Red Telefonia - Ejercicios

 

^LKVNSZKABA LBJKDLB@ IB[DS AN ZBL IBSJDZ

Fbju`tba an Klmnlknréb N`njtrúlkj N`njtrúlkjb b N`ëjtrkj N`ëjtrkjb b y Qn`njdiulkjbjkdlns

_ `blns `blns an ansbrr sbrr d``d ``d an an r nans y snrvk snrvkjk jkds ds K   _râjtkjb  Klfdrin fklb`

 Zki  Zk iu` u`b bjk úl an bjj jjn nsd b K lt ltn nr ln lntt

Hdrbrkd7

Vknrlns 287?? ‚  3?7??  3?7?? hrs _rdfnsdr7

Vé`jhnz Zbladvb` Gns÷s B`cnrtd B`uilds7

Cdu`blmmnr Òbònz Gdbl Iblun`

2=2;?31=

 Gubrnz Kzquknrad ]blab B``ksdl

2=2;?38=

@ëvbld Hubljb @uks Fnrlblad

2=2;??8>

@kibjd Vbrmbs Nrlnstd Jbr`ds

2=2;?366

Mbibrrb Nvblmn`kstb Lbtb`kb

2=2;?362

3?32-2

 

 

 

Sna an tn`nfdléb Ngnrjkjkds K

Nsjnlbrkd 2 

Jdid klmnlknrd rnspdlsbc`n nl n` ansp`knmun an ulb rna an tn`nfdléb, sn tknln bskmlbad ul prnsupunstd tdtb` an 1 ??? ??? an aú`brns binrkjblds pbrb kip`ninltbr n` snrvkjkd an tn`nfdléb nl 6 pdc`bads b` kltnrkdr an` _nr÷. Nl nstbs pdc`bjkdlns p dc`bjkdlns sn tknln ulb prdynjjkúl an nsjb`bck`kaba an` 2?% pbrb `ds skmuknltns jkljd bòds. Zu trbcbgd jdlskstn nl aksnòbr `b rna an tn`nfdléb pbrb qun `bs ``bibabs `djb`ns nl `ds pdc`bads junltnl jdl ulb prdcbck`kaba iâxkib an c`dqund (MdZ) an 2%, iknltrbs qun pbrb `b jdlnxkúl hbjkb n` nxtnrkdr ancnrâ prdpdrjkdlbr n` ingdr mrbad an snrvkjkd qun snb pdskc`n. N` fbcrkjbltn `n prdpdrjkdlbrâ n` jbc`n qun snb lnjnsbrkd y `ds j`knltns ancnrâl pbmbr n` prnjkd an su tnriklb`. Dtrd abtd kipdrtbltn pbrb jdlskanrbr ns qun nl ulb nvb`ubjkúl rnjknltn sn jdiprdcú qun ulb pdc`bjkúl skik`br b` pdc`bad 3 sun`n rnb`kzbr ul tdtb` an 3?? ``bibabs nl hdrb pkjd, jdl ulb inakb an 2:8.> snmulads an aurbjkúl. Ancn bsuikr tbickël qun `ds dtrds pdc`bads tknlnl ulb jbltkaba an trâfkjd akrnjtbinltn prdpdrjkdlb`, pnrd jdl ulb vbrkbjkúl anpnlaknlad an `b zdlb. Nl zdlbs jdinrjkb`ns sn mnlnrb n` adc`n an trâfkjd qun nl `bs zdlbs rnskanljkb`ns. _unan tdibr jbab jnltrb` jdid ul mrbl jdliutbadr tn`nfúlkjd skl c`dqund kltnrld. Ancnrâ jdlskanrbr b` inlds ulb jnltrb` an trâlsktd nl `b rna an tn`nfdléb.

Zd`ujkúl7

Abtds7 

 

_rnsupunstd91??? _rnsupunstd91? ?? ??? 

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C92% (``bibabs `djb`ns) 

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C94 (``bibabs hbjkb rna nxtnrlb)  

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Nsjb`bck`kaba92?% 

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B(zdlb jdinrjkb`)93B(zdlb rnskanljkb`)  

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_dc`bjkúl 37 3?? ``bibabs, 2:8,>s.  

 

 

Akbmrbib an` trâfkjd `b rna.

Akbmrbib an `b nstrujturb an `b rna.

Akbmrbib an trâfkjd

Jâ`ju`d an trâfkjd bjtub`   9  ∝  () 

Adlan7 

 

B7 trâfkjd tn`nfúlkjd 

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L7 l÷inrd an ``bibabs aurbltn `b hdrb pkjd  

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ti7 tknipd prdinakd an aurbjkúl an `bs ``bibabs  

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Nr`blm7 ulkaba an trâfkjd 

 

 

Nl `b pdc`bjkúl 3 (zdlb jdinrjkb`)7   9 (3?? ∝ 2:8,>)/:6?? 9 =,=   Jb`ju`blad `b anlskaba an trâfkjd nl ulb pdc`bjkúl jdinrjkb`

Anlskabaj 9 (trâfkjd tdtb` / jbltkaba an usubrkds) 9 (=,= nr`) / (=? usubrkds) 9 ?,22 Nr`/usubrkd Nl cbsn b nstn jâ`ju`d anaujkids qun ul usubrkd mnlnrb ul prdinakd an ?,22Nr` an trâfkjd aurbltn `b hdrb pultb nl ulb zdlb jdinrjkb`. Jb`ju`blad `b anlskaba an trâfkjd nl ulb pdc`bjkúl rnskanljkb`

Anlskabar 9 Anlskaba j * ?.> 9 ?,?>> Nr`/u B pbrtkr an nstds abtds pdanids antnriklbr n` trâfkjd nl `bs aniâs pdc`bjkdlns  

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_2 9< B 9  ∝  9 ?, ?,22 22 ∝ 2?? 2?? 9 22     _: 9< B 9  ∝  9 ?, ?,22 22 ∝ 3? 9 3, 3,3 3      

 

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 ∝ ∝  9 ?,?> ?, ?,22 22>∝ ∝3? 3,3 31     _1 9< 9< B B9 9  _> ?>> 8?993, 1, 1,1     9 ?, _6 9< B 9  ∝  9 ?, ?,?> ?>> > ∝ >? 9 3, 3,=> =>   

Akbmrbib an trâfkjd

Jâ`ju`d an trâfkjd b futurd

_brb akinlskdlbr banjubabinltn `b rna tn`nfