….. 

Jikuin gf Niclritlrml

Xéemki 97

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

F_XFSMFKAMI K¸ 830 ESÉDMAIQ Sfkí Gfsairtfs „Alksmgfrirêi „Alksmgfrir êi quf kl sí kigi gf Dêsmai sm tik sñnl dufsf aipiz gf fxprfsir

añjl sfr nis .alsis, pfrl dufsf mkaipiznlerigl gf gfjlstrir quf pufgfk  sfr gf gfcfk ltri jikfri jikfri. Kl lcstiktf lcstiktf, , oicmfkgl rfguamr ni kl Dêsmai i nis  Jitfjétmais,  Jitfjé tmais, ni gfjlstriamñk gfjlstriamñk fs fktlkafs plsmcnf, y pmfksl quf pufgl  rfinmzirni alk fn rfguamgl inaikaf gf jm jm alklamjmfktl alklamjmfktl‚.

LC@FWMTLQ 9.  9.  Wrici`ir alk gitls fxpfrmjfktinfs lreikmzigls fk ticnis. 3.  3.  Eridmair y lctfkfr fauiamlkfs i pirtmr gf gitls fxpfrmjfktirnfs y prfgfamr fn aljplrtijmfktl gf nls dfkñjfkls fstugmigls. 1.  1.  Mktfrprftir dêsmaijfktf nls erédmals rfinmzigls

M. 

JIWFSMINFQ

  Ol`is gf pipfn jmnmjftrigis (87)

  Ol`is gf pipfn nleirêtjmais (83)



  Ol`i gf pipfn sfjmnleirêtjmai (89)   Ainauniglri

Klti00 Nls inujkls trifrék i anisf alk fstls jitfrminfs  Klti

MM. 

DVKGIJFKWL WFÑSMAL Nls gitls quf sf lctmfkfk fk uk prlafsl gf jfgmamñk sf lreikmzik drfaufktfjfktf fk ticnis. Nls gitls lrgfkigls fk fstis ticnis, prlplramlkik vinmlsi mkdlrjiamñk iafrai gf nis rfniamlkfs fktf nis aiktmgigfs dêsmais lcsfrvicnfs. Vki intfrkitmvi piri fsticnfafr fstis rfniamlkfs fs alkstrumr rfprfsfktiamlkfs erédmais rfdfrmgis i uk smstfji allrgfkigl gigl. Xiri fstl, klrjinjfktf, sf usik allrgfkigis airtfsmikis y pipfnfs alk gmvmsmlkfs jmnmjftrigis, nleirêtjmais l sfjm-nleirêtjmais. Nis erédmais lctfkmgis sf sufnfk nmkfinmzir (iprlxmjir i uki rfati), diamnmtikgl ni alkstruaamñk gf dñrjunis fxpfrmjfktinfs quf alrrfsplkgfk i nis nfyfs quf elcmfrkik in dfkñjfkl fstugmigl. Aljðkjfktf, sf ialstujcri prlafgfr gf ni smeumfktf dlrji0 i)  i)  Qf eridmaik nls gitls ticunigls fk uk pipfn igfauigl0 jmnmjftrigl, nleirêtjmal, sfjmnleirêtjmal, plnir, fktrf ltrls. c)  c)  Qfeumgijfktf, sf mgfktmdmai fn tmpl gf erédmai lctfkmgi aljpirékglni alk aurvis alklamgis. Wlgi ni fauiamñk tmfkf uki rfprfsfktiamñk rfprfsfktiamñk erédmai y vmafvfrsi. I alktmkuiamñk

Jikuin gf Niclritlrml

Xéemki 96

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

a)  a)  sf jufstrik nis rfprfsfktiamlkfs eridmais gf aurvis, y sus fauiamlkfs quf ipirfafk alk jiylr drfaufkami.

Jikuin gf Niclritlrml

Xéemki 94

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Mgfktmdmaigi ni dlrji gf ni gmstrmcuamñk gf puktls, fk uki smeumfktf ftipi sf prlafgf i rfinmzir fn i`ustf gf aurvi2 usuinjfktf sf usi ni tíakmai gf jêkmjls auigrigls. Fn jlgfnl gf i`ustfs fs klrjinjfktf nmkfin (rfati). Fstl smekmdmai quf ni fauiamñk quf sf cusai tmfkf ni dlrji, y : jx+c 

(9)

Glkgf j fs ni pfkgmfktf y c fs fn mktfrafptl (alkstiktfs ( alkstiktfs i gftfrjmkir). Fk ni iatuinmgig sf aufkti alk prlerijis gf añjputl quf diamnmtik fklrjfjfktf fstf trici`l. Qm in eridmair nls gitls i uk pipfn jmnmjftrigl sf lcsfrvi quf ni gmstrmcuamñk gf puktls kl prfsfkti uki tfkgfkami nmkfin, alkvfkgré usir pipfn nleirêtjmal l sfjmnleirêtjmal sfeðk quf ni erédmai jufstrf uki tfkgfkami nmkfin. Vki fauiamñk pltfkamin y : bx ᶬ  , alk k‡9, eridmaigi fk pipfn nleirêtjmal gi uki rfati alk pfkgmfktf j : k  y lrgfkigi fk fn lrmefk c : b . fk fstf aisl a isl sf rfaljmfkgi prfdfrfktfjfktf, usir pipfn nleirêtjmal 1 x 1. Glkgf aigi amanl fsté islamigl i uki pltfkami gf cisf 98. Fn lrmefk gf uk f`f allrgfkigl nleirêtjmal pufgf ircmtrirmijfktf fjpfzir alk0 …, 98-9, 98¸, 989, 983  , 981, … 

Xiri rfniamlkfs fxplkfkaminfs sf rfaljmfkgi utmnmzir pipfn sfjmnleirêtjmal. Xiri fauiamlkfs gf aurvis, fs plsmcnf alkstrumr erédmais nmkfinfs fk pipfn jmnmjftrigl, gfpfkgmfkgl gf ni dukamñk y nls vinlrfs ismekigls i nls f`fs allrgfkigls

y: 9,6 x 3

F`fjpnl0

 Icsamsi Lrgfkigi y0

x0

8 8

9 9,6

3 4,8

1 91,6

Erédmai0 Xiréclni

7

 Icsamsi

37,8

Lrgfkigi y0

x 30

8

9

8

9,6 4,8

7

=

94

91,6

37

Erédmai0 Sfati

Gf ni gmstrmcuamñk nmkfin gf puktls lctfkmgi fk fn pipfn jmnmjftrigl, nleirêtjmal l sfjmnleirêtjmal sf ainauni ni pfkgmfktf j y ni lrgfkigi fk fn lrmefk c ( mktfrsfaamñk gf ni rfati alk fn f`f gf ni lrgfkigi, gfkljmkigi lrgfkigi fk fn lrmefk).

 fs fkalktrir ni aurvi gf jf`lr i`ustf (rfati). (r fati). Nl jés igfauigl fs ipnmair fn jítlgl gf Nmkfinmzir  fs jêkmjls auigrigls.

Jikuin gf Niclritlrml

Xéemki 95

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

JÍWLGL GF JÊKMJLQ AVIGSIGLQ Alk nls gitls xm , ym  alkstruyf ni smeumfktf Wicni0

    

    

      

     

  

  

    

  

. . .

. . .

 

. . .

 

 

. . .

 

 

 

 

 

Nufel, sf ainauni ni pfkgmfktf „j‚ y fn mktfrafptl „c‚ fk fn lrmefk, gf ni jikfri smeumfktf0

 ∙   ∓ ∙   ∙   ∓  ∙    ∙  :

 ,

Glkgf p fs fn kðjfrl gf jfgmgis.

∙   ∙ 3∙  ∙      :  ∙   ∙ 3

(3) 

Ni dñrjuni fxpfrmjfktin fs ni fauiamñk gf ni rfati, y : jx + c 

Vki vfz i`ustigi ni gmstrmcuamñk nmkfin, sf prlafgf i oiafr nls aénaunls piri fkalktrir ni dñrjuni fxpfrmjfktin cusaigi y eridmair prmjfrl fk pipfn jmnmjftrigl. Xiri lctfkfr nis gmstrmcuamlkfs nmkfinfs gf nis dñrjunis fxpfrmjfktinfs smeumfktfs, alkvmfkf eridmair fk0

: ……………………………

Xipfn nleirêtjmal

…….



,11   Alksmgfrikgl quf, 98 : ,11 .  :  98  , :  ………….

Xipfn sfjmnleirêtjmal

Gigl quf fn i`ustf nmkfin sf rfinmzi alk fn jítlgl gf nls jêkmjls auigrigls, ni ticni sf alkvmfrtf fk nleirêtjmai y sfjmnleirêtjmai. Aumgf alnlair nls vinlrfs alk rfglkgfl i jêkmjl auitrl gfamjinfs fk aigi alnujki. Lcsfrvf quf nis fauiamlkfs gf ni rfati fk fsis fsainis slk0

nlee:: nle+n e +nle ,  nle: e :  +nle

 

Nufel fn vinlr gf „c‚ lctfkmgl plr ni dñrjuni sfré c·quf alrrfsplkgf i nle c plr nl auin c fs ainaunigi aljl iktmnleirmtjl gf c”. Isê,   

 :   ″ Jikuin gf Niclritlrml

Xéemki 9?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Fk aisl gf kl sfr kfafsirml oiafr fn i`ustf, j sf ainauniré alk ni pfkgmfktf gf ni gmstrmcuamñk nmkfin y fn vinlr c sfré fn alrrfsplkgmfktf in puktl gf alrtf in prlnlkeir ni rfati oisti alrtir fn f`f gf ni lrgfkigi.

MMM. 

XSLAFGMJMFKWL Qf ikinmzirék nls gitls lctfkmgls l ctfkmgls gf nls smeumfktfs fxpfrmjfktls0   Ainfktijmfktl gfn ieui.   Fviauiamñk gf ieui gf uk gfpñsmtl.   Iatmvmgig rigmiatmvi gfn rigñk.

∄

9.  9.  Fk ni ticni 9, sf tmfkfk nis jfgmgis gfn mkarfjfktl gf tfjpfrituri (gmdfrfkami gf tfjpfrituri alk nis tfjpfrituris mkmaminfs) piri gls vlnðjfkfs gf ieui y fn tmfjpl gf ainfktijmfktl. Sfqufrmjmfktl00 Vki ol`i gf pipfn jmnmjftrigl. Sfqufrmjmfktl Wicni 9 Tieui (jn)

988

W(jmk) 9 3 1 7

4,6 91,8 9=,6 35,8

968  

 

∄ ° ∄ ° 7,6 =,8 97,8 9?,8

3.  3.  Ni Wicni 3, jufstri jufstri gitls gf jfgmgis gfn tmfjpl tmfjpl t gf fviauiamñk fviauiamñk gf ieui gf uk gfpñsmtl i trivís gf uki nnivf gf amfrtl gméjftrl G gf sinmgi, tljigis piri auitrl nnivfs gf gmdfrfktfs gméjftrls y tlgis jfgmgis i meuin inturi o gf ieui gfn jmsjl gfpñsmtl. Sfqufrmjmfktl00 3 ol`is gf pipfn Sfqufrmjmfktl pipfn jmnmjftrigl y 3 ol`is ol`is gf pipfn nleirêtjmals. nleirêtjmals. Wicni 3 o (aj) G (aj) 9,6 3,8 1,8 6,8

18 7 t (s)9 Wmfjpl 98 gf viamigl 51,8 71,8 34,5 91,6 79,3 31,5 96,8 5,3 9?,7 98,6 4,? 1,5 4,? 1,= 3,3 9,6

Oiei uki erédmai gf t vfrsus G y t vfrsus o. Vsf pipfn jmnmjftrigl. Mktfrprftf (Xfeuf ni erédmai iquê) 1.  1.  Ni Wicni 1, jufstri nls plrafkti`fs gf nis jfgmgis gf ni iatmvmgig rigmiatmvi gfn rigñk. Fn gêi afrl sf gftfatñ uki gfsmktferiamñk gf 7,1 x 98 9? kðanfls. Sfqufrmjmfktl00 Vki ol`i jmnmjftrigi y 3 uki ol`i sfjmnleirêtjmai. Sfqufrmjmfktl

Jikuin gf Niclritlrml

Xéemki 9=

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

t  (gêis)

I (%)

8 988

Dêsmai Efkfrin M

Wicni 1 9 3 1 7 6 4 5 ? = 98 ?7 58 6= 7= 79 17 35 37 38 95

Oiei uki erédmai gf I vfrsus t. Vsf pipfn jmnmjftrigl. Mktfrprftf F_XFSMJFKWL k° 83 ESÉDMAIQ INVJKL0

DFAOI T° C° gfn Xrldfslr 

JIWSMAVNI0

MT. 

FTINVIAMÑK 9.  9.  Ig`uktir ni erédmai gf ni ticni 9 y oinnir ni fauiamñk fxpfrmjfktin plr fn jítlgl gf jêkmjls auigrigls. Mktfrprftir dêsmaijfktf nls rfsuntigls ainaunigls 3.  3.  Qm ni dufktf gf ainlr fs alkstiktf y ni tfjpfrituri mkmamin gfn ieui duf gf 38¸a. ¼Auén fs fn tmfjpl quf triksaurrmré piri quf fn vlnujfk gf ieui gf 988 jn inaikaf ni tfjpfrituri gf fcunnmamñk< …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

1.  1.  Ikinmaf, gmsauti ni erédmai lctfkmgi gf ni Wicni 9. ¼Auén fs fn smekmdmaigl dêsmal gf ni pfkgmfktf y fn mktfrafptl< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

7.  7.  Alksmgfrikgl nis gmstrmcuamlkfs kl nmkfinfs alrrfsplkgmfktfs eridmquf0 i)  i)  t : t (o) fk pipfn nleirêtjmal. c)  c)  I : I (t) fk pipfn sfjmnleirmtjmal. a)  a)  t : t (G) fk pipfn nleirêtjmal. g)  g)  Xrmjfrl ainaunf z:9/g3 y nufel eridmquf t : t (z) fk pipfn jmnmjftrigl. (Xfeuf nis erédmais iquê) 6.  6.  Oinnf fn tmfjpl fk quf nls kðanfls gf rigñk sudrfk uki gfsmktferiamñk gfn 68%. …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… …………………………………

Jikuin gf Niclritlrml

Xéemki 38

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..………  …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………….. ……………….. 

4.  4.  Fkaufktrf nls kufvls vinlrfs fxpfrmjfktinfs gf sinmgi

  lctfkmgls usikgl usikgl ni dñrjuni fxpfrmjfktin fxpfrmjfktin alk nls vinlrfs

in aisl t: t (G).    ipnmaigl  

…………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

5.  5.  Oinnf nls tmfjpls gf viamigl gfn ieui sm0 AIQLQ

?.  ?.  Ainaunf

GMIJFWSL G (aj) G (aj)

89 83

38 78

7,8 9,8

81 87

36 7=

1,6 9,8

 : ∐  W (s) w

INWVSI o (aj)

WMFJXL t (s) t (s)

  piri nis inturis y gméjftrls alrrfsplkgmfktfs i0 51,8

71,8

34,5

96,8

98,6

1,=

9,6

=.  =.  Eridmquf t : t   (w) fk pipfn jmnmjftrigl. Qmn ni gmstrmcuamñk fs nmkfin gftfrjmkf fn i`ustf rfspfatmvl. Nufel fkaufktrf ni fauiamñk fxpfrmjfktin alrrfsplkgmfktf , t: t (o, g ) (Xfeuf ni erédmai iquê)



  lctfkmgls usikgl ni dñrjuni fxpfrmjfktin fxpfrmjfktin alk nls vinlrfs gf sinmgi sinmgi 98. Aljpirf nls vinlrfs 98.    fxpfrmjfktinfs ipnmaigl in aisl t: t (o)



……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

Gmcu`f slcrf pipfn jmnmjftrigl uki fsaini nleirêtjmai olrmzlktin gf 3 amanls (gíaigis), aigi amanl am anl tfkgré uki nlkemtug gf 98 aj, y uki fsaini vfrtmain gf 7 amanls2 aigi amanl gf nlkemtug gf 6 aj. Eridmquf nls puktls I (4,8, 86), C (38,6), A (78,18). (Xfeuf ni erédmai iquê)

Jikuin gf Niclritlrml

Xéemki 39

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

93. Ni erédmai jufstri fn aljplrtijmfktl gf nis virmicnfs X y S fk pipfn nleirêtjmal piri ineukls vinlrfs dm`ls gf ni virmicnf Y. Qfeðk fstl fkaufktrf0   Fn vinlr gf X piri S : 4,6 y Y : 76 Iprlxmjigijfktf.   Ni fauiamñk quf rfniamlki X y Y alksmgfrikgl S : =   Ni fauiamñk quf rfniamlki Nis trfs virmicnfs. (Xfeuf iquê nl pfgmgl)

T. 

ALKANVQMLKFQ …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..………… … …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ……………………………………………………………..……… …………………………..……… 

TM. 

LCQFSTIAMLKFQ ] SFALJFKGIAMLKFQ ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..………… … …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… …………………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ……………………………………………………………..……… …………………………..……… 

Jikuin gf Niclritlrml

Xéemki 33

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

XSÉAWMAI K¸ 810 JLTMJMFKWL GF VK XSL]FAWMN Einmnfl Einmnfm kiamñk fk Xmsi fn 96 gf dfcrfrl gf 9647. Alksmeumñ aljpnftir ni ðntmji y jés mjplrtiktf gf sus lcris0 nls Gmsalrsm f gmjlstrizmlkm jitfjitmaof mktlrkl i guf kufvf samfkzf, pucnmaigl fk Nfmgfk plr Nums Fnsfvmr fk 941?. Xirtmfkgl gf ni gmsausmñk slcrf ni fstruaturi y ni  rfsmstfkami gf nls jitfrminfs, jitfrminfs, sfktñ nis cisfs dêsmais y jitfjétmais jitfjétmais piri uk ikénmsms gfn jlvmjmfkt jlvmjmfktl, l, quf nf pfrjmtmñ gfjlstrir nis nfyfs gf aiêgi gf nls erivfs fk fn viaêl y fniclrir uki tflrêi aljpnfti gfn gmspirl gf prlyfatmnf prlyfatmnfs. s. Ni lcri fstici gfstmkigi i alkvfrtmrsf fk ni pmfgri ikeunir gf ni amfkami gf ni jfaékmai alkstrumgi plr nls amfktêdmals gf ni smeumfktf efkfriamñk, alk Kfwtlk i ni aicfzi.

M. 

LC@FWMTLQ 9.  9.  Mkvfstmeir ni mkgfpfkgfkami gf nis aljplkfktfs olrmzlktin y vfrtmain gfn jlvmjmfktl piricñnmal. 3.  3.  Oinnir fxpfrmjfktinjfktf ni fauiamñk gf ni triyfatlrmi gf uk prlyfatmn nikzigl in imrf alk uki amfrti ripmgfz y ékeunl gf gmspirl mkmamin quf aif ci`l fn fdfatl gf ni erivfgig. e rivfgig. 1.  1.  Gfsirrlnnir oicmnmgig fk fn usl gf nis tíakmais gf eridmaiamñk y nmkfinmziamñk quf pfrjmtfk fkalktrir fxpfrmjfktinjfktf ni fauiamñk quf rfniamlki gls virmicnfs. Fk fstf aisl nis allrgfkigis (x,y) gf ni triyfatlrmi gfn prlyfatmn quf sf nikzi.

MM. 

FYVMXLQ /JIWFSMINFQ 9 Qlplrtf ukmvfrsin 9 Sijpi iaikinigi 9 Xrfksi 9 Sfeni gf 9 j 9 Amkti igofsmvi

MMM. 

9 Arlkñjftrl 9 Aikmai (gf vmgrml/iafrl) 9 Xnljigi 9 Xipfn aircñk

DVKGIJFKWL WFÑSMAL Xiri quf fn jlvmjmfktl sfi gf triyfatlrmi aurvi0 piréclni aljpnfti, auikgl sf nikzi uk aloftfamnnl lcnmaul fk iùl kufvl, l gf jfgmi piréclni auikgl tmkqufis uk lc`ftl tin aljl uki pfnltmti gf pmke plke gf ni pirtf supfrmlr gf ni jfsi y fsti aif ipirtigi gf ni jfsi fk fn pmsl. Ltrls f`fjpnls slk ni riqufti gf tfkms l gf pmke plke elnpfi i ni pfnlti piri uki triyfatlrmi aurvi. Fn lc`ftl oi rfamcmgl uk mjpunsl quf nf gi lrmemkinjfktf uki vfnlamgig gf J.S.V., pfrl aljl fstf aufrpl y klsltrls kls fkalktrijls fk fn aijpl erivmtitlrml quf f`fraf ni dufrzi gf erivfgig y fs alkstiktf, fn lc`ftl fk su triyfatlrmi fsté sljftmgl i fsti dufrzi y su triyfatlrmi aurvi fs uk rfsuntigl gf fstis gls vfnlamgigfs vfnlamgigfs gfn JS2 V y ni vfnlamgig virmicnfs gf vy  quf gf aiêgi (ni tmfrri itrif i tlgls nls aufrpls). Xlr nl quf fn inaikaf nl gi ni fauiamñk gfn J.S.V. 0 x : Tlt

Jikuin gf Niclritlrml

Xéemki 31

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Quplkei ustfg uki rfemñk mkerévmgi gfn ukmvfrsl. Qm slntiri uki aikmai fk fsi zlki, fsti kl sf jlvfrêi. Fk aijcml, sm nikzir ni aikmai fsti sfeumrêi jlvmíkglsf ukmdlrjfjfktf alk ni jmsji vfnlamgig gf nikzijmfktl (JSV). Ni fauiamñk gf ni plsmamñk _ : _ + vt  fs2  fs2 oicni gf tik nf`ls fsté fn lc`ftl. Ni fauiamñk gf ni ripmgfz

 : ∓  

  gmaf quf tik répmgl sf jufvf fn lc`ftl. Xfrl fstijls fk

ni Wmfrri. Qm slntiri ustfg iquê ni aikmai ¼Yuí suafgfrêi< …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

Fauiamñk gf ni plsmamñk gf ni pirtêauni fk ni vfrtmain fs0

 :  +    + 

 et  3



Qm sf alksmgfri nis alkgmamlkfs mkmaminfs0 Xiri Ipnmaikgl fsti a.m. fk ni fauiamñk iktfrmlr, qufgi aljl0

 : 8    :8,  : 8  :   

 

Glkgf, e fs ni iafnfriamñk erivfgig0 e: =.55

….

¹

Fa. Wriyfatlrmi 

 l.98j/s3 

Ni fauiamñk gf ni vfnlamgig gf ni pirtêauni qufgi aljl

:

 

Iolri, sm sf nikzi ni aikmai fk uki gmrfaamñkFstf kl vfrtmain fvmgfktfjfktf ni triyfatlrmi sfré piricñnmai. tmpl gf jlvmjmfktl klrjinjfktf sf gfsarmcf aljl uk jlvmjmfktl aljpufstl2 gf uk nigl alk uki aljplkfktf olrmzlktin gfn jlvmjmfktl (JSV) y gf ltrl uki aljplkfktf vfrtmain (aiêgi nmcrf). Fk igfniktf, ni mgfi sfré lctfkfr rfemstrls plr sfpirigls gf fstls jlvmjmfktls aljplkfktfs gfn jlvmjmfktl.

MT. 

XSLAFGMJMFKWL JLKWI@F Jlktf fn fqumpl tin aljl jufstri fn gmsfùl fxpfrmjfktin fxpfrmjfktin gf ni Dmeuri.

Jikuin gf Niclritlrml

Xéemki 37

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Aumgf gf quf ni rijpi qufgf dm`i tin quf auikgl ni aikmai sf gfsprfkgi gf fnni nl oiei olrmzlktinjfktf. Ni sfaamñk IC, olrmzlktin, gf ni rijpi a gfcf fstir i uki inturi kl jfklr gf 18 aj rfspfatl in pmsl l ni jfsi gf trici`l. Oiei prufcis piri ucmair fn puktl gfsgf glkgf sf slntiri ni aikmai. Vcmaigl fn puktl gf nikzijmfktl, fstf sfré uk puktl dm`l X. Jirquf fsi plsmamñk. OXI : …………………. aj  9.  9.  Alnlquf fk fn pmsl fn pipfn aircñk y pipfn clkg. 3.  3.  Jmgi ni nlkemtug gf ni inturi o. (Vsf ni pnljigi, quf pisf plr nls puktls C y A).   1.  1.  Ainaunf fn tmfjpl t quf tirgi ni aikmai fk aifr gf C i G. Vsf ni n i fauiamñk0 ………………………………………………………………… …………………………………………………………………  Lpfrl isê0 ……………………………………………………………………… …………………………………………………………………………. …. 

ℋ: \\\\\\\\\\¹\\\\\\\\\\\

t  :…………………….. ……… 

¹

7.  7.  Wriaf nis erédmais0 y vfrsus x y ni y vfrsus x³ Mktfrprftf nis erédmais. (ijcis fk uk pipfn jmnmjftrigl) Ainaunf ni ripmgfz gf sinmgi. sinmgi. 6.  6.  Oiei uk fstmjigl gfn inaikaf olrmzlktin AG gf ni aikmai. Ainaunf fn inaikaf. Vsf ni n i fauiamñk0 …………………………………………………………. ………………………………………………………….  Lpfrf isê0 …………………………………………………………… ………………………………………………………………….. ……..  Inaikaf _ :……………………. ……………… 

¹

Oiei rfvmsir fstf fstmjigl plr fn prldfslr.

4.  4.  Jirquf ni plsmamñk tfñrmai glkgf ustfg prfgm`l mjpiatirêi ni aikmai. Qufntf ni aikmai gfsgf fn puktl X. ¼Fk quí plsmamñk aif ni aikmai< x:……………………………… :……………………………………………………………… …………………………………………………………… ……………………………  I pirtmr gf nls vinlrfs gf su inaikaf fxpfrmjfktin y gf su vinlr tfñrmal, ainaunf fn frrlr fxpfrmjfktin plrafktuin.

  / 

: ………………………………………………………………. ……………………………………………………………….

Ni aiusi gf kl iafrtir fk fn nueir gf mjpiatl fs0 …………………………………………………………………… ……………………………… ……………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ……………………………… ……………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

5.  5.  Sfpmti ni lpfriamñk gfn pisl 7,6 alnlaikgl, uki ol`i gf pipfn cnikal slcrf pipfn ainal. Sfpmti fstf pisl amkal vfafs. Aljpnftf ni ticni 9. Eridmquf y vfrsus x. y y vfrsus x3. Mktfrprftf ni erédmai. (Vsf pipfn jmnmjftrigl). (Xfeuf su erédmai quf iquê) WICNI 9

Jikuin gf Niclritlrml

Xéemki 36

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

] (aj)

     1     



 (aj)



 (aj)

1

 (aj)

Dêsmai Efkfrin M



 (aj)



̆

 (aj)

 (aj)  (aj)



 (aj3)

?.  ?.  Aijcmf gf inturi in puktl X y rfpmti fn pisl pisl 5. =.  =.  ¼Yuí vfnlamgig nnfvi ni clni fk fn mkstiktf gfn mjpiatl alk fn pipfn<   T :…………… …………………………..

¹

98.  Alksmgfrikgl fn vinlr prljfgml gf ni iafnfriamñk gf ni erivfgig fk Nmji aljl =,5? j/s 3, 98.  fkaufktrf ni jiekmtug gf ni vfnlamgig mkmamin auikgl ni clni pisi plr fn lrmefk gf aallrgfkigis. llrgfkigis. ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

99.  Quplkei quf kl alklaf ni vfnlamgig gf sinmgi gf ni aikmai. Qufntf ni aikmai gfsgf fn puktl X. 99.  Jmgi fn inaikaf olrmzlktin (smk oiafr ni prfgmaamñk). Fdfatði fn aénaunl i ni mkvfrsi piri oinnir ni ripmgfz gf sinmgi gf ni aikmai. …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………………… ………………………………… 

93.   Sfpmti fn pisl 98 aijcmikgl gf inturi 93. in turi gfn puktl X y/l aijcmikgl ai aikmais kmais (jisis gmdfrfktfs).

……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… 

Lcsfrviamñk0 Fstf fs uk cufk jítlgl piri ainaunir ripmgfafs fk efkfrin. Jikuin gf Niclritlrml

Xéemki 34

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

F_XFSMJFKWL K° 81 JLTMJMFKWL GF VK XSL]FAWMN INVJKL0

 

Dêsmai Efkfrin M

DFAOI T°C° gfn Xrldfslr

JIWSMAVNI0

T. 

FTINVIAMÑK 9.  9.  ¼Añjl usirêi ni alksfrviamñk gf ni fkfreêi piri oinnir ni vfnlamgig gf ni fsdfri, quf fs ni fsdfri quf fsté fk ni pirtf supfrmlr gf ni rijpi alk fkfreêi pltfkamin y sf gfsnmzi y sinf gfspfgmgi alk fkfreêi amkítmai< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………¼Xlr quí Vg. idmrjirêi quf fn

dêsmal in tljir aljl virmicnf vir micnf mkgfpfkgmfktf fn rltunigl aljl f`f ] y nnii virmicnf gfpfkgmfktf fk fn f`f _, fsté aljftmfkgl uk frrlr, añjl usi nis Jitfjétmais uk dêsmal< …………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………… ……………………………… 

3.  3.  Mkvfstmeuf slcrf añjl sf alnlai uk sitínmtf quf emri inrfgfglr gf ni tmfrri. ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

1.  ¼Yuí airiatfrêstmais tmfkf uk sitínmtf eflfstiamlkirml y quf usl sf nf gi< ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

7.  7.  Sfinmaf uki fxpfrmfkami sfkamnni alnlaikgl nls f`fs fk uki ol`i jmnmjftrigi y gfsgf fn lrmefk mjpunsiri alk su gfgl puneir ni sinmgi gf ni aikmai fktmktigi alk gmrfaamñk lcnmaui, rfpmti piri ltris gls tmkaigis. Alnlquf fsti ol`i trici`igi. ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..……… 

Jikuin gf Niclritlrml

Xéemki 35

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

6.  6.  Lcsfrvf nis 81 triyfatlrmis. Xlgrêi oiafr uki slnuamñk piri uki gf fnnis, pufs tmfkfk fn inaikaf y ni inturi jéxmji y fn ékeunl gf tmrl. Gfsarmci ni triyfatlrmi. ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………..……… ………………………..……… 

TM. 

ALKANVQMLKFQ …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..………… … ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………………………………………..……… …………………………..……… 

TMM. 

LCQFSTIAMLKFQ ] SFALJFKGIAMLKFQ …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………..……… ……………………………..………… … …………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… ……………………………………………………………..……… …………………………..……… 

Jikuin gf Niclritlrml

Xéemki 3?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

M.9  F_XFSMFKAMI K¸ 87 - ALKGMAMLKFQ GF FYVMNMCSML MQIIA KFUWLK Dêsmal. Kiamñ0 7 gf fkfrl 9471 (iùl fk quf jlrêi Einmnfl)fk Llnstolrpf Nmkalnksomrf, Mkenitfrri. Dinnfamñ0 19 gf jirzl 535 fk Nlkgrfs, Mkenitfrri. Gfsaucrmñ nls prmkampmls gfn aénaunl gmdfrfkamin f mktferin oiami 9446-9444. Fniclrñ in jfkls trfs fkdlqufs gmdfrfktfs gf su kufvl ikénmsms. Xucnmai fk 94?5 sus aínfcrfs Xomnlslpomgf kiturinms prmkampmi jitofjitmai. Nls trfs nmcrls gf fsti lcri alktmfkfk nls dukgijfktls gf ni dêsmai y ni istrlkljêi fsarmtls fk fn nfkeui`f gf ni efljftrêi puri. Fn nmcrl M alktmfkfk fn jítlgl gf nis „prmjfris y ðntmjis rizlkfs‚ y, ci`l ni dlrji gf kltis l gf fsalnmls, sf fkaufktri aljl ikfxl gfn nmcrl MMM ni tflrêi gf nis dnuxmlkfs.

M. 

LC@FWMTLQ 9.  9.  Mkvfstmeir slcrf nis alkgmamlkfs piri quf uk smstfji sf fkaufktrf fk fqumnmcrml 3.  Mkvfstmeir fn aljplrtijmfktl gf nis  dufrzis alkaurrfktfs alkaurrfktfs y nis dufrzis pirinfnis

MM. 

FYVMXLQ ] JIWFSMINFQ 3 3 Qlplrtf Xlnfi ukmvfrsin 9 @ufel gf pfsis 9 rfeni pitrñk (alk lrmdmamls) Aufrgi

MMM. 

3 Anijppfsis l ieirrigfri 1 Xlrti 3 Gmkijñjftrls 9 Cinikzi 9 Wicnfrl

DVKGIJFKWL WFÑSMAL Xiri quf uk aufrpl rêemgl sf fkaufktrf fk fqumnmcrml jfaékmal, gfcf gf fstir fk0 i)  i)  FYVMNMCSML GF WSIQNIAMLK „Vk aufrpl sf fkaufktri fk fqumnmcrml gf trisniamñk auikgl ni suji vfatlrmin gf tlgis nis

 dufrzis quf iatðik slcrf fn aufrpl fs kuni.‚  

Fstl laurrf auikgl fn aufrpl klafktrl sf trisnigi l auikgl alkgfsgf vfnlamgig alkstiktf2 fs gfamr, auikgl ni iafnfriamñk nmkfin gfn gf jisi fs kuni,sflcsfrvigl ljufvf csfrvigl uk smstfji gf rfdfrfkami mkframin. ∙D : 8

c)  c)  FYVMNMCSML GF SLWIAMLK „Vk aufrpl sf fkaufktri fk fqumnmcrml gf rltiamñk auikgl ni suji gf nls jljfktls gf dufrzi (tlrqufs) rfspfatl i uk puktl gf emrl fs kunl‚  

Fstl laurrf auikgl ni iafnfriamñk ikeunir inrfgfglr gf auinqumfr f`f fs kuni. ∙r : 8

Xiri vfrmdmair quf sf aujpnf fsti sfeukgi alkgmamñk sf rfinmzik nls smeumfktfs pisls. 9)  9)  Qf mgfktmdmai tlgis nis dufrzis ipnmaigis slcrf fn aufrpl Jikuin gf Niclritlrml

Xéemki 3=

   

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

3)  3)  Qf fsalef uk puktl gf emrl rfspfatl in auin sf ikinmzirék nls jljfktls gf dufrzis. 1)  1)  Qf fkaufktri aigi ukl gf nls jljfktls gf dufrzis rfspfatl in puktl gf emrl fsalemgl. 7)  7)  Qf rfinmzi ni suji gf tlrqufs y sf meuini i afrl. Wfkei uki aufkti quf fsti dlrjuniamñk, sf rfdmfrf slnl in aisl auikgl a uikgl nis dufrzis y nis gmstikamis fstík slcrf uk jmsjl pnikl. Fs gfamr, fstf kl fs uk prlcnfji trmgmjfksmlkin. Ni suji gf nls jljfktls gf dufrzis rfspfatl rfspfatl i auinqumfr puktl, gfktrl l dufri gfn gfn aufrpl gfcf sfr kunl. F`fjpnls. Qfi uk aufrpl rêemgl fk dlrji gf virmnni, gf pfsl gfsprfamicnf.

D Fk ni Dmeuri 9, ni dufrzi rfsuntiktf slcrf fn aufrpl aufrpl fs kuni, pfrl fn jljfktl gf dufrzi rfspfatl i su afktrl fs 3D 3Dg. Glkgf, g   fs ni gmstikami gfsgf fn puktl gf ipnmaiamñk gf nis dufrzis (D ( D y  ‑ D) in afktrl gf ni vmei. Fk fstf aisl ni virmnni kl virmiré su plsmamñk iukquf g D

tfkgfré i emrir gf jikfri iktm olrirmi.

uri 9

Fk ni dmeuri 3, ni dufrzi rfsuntiktf fs 3D y fn jljfktl gf dufrzi rfspfatl i su afktrl fs kunl. Xlr nl tiktl fxmstf uk fqumnmcrml  gf rltiamñk pfrl kl gf trisniamñk. Fk fstf aisl ni virmnni isamfkgf vfrtmainjfktf smk rltir.

D

D

Dmeuri 3

D

D

Ni dmeuri 1, jufstri ni virmnni fk fqumnmcrml tiktl gf trisniamñk aljl gf rltiamñk2 plr nl tiktl ni virmnni sf fkaufktri fk rfplsl „icslnutl‚ rfspfatl i su

smstfji gf rfdfrfkami.

Dmeuri 1

Jikuin gf Niclritlrml

Xéemki 18

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

MT. 

 

Dêsmai Efkfrin M

XSLAFGMJMFKWL JLKWI@F 9 Jlktf fn fqumpl tin aljl sf jufstri fk fn gmsfùl fxpfrmjfktin 9, gf ni dmeuri 7. Quspfkgi fk nls fxtrfjls gf ni aufrgi cnlqufs gf pfsls gmdfrfktfs D9  y D3  y fk fn afktrl uk cnlquf gf pfsl D1 tin quf D 9  + D3 : D1. Gf`f quf fn smstfji sf fsticmnmaf. Sfaufrgf quf gfcf aujpnmrsf ni nfy gf ni gfsmeuingig gf nls nigls gfn trmékeunl0 „Vk nigl fs jfklr quf ni suji gf nls ltrls gls y jiylr quf su gmdfrfkami‚. 

9.  9.  Xfeuf uk pipfn fk fn ticnfrl y alnlquf fstf fk ni pirtf plstfrmlr gf ni aufrgi2 jirquf fk fn pipfn nis gmrfaamlkfs gf nis tfksmlkfs gf nis aufrgis. 3.  3.  Sftmrf fn pipfn y ikltf fk aigi nêkfi nls vinlrfs gf nls pfsls alrrfsplkgmfktfs. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. 

1.  1.  Aljpnftf fk fn pipfn fn pirinfnlerijl alk uki fsaini alkvfkmfktf piri nls vinlrfs gf D9 y D3. ¼Alkaufrgi su rfsuntigl plr fn jítlgl erédmal alk fn aufrpl D 1 < ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

¼Yuí gmdfrfkamis oiy fktrf rfsuntiktf y fqumnmcriktf< …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

7.  7.  Sfpmti nls pisls 3, 1, 7 y 6 6.  6.  Alnlquf trfs cnlqufs gf meuin pfsl y jmgi nls ékeunls0 ι, γ y α quf sf dlrjik inrfgfglr gfn puktl. ι : ……………….. γ : …………… α : ……………………….  Jikuin gf Niclritlrml

Xéemki 19

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

¼Alkaufrgik alk fn vinlr tfñrmal gf 938¸< @ustmdmquf su rfspufsti. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. 

¼Fk quí aisls nls gmkijñjftrls jirairék meuin vinlr< …………………………………………………………..  Oiei uk erédmal quf fxprfsf vmsuinjfktf nl quf fxpnmquf su rfspufsti. 4.  4.  Alnlquf trfs cnlqufs auyls pfsls fstík fk rfniamñk 10706 Jmgi nls ékeunls quf dlrjfk fktrf fnnls. fn nls. Tfrmdmquf quf fn ékeunl fktrf nis Aufrgis sfi =8¸. ……………………………………………………………….  ……………………………………………………………….  ¼Yuí rfsuntirêi sm ni rfniamñk dufri 930 910 6< ……………………………………………………………….  ……………………………………………………………….  Eridmquf Iquê

JLKWI@F 3 Jlktf fn fqumpl tin aljl jufstri fn gmsfùl fxpfrmjfktin 3, gf ni Dmeuri 6. 9.  9.  Alnlquf nls gmkijñjftrls fk nls ieu`frls fk 98 aj y 58 aj. Ikltf nis nfaturis gf aigi gmkijñjftrl. D9  :……………………………..  D3  :…………………………….. 

3.  3.  Alnlquf fk fn ieu`frl ucmaigl fk fn afktrl gf erivfgig gf ni rfeni uk cnlquf gf jisi 788 je y ikltf nis nfaturis fk aigi gmkijñjftrl. D9:……………………………………..

D3:………………………………………………. 

1.  Gfspniaf fn cnlquf gf pfsl D in ieu`frl i 18 aj gfn prmjfr gmkijñjftrl y ikltf nis nfaturis gf ijcls. Jikuin gf Niclritlrml

Xéemki 13

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

D9:……………………………………..

Dêsmai Efkfrin M

D3:………………………………………………. 

7.  7.  Igmamlkf uk cnlquf gf jisi 388 e i 98 aj gfn sfeukgl gmkijñjftrl y ikltf nis nfaturis gf ijcls D9:……………………………………..

D3:………………………………………………. 

¼Qlk meuinfs nis nfaturis fk nls gmkijñjftrls fk nls pisls 5 y ?< ¼Xlr quí< …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

F_XFSMJFKWL K° 87 FYVMNMCSML

DFAOI

INVJKL0 JIWSMAVNI0

T. 

T°C° gfn Xrldfslr

FTINVIAMÑK 9.  9.  Fkaufktrf tfñrmaijfktf fn vinlr gf ni fqumnmcriktf plr aigi ukl gf nls trfs jítlgls smeumfktfs0 nfy gf Nijy ( gf nls sfkls), nfy gfn alsfkl, plr gfsaljplsmamñk rfatikeunir . Aljpirf nis jiekmtugfs gf S1 y nls ékeunls ι, γ, α oinnigls alk fn lctfkmgl fk fn pisl 7 y nls jfgmgls fxpfrmjfktinjfktf. Alkdfaamlkf uk auigrl gf sus rfsuntigls y gf nls frrlrfs fxpfrmjfktinfs plrafktuinfs alk rfspfatl i ni fqumnmcriktf alnlaigi. …………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

3.  3.  Ainaunf tfñrmaijfktf nis rfiaamlkfs fk nls puktls gf suspfksmñk piri nls pisls = y 98 y aljpirf alk nis nfaturis fk nls gmkijñjftrls. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

1.  ¼Yuí lcsfrvi gf nis dufrzis quf iatðik slcf ni rfeni iaikinigi<

Jikuin gf Niclritlrml

Xéemki 11

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

TM. 

ALKANVQMLKFQ ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

TMM. 

LCQFSTIAMLKFQ ] SFALJFKGIAMLKFQ ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………… ……………….………………………………………………………………………………………… ……………….……………………………………………………… …………………………………………………………………… …………………………………… … …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………… …… 

Jikuin gf Niclritlrml

Xéemki 17

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

XSÉAWMAI K¸ 860 FKFSEÊI XLWFKAMIN FNÉQWMAI ] ESITMWIWLSMI  

Slcfrt Ollbf

Fsowitfr, Mkenitfrri, 9416 ‑  Nlkgrfs,   Nlkgrfs, 9581) Dêsmal y istrñkljl mkenís. Fk 9566 Slcfrt Ollbf alniclrñ alk Slcfrt Clynf fk ni alkstruaamñk gf uki cljci gf imrf. Amkal iùls jés tirgf dlrjunñ ni nfy gf ni fnistmamgig quf nnfvi su kljcrf, quf fsticnfaf ni rfniamñk gf prlplramlkinmgig gmrfati fktrf fn mrijmfktl sudrmgl plr uk aufrpl sñnmgl y ni dufrzi ipnmaigi piri prlguamr fsf mrijmfktl. Fk fsti nfy sf dukgijfkti fn fstugml gf ni fnistmamgig gf nls jitfrminfs.

M. 

LC@FWMTLQ 9.  9.  Mkvfstmeir slcrf nls aijcmls gf fkfreêi pltfkamin fnéstmai fk uk smstfji cnlquf-rfslrtf. 3.  Fsticnfafr gmdfrfkamis fktrf nis fkfreêis pltfkaminfs fnéstmai y erivmtitlrmi.

MM. 

FYVMXLQ ] JIWFSMINFQ 9 Cinikzi 9 Qlplrtf Vkmvfrsin 9 @ufel gf pfsis 9 Sfeni eriguigi gf 9 j Wrifr ol`is gf pipfn jmnmjftrigl (6) Xfsis rikurigis0 688e, 988e, 68e, 38e, 98e

MMM. 

9 Sfslrtf 9 Ainjp 9 Xlrti pfsis 9 Xrfksi gf 6‚ 

Xfsis0 8,6 be y 9 be

DVKGIJFKWL WFÑSMAL Qñnmgls fnéstmals, slk iqufnnls aufrpls quf in afsir ni aiusi quf nl nlss gfdlrji rfaupfrik su alkdmeuriamñk (dlrji y tijiùl). Fstl fs vénmgl jmfktris kl fxafgi amfrtl nêjmtf fnéstmal. Fk rfinmgig, tlgls nls aufrpls slk gfdlrjicnfs fk jiylr l jfklr jfgmgi. Nls rfslrtfs sf fstmrik auikgl slk sljftmgls i dufrzis gf triaamñk. I jiylr fstmrijmfktl jiylr triaamñk2 sf lcsfrvi quf ni dufrzi fnéstmai kl fs alkstiktf. Ni nfy gf Ollbf rfniamlki ni jiekmtug gf ni dufrzi fnéstmai alk ni fnlkeiamñk (gfdlrjiamñk)   (9)

 :

Glkgf, b fs ni alkstiktf fnéstmai (gfn rfslrtf)2 su vinlr gfpfkgf gf ni dlrji y nis prlpmfgigfs fnéstmais gfn aufrpl. Fn smekl kfeitmvl mkgmai quf ni dufrzi fnéstmai gfn rfslrtf smfjprf sf lplkf i ni gfdlrjiamñk (fstmrijmfktl l aljprfsmñk). Fn ofaol gf quf uk rfslrtf fstmrigl tmfkgi i rferfsir i su alkdmeuriamñk lrmemkin (dlrji y tijiùl) auikgl afsi ni aiusi quf nl gfdlrji, sf mktfrprfti aljl quf fn rfslrtf tmfkfk injiafkigl Jikuin gf Niclritlrml

Xéemki 16

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

fkfreêi fk dlrji gf fkfreêi pltfkamin fnéstmai, auyl vinlr fs meuin in trici`l rfinmzigl plr ni dufrzi quf nl fstmri.

 :  :        :

 

(3)

Glkgf, x fs ni gfdlrjiamñk gfn rfslrtf f`framgi plr uki dufrzi jfgmi gf jiekmtug Bx/   3

 

Fk ni Dme. 9, fs ni plsmamñk gfn fxtrfjl mkdfrmlr gfn rfslrtf, nmcrf gf ni iaamñk gf dufrzis fxtfrkis fs (smstfji gf rfdfrfkami piri jfgmr fstmrijmfktls gfn rfslrtf). In alnlair uk cnlquf gf jisi j fn fxtrfjl nmcrf gfn rfslrtf fstf sf fstmri uki pfqufùi gmstikami gfsafkgmfkgl gf ni plsmamñk  i ni  

 



Gfsafkgmfkgl y slstfkmfkgl fn cnlquf afri i ni plsmamñk  piri nufel gf`irnl nmcrf, sf lcsfrviré y   . prmjfrl quf fstf gfsafkgfré i plsmamñk   y nufel fjpfziré i vmcrir fktrf Xlstfrmlrjfktf gfspuís gf uk tmfjpl prugfkamin fn cnlquf nnfeiré in rfplsl.



 

Ci`l fstis alkgmamlkfs fn trici`l rfinmzigl plr ni dufrzi erivmtitlrmi piri fstmri fn rfslrtf rfslr tf gf   fsti glgl plr, plr,



 :        :      

 

(1)

i



∄

Fstl alrrfsplkgf, prfamsijfktf, in aijcml gf fkfreêi pltfkamin fnéstmai   (fnéstmai) injiafkigi fk fn rfslrtf. Lcsfrvf quf sf pufgf aijcmir a ijcmir gf kljcrf i ni allrgfkigi x plr y . Gf ltrl nigl, fn aijcml gf ni fkfreêi pltfkami erivmtitlrmi  (erivmtitlrml) fxpfrmjfktigi plr fn cnlquf fsté gigi plr,

∄ ∄  :∄:  

 

Oiamfkgl uki aijcml gf allrgfkigi gf x plr y, ni fauiamñk (7) qufgi aljl,

∄  :∄:        :    :  

 

Glkgf, y9 f y3  sf pufgfk gftfrjmkir gftfrjmkir uki vfz alklamgis alklamgis Gfkljmkikgl O i ni gmstikami aljprfkgmgi fktrf quf sf jmgf déamnjfktf)0  ,

Jikuin gf Niclritlrml

y

y

 .

 , sf aujpnf quf (O fs uki aiktmgig  

Xéemki 14

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

MT. 

Dêsmai Efkfrin M

XSLAFGMJMFKWL JLKWI@F Jlktf fn fqumpl tin aljl sf jufstri fk fn gmsfùl Fxpfrmjfktin jlstrigl fk ni Dmeuri 9. Oiei almkamgmr fn fxtrfjl mkdfrmlr gfn rfslrtf alk fn afrl gf ni fsaini eriguigi l uk puktl gf ísti, quf nf pfrjmti tfkfr déamnfs nfaturis.

 : 78 

F`fjpnl. , sfré fn smstfji gf rfdfrfkami piri jfgmr nls fstmrijmfktls gfn rfslrtf. 9.  9.  Aufneuf ni plrti pfsis gfn fxtrfjl mkdfrmlr gfn rfslrtf. Fk fstis alkgmamlkfs fs plsmcnf quf sf prlguzai prlguzai uk pfqufùl fstmrijmfktl fk fn rfslrtf. Qm fstf fs fn aisl, ikltf ni jisi gf ni plrti pfsi y fn fstmrijmfktl prlguamgl fk fn rfslrtf fk ni Wicni 9. 3.  3.  Quafsmvijfktf, igmamlkf cnlqufs, pirtmfkgl plr f`fjpnl gf 188 e, y rfemstrf nis plsmamlkfs gf nls fstmrijmfktls gfn rfslrtf fk ni Wicni 9.

Klti Mjplrtiktf ¡Aumgf gf kl pisir fn nêjmtf n êjmtf fnéstmal gfn rfslrtf!

WICNI 9 Cnlquf Quspfkgmgl j (be)

Jikuin gf Niclritlrml

Dufrzi Ipnmaigi D (K)

Fstmrijmfktl gfn rfslrtf Igmamlkikgl Sftmrikgl cnlqufs cnlqufs Xrljfgml y (aj) y (aj) ] (aj)

B K/aj   K/aj

Xéemki 15

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

1.  1.  Fstikgl fn cnlquf gf pfsl jéxmjl alksmgfrigl iuk suspfkgmgl, rftmrf ukl i ukl nls cnlqufs y rfemstrf nis kufvis plsmamlkfs fk ni Wicni 9. 7.  7.  Ainaunf fn prljfgml gf nis nfaturis y aljpnftf ni Wicni 9. Eridmquf f mktfrprftf ni dufrzi (D) ipnmaigi vfrsus fn fstmrijmfktl (x) gfn rfslrtf. (Xfeuf su erédmai iquê) ¼D fs prlplramlkin i x< ¼Gf quí tmpl< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………………… ……………………………………………. …. 

I pirtmr gf ni pfkgmfktf gf ni erédmai D   vs.  x , Gftfrjmkf ni alkstiktf fnéstmai gfn rfslrtf. b:………………………, jêkmjls auigrigls.  Gf sus rfsuntigls, lcsfrvf ni pírgmgi gf fkfreêi pltfkamin erivmtitlrmi y fn iujfktl gf ni fkfreêi pltfkamin fnéstmai gfn rfslrtf auikgl fn cnlquf aif. ¼Yuí rfniamñk oiy fktrf fnnis< …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

Qmjuntékfijfktf, eridmquf nis gls dlrjis gf fkfreêi fk dukamñk gf nls fstmrijmfktls gfn rfslrtf. Gf uki mktfrprftiamñk igfauigi. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. 

(Xfeuf su erédmai iquê) ¼Qf alksfrvi ni fkfreêi fk fstis mktfriaamlkfs fktrf cnlquf y rfslrtf< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. 

6.  Gfn fxtrfjl mkdfrmlr gfn rfslrtf suspfkgi uk cnlquf gf jisi 8,6 be (l ni quf suemfri su prldfslr). Qlstfkei fn cnlquf alk ni jikl y nufel oéeinl gfsafkgfr oisti quf fn rfslrtf sf fstmrf 3 aj. Sfemstrf fstf vinlr fk ni Wicni 3 aljl _ 9.  4.  4.  Qufntf fn cnlquf gf jikfri quf aimei nmcrfjfktf. Gfspuís gf gls l jés mktfktls lcsfrvf ni plsmamñk iprlxmjigi gfn puktl jés ci`l gf ni aiêgi. Sfemstrf ni nfaturi fk ni Wicni 3 aljl _ 3. ¼Auén fs ni suji gf nis fkfreêis pltfkaminfs auikgl fn cnlquf nnfei i ni jmtig gf su aiêgi< …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

Jikuin gf Niclritlrml

Xéemki 1?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

WICNI 3     (j) (j)

   : 93    : 93   ∄   ∄ : ∄ : ∄

  (j)

  (j)

 

(@)

 

(@) (@)  

 

(@) (@)  

 

 

(@)

(@)

(@)



5.  5.  Sfpmti nls pisls (4) y (5) alksmgfrikgl kufvls vinlrfs piri 0 1 aj, 7 aj, 6aj y 4 aj. Ikltf fstls vinlrfs y aljpnftf ni Wicni 3. Eridmquf ni suji gf nis fkfreêis pltfkaminfs fk dukamñk gf nls fstmrijmfktls gfn rfslrtf. (Xfeuf ni erédmai iquê)

Jikuin gf Niclritlrml

Xéemki 1=

 

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

¼Yuí pufgf gfguamr ustfg gf fstf erédmal< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

¼Ci`l quí alkgmamlkfs ni suji gf nis fkfreêis amkítmai y pltfkamin gf uk smstfji pfrjikfaf alkstiktf< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

Gftfrjmkf fxpfrmjfktinjfktf fn vinlr gf ni alkstiktf b. (Quefrfkami0 Gftfrjêkfnl i pirtmr gf

      vfrsus

l

 vfrsus

)

Oiei uk aljfktirml in rfspfatl. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. 

Aljpirf fn vinlr gf b  gftfrjmkigl  gftfrjmkigl alk fn fkalktrigl fk 1. ¼Yuí alkanuyf< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………. ……. 

F_XFSMJFKWL K° 86 FKFSEMI XLWFKAMIN INVJKL0

DFAOI T° C° gfn Xrldfslr

JIWSMAVNI0

Jikuin gf Niclritlrml

Xéemki 78

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

T. 

 

Dêsmai Efkfrin M

FTINVIAMÑK 9.  9.  Gfn pisl 1, oinnf fn érfi ci`l ni aurvi D vs. v s. x ¼Dêsmaijfktf, quí smekmdmai fsti érfi< …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

3.  3.  Qm piri amfrtl rfslrtf ni erédmai D vs. x kl dufri nmkfin ipiri fn fstmrijmfktl alrrfsplkgmfktf. ¼Añjl fkalktrirêi ni fkfreêi pltfkamin injiafkigi fk fn rfslrtf< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ………………………………………… ……… 

Xisigl fn nêjmtf fnéstmal, gf fstmrijmfktl, ¼quí suafgf alk fn jitfrmin< Fxpnmquf plr quí suafgf fstl.

…………………………………………………  ………………………………………………… 

1.  1.  Ni smeumfktf erédmai, pnltfigi fk Xipfn jmnmjftrigl, jufstri gitls fxpfrmjfktinfs (puktls) y ni fauiamñk gf i`ustf rfspfatmvl (nêkfi alktmkui) lctfkmgl jfgmiktf uk sldtwirf, quf alrrfsplkgfk i uk smstfji cnlqufrfslrtf suspfkgmgl. Mgfktmdmquf nis virmicnfs quf alrrfsplkgfk i ni fauiamñk gf i`ustf jlstrigi, fkaufktrf ni alkstiktf fnéstmai gfn rfslrtf y ni fkfreêi quf tfkgrêi fn rfslrtf piri uki fnlkeiamñk fnlkeiam ñk gf 9? aj. …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ………………………………………………………………… 

7.  7.  I pirtmr gf ni erédmai gf fkfreêi pltfkamin erivmtitlrmi Ve vfrsus fnlkeiamñk x, ig`ukti, fkaufktrf ni jiekmtug gfn cnlquf suspfkgml fk fn rfslrtf y ni fkfreêi pltfkamin erivmtitlrmi piri x : ?6 aj. …………………………………………………………………… ………………………………… …………………………………………………………… …………………………  ……………………………………………………………………………………………..  ……………………………………………… 

91



 

 9,1

Jikuin gf Niclritlrml

Xéemki 79

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

TM. 

 

Dêsmai Efkfrin M

ALKANVQMLKFQ ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

TMM. 

LCQFSTIAMLKFQ ] SFALJFKGIAMLKFQ …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ………………………………………. ……. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… …………………………………………… ………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………. …………. 

Jikuin gf Niclritlrml

Xéemki 73

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

XSÉAWMAI K¸ 840 JLTMJMFKWL SFAWMNMKFL VKMDLSJF 9.  9. 

LC@FWMTLQ

9.9. Gftfrjmkir Gftfrjmkir ni fauiamñk olrirmi gf uk jñvmn alk jlvmjmfktl rfatmnêkfl ukmdlrjf (J.S.V) 9.3. Gftfrjmkir Gftfrjmkir ni vfnlamgig gf uk jñvmn alk J.S.V. 3.  3. 

DVKGIJFKWL WFÑSMAL  WFÑSMAL 

Aljl f`fjpnl alksmgfrfjls uk jñvmn (airrmtl) gfspnizékglsf i vfnlamgig alkstiktf (v ( v) i nl nirel gfn f`f _, aljl sf jufstri fk ni Dmeuri 9. Ni gmstikami in lrmefk L fs ni allrgfkigi  x  quf   quf rfprfsfkti ni plsmamñk gfn jñvmn fk auinqumfr mkstiktf t. v : alkstiktf. 

]

L 

tl 

t 

xl 

x 

_

  x  

Dmeuri 9. Jlvmjmfktl Sfatmnêkfl Sfatmnêkfl Vkmdlrjf Qm fn jñvmn gf ni Dmeuri 9 fk fn mkstiktf t l fsté fk ni plsmamñk xl y nufel fk ltrl mkstiktf dmkin t fsté fk ni plsmamñk x , fn gfspnizijmfktl gfspnizijmfktl fk  fk fn mktfrvinl gf tmfjpl t : (t ‑ tl) fs fn vfatlr x quf ukf ni plsmamñk xl alk ni plsmamñk x. Aljl fstf vfatlr fs pirinfnl in f`f x, su jñgunl fsté gigl plr ni fxprfsmñk x : x  ‑ xl. Fn jñgunl gf ni vfnlamgig jfgmi gfn jñvmn fs fn gfspnizijmfktl  x fktrf fn tmfjpl  t. Fstl fs0 vj :

x  : t

x  xl t  tl

 

(9)

Gf ni Fauiamñk 9 sf pufgf lctfkfr0 x : x l + vjt ‑ vjtl

(3) 

Qm tl : 8, y gigl gigl quf fk fn J.S.V. v j : v, ni Fauiamñk 3 qufgi aljl0

x : xl + v t

Jikuin gf Niclritlrml

(1)

Xéemki 71

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Qfeðk ísti fxprfsmñk, fxmstf uki rfniamñk nmkfin fktrf x y t, nufel ni erédmai sfré uki rfati gf ni dlrji2 x: I+Ct

(7)

x

x

xl 

t t

Dmeuri 3. Erédmai gf gf x vs. t gfn Jlvmjmfktl Sfatmnêkfl Vkmdlrjf.

Fn mktfrafptl (lrgfkigi alrrfsplkgmfktf i x : 8), fs ni plsmamñk mkmamin mkma min x l : I y ni pfkgmfktf C gf ni rfati fs ni vfnlamgig gfn jñvmn, v : C.

1. SFQVJFK (

)

………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………………… ………………………………………………… ……………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………………… ………………………………………………… ……………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………………… ………………………………………………… ……………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………………… ………………………………………………… ……………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… ……………………………………………………………………… ………………………………………………… …………… ………………………………………………………………………… ………………………………… ………………………………………………………………………… …………………………………………………………….. ………………………….. 

Jikuin gf Niclritlrml

Xéemki 77

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

7. JIWFSMINFQ F MKQWSVJFKWLQ MKQWSVJFKWLQ (

Dêsmai Efkfrin M

) 

Jitfrminfs

Mkstrujfktls

6. XSLAFGMJMFKWL ] GIWLQ F_XFSMJFKWINFQ F_XFSMJFKWINFQ (

Xrfamsmñk

) 

6.9. Mkstinf fn fqumpl aljl sf jufstri fk ni Dmeuri 1 y fnm`i uki mkanmkiamñk igfauigi piri fn tucl i dmk gf quf ni curcu`i gf imrf sf gfspniaf i vfnlamgig vfnlam gig alkstiktf gfsgf fn fxtrfjl mkdfrmlr oiami ni pirtf jés inti. 6.3. Alk ni mkanmkiamñk igfauigi gfn tucl slcrf ni jfsi y alk ni curcu`i fk ni pirtf mkdfrmlr jmgi fn tmfjpl 6.3.  quf tirgi fk gfspnizirsf gfsgf xl : 98 aj i x : 38 aj. Sfinmaf Sfinmaf fsti jfgmgi jfgmgi auitrl vfafs y ikltf sus rfsuntigls fk ni Wicni 9. 6.1. Mkvmrtmfkgl ni mkanmkiamñk gfn tucl vufnvi i rfucmair ni curcu`i fk ni plsmamñk mkdfrmlr. Sfpmti nis 6.1.  jfgmamlkfs gfn êtfj iktfrmlr piri nls vinlrfs gf x gf ni Wicni 9.

Wucl alk ieui

Curcu`i gf imrf

.

.

18

38

98

 x

Dmeuri 1. Curcu`i fk jlvmjmfktl.

Jikuin gf Niclritlrml

Xéemki 76

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Wicni 9. Gitls fxpfrmjfktinfs gf gfspnizijmfktl y tmfjpl. x (aj)

4.

Η x (aj) 

9

38,8

98

3

18,8

38

1

78,8

18

7

68,8

78

6

48,8

68

4

58,8

48

5

?8,8

58

?

=8,8

?8

t9  (s) t3  (s) t1  (s) t7  (s)

XSLAFQIJMFKWL ] IKÉNMQMQ (

t (s)

v (aj/s)

)

Jítlgl Erédmal.

4.9.

Aljpnftir ni Wicni 9 ainaunikgl fn tmfjpl prljfgml prljfgml y ni vfnlamgig vfnlamgig v : Ηx /Η t, alk Ηt : t. 

4.3.

Eridmair fk pipfn jmnmjftrigl ni plsmamñk fk dukamñk gfn tmfjpl (x vs. t). Fk fn jmsjl erédmal ainaunir ni pfkgmfktf, fn mktfrafptl y ni fauiamñk gf ni rfati rfprfsfktitmvi.

I : ........................................................... C : ............................................................. Fauiamñk fjpêrmai fjpêrmai (x vs t)0 ........................................................................................................

4.1.  ¼Auén fs fn smekmdmaigl dêsmal gf C< 4.1. ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… ………………………………………… ……… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………….. ………………………….. 

4.7 Ni vfnlamgig lctfkmgi plr fstf jítlgl fs v : ...................................................................

Jítlgl Fstigêstmal.  Fstigêstmal.  Jikuin gf Niclritlrml

Xéemki 74

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

4.6.

Dêsmai Efkfrin M

Aljpnftir ni Wicni 3. Kñtfsf Kñtfsf quf nis virmicnfs jiyðsaunis _ f ] alrrfsplkgfk alrrfsplkgfk i nis virmicnfs jfgmgis t (tmfjpl) y x (plsmamñk), rfspfatmvijfktf.

Wicni 3. Auigrigls Jêkmjls. Jêkmjls .

K

_m (s)

]m (aj)

_m ]m  (s.aj)

_m3  (aj3)

] ` 3 (aj3)

9 3 1 7 6 4 5 ?  

4.4.  Alk nis Fauiamlkfs ? y = gf ni Xréatmai slcrf Fauiamlkfs Fjpêrmais ainaunir ni pfkgmfktf, fn 4.4. mktfrafptl y fsarmcmr ni fauiamñk gf ni rfati rfprfsfktitmvi. . I : .........................................................

C : ...................................... ....................

Fauiamñk fjpêrmai (x vs t) 0 .....................................................................................................

4.5.  Alk nls vinlrfs gf I y C oinnigls 4.5. oinnigls fk fn mtfj 6.4 y alk nis Fauiamlkfs 99 y 93 gf ni Xréatmai slcrf Fauiamlkfs Fjpêrmais, gftfrjmkf nis mkafrtmgujcrfs I y C

I : ................................................. Jikuin gf Niclritlrml

C : ..................................................................... Xéemki 75

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

4.?

 

Dêsmai Efkfrin M

Ni vfnlamgig lctfkmgi plr fstf jítlgl fs0 v : ....................................   ................

4.=. Wfkmfkgl fk aufkti fn vinlr gf ni plsmamñk mkmamin gf ni curcu`i gf imrf fk sus jfgmamlkfs, fvinðf gf jlgl smjpnf fstigêstmal. Fsarmcinifngfsvmiamñk rfsuntigl. plrafktuin gfn vinlr gfn mktfrafptl I  lctfkmgl fk fn jítlgl

% :

5

SFQVNWIGLQ (

Jítlgl

x l   I xl

 988% : .......................................................................................

) 

Fauiamñk fjpêrmai (x vs t)

Tfnlamgig gf ni curcu`i

Erédmal

 

Fstigêstmal

?.

ALKANVQMLKFQ (

)

?.9 ¼Yuí rfsuntigls erédmals l kujírmals gfjufstrik gfjufstrik quf fn jlvmjmfktl gf ni curcu`i fs rfatmnêkfl rfatmnêkfl ukmdlrjf< ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………………… ……………………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………….. ………………………….. 

?.3.  ¼Jfkamlkf in jfkls gls dfkñjfkls dêsmals alk vfnlamgig alkstiktf< ?.3. al kstiktf< …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… …………………………………………………………………… ………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………… ……………………………………………… …………… ………………………………………………………………………………………………..  Jikuin gf Niclritlrml

Xéemki 7?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

?.1.  ¼Xlr quí ni vfnlamgig jfgmi fs meuin i ni vfnlamgig mkstiktékfi fk uk J.S.V.< ?.1. …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… ……………………………………………………………………………………………………… …………………………………………………………………… …………………………………………………………………………… ……………………………………………… …… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… ……………………………………………………………………………………………….. 

=.

CMCNMLESIDÊI (….............)  (Mkgmquf0 Iutlr, Wêtunl, Fgmtlrmin, dfaoi, fgmamñk, péemki)

…………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… ……………………………………………………………………………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… …………………………………………………………………… ………………………………… …………………………………………………………………… ………………………………………………………………………… ……………………………………………… ……… ……………………………………………………………………………………………….. 

98.   98.

AINMGIG ]  ] XVKWVINMGIG (

Jikuin gf Niclritlrml

) 

Xéemki 7=

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

XSÉAWMAI K¸ 850 FYVMNMCSML GF DVFSPIQ ] JLJFKWLQ 9.  9.  LC@FWMTL Aljprlcir nis alkgmamlkfs gf fqumnmcrml gf trisniamñk y gf rltiamñk. 3.  3.  DVKGIJFKWL WFLSMAL Qfeðk kufstris lcsfrviamlkfs gmirmis, nls aufrpls aijcmik su vfnlamgig slnijfktf plr mktfriaamñk alk ltrls aufrpls. Qf fxpnmai fsti mktfriaamñk gfcmgl i quf nls aufrpls f`frafk dufrzis jutuis fktrf sê l quf ni mktfriaamñk sf jmgf plr uki aiktmgig dêsmai nnijigi dufrzi.

Ni mgfi prmjirmi quf tfkfjls iafrai gf ni dufrzi, fs ni sfksiamñk gf fsdufrzl jusaunir quf oiafjls piri gfdlrjir auinqumfr lc`ftl fnéstmal, uk rfslrtf plr f`fjpnl f`fjpnl Dmeuri 9 (i), l piri iafnfrir uk aufrpl Dmeuri 9 (c). Isê tfkfjls ni klamñk gf gls fdfatls quf pufgfk prlguamr nis dufrzis ipnmaigi i uk aufrpl0 fdfatl fnéstmal l gfdlrjiamñk gfn aufrpl y fdfatl gmkéjmal l iafnfriamñk gfn aufrpl

Ni gfdlrjiamñk aljl ni iafnfriamñk gf uk aufrpl gfpfkgfk gf ni gmrfaamñk y gf quí tik erikgf sfi ni dufrzi ipnmaigi, plr nl tiktl ni dufrzi fs uki jiekmtug vfatlrmin

i D

D

(i)

(c) Dmeuri (9)

Vki dufrzi fjpnfigi alk drfaufkami fs fn pfsl U gf uk aufrpl, fn auin sf gfdmkf aljl ni dufrzi alk quf ni tmfrri itrif in aufrpl alk ni iafnfriamñk gf ni erivfgig.

U : j e 

(9)

Fk fn Qmstfji Mktfrkiamlkin gf ukmgigfs, ni ukmgig gf dufrzi fs fn kfwtlk (K).

Jikuin gf Niclritlrml

Xéemki 68

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Fqumnmcrml gf uki pirtêauni

D9  D3 

L D1 

Dmeuri (3) trfs dufrzis iatuikgl Vk aufrpl l pirtêauni, sf fkaufktri fk fqumnmcrml gf trisniamñk sm k kl l fsté iafnfrigl. Fstl kl smekmdmai quf kl sf ipnmqufk dufrzis in aufrpl, smkl quf sm oiy virmis dufrzis quf iatðik, slnl sf rfqumfrf quf ni dufrzi kfti l suji vfatlrmin gf tlgis fnnis sfi afrl slnl isê kl oicré iafnfriamñk y ni vfnlamgig pfrjikfafré alkstiktf l fstiré fk rfplsl.

Ni Dmeuri (3) jufstri uk smstfji gf dufrzis auyis gmrfaamlkfs sf alrtik fk fn puktl L (kugl), fn auin sf alksmgfri aljl uki pirtêauni. Fstis dufrzis sf nnijik alkaurrfktfs alkaurrfktfs.. Auikgl uki pirtêauni fsté su`fti i ni iaamñk gf dufrzis alkaurrfktfs aljl fk fstf aisl, su fstigl gf fqumnmcrml sf fxprfsi gfn smeumfktf jlgl Vki pirtêauni sf fkaufktri fk fqumnmcrml sm ni suji g gf f tlgis nis dufrzis quf iatðik slcrf fnni, fs afrl

 m D m  8    

l cmfk0

Fstl mjpnmai quf0

 



 m Dm  x  8  



 



 m Dm y  8  

(3)

 



 m Dm z  8  

(1)

Fsti alkgmamñk isfeuri fn fqumnmcrml gf trisniamñk

Jikuin gf Niclritlrml

Xéemki 69

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Jljfktl l tlrquf gf uki dufrzi





Alksmgfrfjls uki dufrzi D quf iatði slcrf fn puktl 8 gf gf uk aufrpl rêemgl, sfi r   fn vfatlr gf  gf plsmamñk 



rfspfatl in puktl L sf gfdmkf gf fstf puktl, puktl, aljl sf mkgmai fk ni dmeuri (1) Fn tlrquf tl rquf   gf ni dufrzi D  alk rfspfatl  aljl fn vfatlr0  r  D   





ο  ο 

L

c

Dmeuri (1)

Fk fn trmékeunl rfatékeunl gf ni Dmeuri (1), sfk    :

 c r 

  gf glkgf

c : r sfk  , juntmpnmaikgl ijcls



jmfjcrls gf fsti fauiamñk plr D sf tmfkf D c : r D sfk    : r     D 

:

   :      gf fstl rfsunti ni 

fauiamñk fsainir0   

  

 : D c

(7)

 fs fn tlrquf, c fs fn crizl gf jljfktl y D fs ni dufrzi. Ni ukmgig gf tlrquf fs fn Kj .

In ipnmair uk tlrquf oiy quf rfalrgir fn fdfatl gf rltiamñk quf prlguaf. Vsirfjls fn alkvfkml0

Sltiamñk iktmolrirmi

Jikuin gf Niclritlrml

  

  (+ )

Sltiamñk olrirmi

  

 (- )

Xéemki 63

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Fqumnmcrml gf uk aufrpl rêemgl Vk aufrpl rêemgl fsté fk fqumnmcrml sm aujpnf gls alkgmamlkfs0 Xrmjfri alkgmamñk gf fqumnmcrml Ni dufrzi fxtfrki rfsuntiktf rfsuntiktf quf iatði slcrf ín, fs afrl  



 m D m  8  

 



m  Dm x   8  

l cmfk0

 



 m Dm   y  8  

 



 m Dm  z  8  

Fxprfsi fn fqumnmcrml gf trisniamñk, isfeuri quf fn aufrpl kl sf trisnigf iafnfrigijfktf Qfeukgi alkgmamñk gf fqumnmcrml fqumnmcrml Fn tlrquf rfsuntiktf rfspfatl i uk f`f, gf tlgis nis dufrzis quf iatðik slcrf fn aufrpl, fs afrl Ρ χl    

8 

(6)

Fxprfsi fn fqumnmcrml gf rltiamñk, isfeuri quf fn aufrpl kl rltf iafnfrigijfktf 





F`fjpnl 9. 9. Fk ni dmeuri 7 (i) sf jufstrik trfs dufrzis alkaurrfktfs D  , D , D  fk fqumnmcrml. Fk ni Dmeuri 3

9

1

7 (c) sf jufstrik nis n is dufrzis gfsaljpufstis fk sus aljplkfktfs rfatékeunis

: D3 sfk : D9 sfk ο

ο 

 

ο 

: -D9 alsο

 

: D3 als

: -D1  

(i)

(c)

Dmeuri (7)

Jikuin gf Niclritlrml

Xéemki 61

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Lcsfrvf quf sm slnijfktf alksmgfrijls nls jñgunls gf nis dufrzis, tfkfjls0

D9x : - D9 als    ,

D3x : D3 als    , D9y : D9 sfk    , D3y : D3 sfk   

(4)

Ipnmaikgl ni prmjfri alkgmamñk gf fqumnmcrml sf tmfkf0

D9 als ο + D3 als    : 8

D3 sfk ο + D3 sfk   - D1 : 8

F`fjpnl 3. 3. Fk ni dmeuri 6 sf tmfkf uki cirri oljleíkfi, gf pfsl U : 38 K, nlkemtug N : 8,4 j quf pufgf pmvltfir inrfgfglr gf su afktrl gf erivfgig er ivfgig fk su puktl jfgml, puktl L. Ni cirri sf fkaufktri fk fqumnmcrml alk nis dufrzis i nis quf fsté sljftmgi, fstl fs, uki dufrzi D 9 quf sf gfsfi gftfrjmkir, D3 :18 K, D1 : 98 K y ni dufrzi gf rfiaamñk D fk fn pmvltf quf tijcmík sf gfsfi alklafr. Igfjés sf gik nis gmstikamis c9, c3, c1 gfn pmvltf i nis nis dufrzis rfspfatmvis. rfspfatmvis. Gftfrjmkir D9  y D.

D

N : 8,4 j c9 : 8,9 j

c1  c9  I

c3  L

C

c3 : 8,96 j c1 : 8,36 j

D1 : 98 K D3 :18 K D9  U : 38 K

Dmeuri (6) Ipnmaikgl ni prmjfri alkgmamlkfs gf fqumnmcrml

 D]    8   D ‑ D9 ‑ 38 K ‑ 18 K ‑ 98 K : 8 D ‑ D9 : 48 K

(5)

Ipnmaikgl ni sfeukgi alkgmamñk gf fqumnmcrml, rfspfatl in puktl L (pmvltf) Jikuin gf Niclritlrml

Xéemki 67

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Ρ χl    

Dêsmai Efkfrin M

8 

D9 c9 ‑D3 c3  ‑ ‑ D1 c1 : 8 D9 ( 8,9 j )  ‑ 18 (8,96) Kj ‑ 98 (8,36) Kj Kj : 8 D9 : 58 K Sffjpnizikgl fk ni fauiamñk (5) 1.  1.  SFQVJFK (

D : 918 K

)

…………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… …………………………………………………… ………………… …………………………………………………………………… ………………………………… …………………………………………………………………………… …………………………………………………………………………… ………………………………………………… ……………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… …………………………………………………… ………………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… …………………………………………………… ………………… …………………………………………………………………… ………………………………… ………………………………………………………………………… ………………………………………………………………………… …………………………………………………… ………………… ………………………………………………………………………… 

7.  7.  JIWFSMINFQ F MKQWSVJFKWLQ ( JIWFSMINFQ

Jikuin gf Niclritlrml

)

MKQWSVJFKWLQ

XSFAMQMLK

Xéemki 66

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

6. XSLAFGMJMFKWL ] GIWLQ F_XFSJFKWINFQ (

Dêsmai Efkfrin M

)

Xiri fn fqumnmcrml gf uki pirtêauni

   D3 : j3 e

D9 : j9 e

D1 : j1 e

6.9   6.9

Dmeuri (4) Mkstinf fn fqumpl sfeðk sf jufstri fk ni Dmeuri 4.

6.3  Alnlquf jisis fk nls visls oisti alksfeumr fn fqumnmcrml. 6.3  6.1   6.1

Fk ni plsmamñk oinnigi fk fn mtfj iktfrmlr gftfrjmkf nls ékeunls ο y    quf dlrjik nls omnls alk

rfspfatl i ni olrmzlktin, ikltf nls vinlrfs fk ni Wicni 9. 6.7   Sfinmaf 3 jfgmamlkfs jés, virmikgl fk aigi aisl nis dufrzis aijcmikgl nis jisis gf nls visls. Nls 6.7 gitls lctfkmgls sf ikltik fk ni Wicni 9. Wicni 9 K

j9 (be)

j3 (be)

j1 (be)

D9 (K)

D3 (K)

D1 (K)

ο ( l)

   ( l)

9 3 1

Jikuin gf Niclritlrml

Xéemki 64

   

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Xiri fn fqumnmcrml gf uk aufrpl rêemgl

C I

I

c3

c9

c1 C

L

L D9 : j9 e

D3 : j3 e

D1 : j1 e

Dmeuri 5 c

Dmeuri 5i

6.6   Mkstinf fn fqumpl aljl sf jufstri 6.6 jufstri fk ni Dmeuri 5(i), isfeurf ni olrmzlkticmnmgig gf ni cirri IC aalk lk nls tlrkmnnls quf fsték fk nls fxtrfjls gf ni cirri. 6.4   Alnlquf 1 pfsis slcrf ni cirri aljl mkgmai ni Dmeuri 5(c) y cusquf fk fsti vfz ni olrmzlktinmgig gf 6.4 ni cirri, ucmaikgl igfauigijfktf nis pfsis. 6.5   Fkaufktrf nls crizls gf jljfktl gf nis dufrzis jmgmfkgl, alk ni wmkaoi, nis gmstikamis gfn pmvltf 6.5 in puktl gf ipnmaiamñk gf nis dufrzis fk ni cirri. 6.?   Sfpmti plr 1 vfafs fn pisl iktfrmlr piri ltris jisis alk ltrls crizls gf jljfktl. Ikltf sus gitls 6.? fk ni Wicni 3 Wicni 3

K

j9 (be)

j3 (be)

j1 (be)

D9 (K)

D3 (K)

D1 (K)

c9 (j)

c3 (j)

c1 (j)

9 3 1

Jikuin gf Niclritlrml

Xéemki 65

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

4  XSLAFQIJMFKWL ] IKINMQMQ

(

Dêsmai Efkfrin M

)

Fqumnmcrml gf uki pirtêauni

4.9   Alk nls gitls fxpfrmjfktinfs ikltigls fk ni Wicni 9 y oiamfkgl usl gf nis Fauiamlkfs (4) oiei nls 4.9 aénaunls rfspfatmvls y nnfkf ni Wicni 1 y ni Wicni 7.

Wicni 10 Aljplkfktfs 10 Aljplkfktfs x, gf nis dufrzis dufrzis

K

D9x (K)

D3x (K)

D1x (K)

Ρ Dmx (K)

D1y (K)

Ρ Dmy (K)

9 3 1

Wicni 70 Aljplkfktfs 70 Aljplkfktfs y, gf nis dufrzis

K

D9y (K)

D3y (K)

9 3 1

Jikuin gf Niclritlrml

Xéemki 6?

 

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

Dêsmai Efkfrin M

Fqumnmcrml gfn aufrpl rêemgl  rêemgl 

4.3   Alk nls gitls ikltigls fk ni Wicni 3, oiamfkgl usl gf ni Fauiamñk (7) y fn alkvfkml gf rltiamñk gf 4.3 nls jljfktls, oiei nls aénaunls gf nls jljfktls gf nis dufrzis, rfspfatl in pmvltf (puktl L) ikltf nls vinlrfs fk ni Wicni 6

Wicni 6. Tinlrfs gf nls jljfktls gf nis dufrzi

K

χ9 (Kj)

χ3 (Kj)

χ1  (Kj)

Ρ χl  (Kj)

9 3 1

5 

SFQVNWIGLQ

(

)

Fqumnmcrml gf uki cirri 9° Alkgmamñk K

Ρ Dx 

3° Alkgmamñk Ρ Dy 

Ρ χl 

9 3 1

? 

ALKANVQMLKFQ

Jikuin gf Niclritlrml

(

) Xéemki 6=

 

Vkmvfrsmgig Kiamlkin @lref Cisigrf Erlojikk Diauntig gf Amfkamis Gfpirtijfktl Iaigíjmal gf Dêsmai

 

Dêsmai Efkfrin M

?.9   ¼Wlgis nis dufrzis quf mktfrvmfkfk fk fn fqumnmcrml tmfkfk tlrquf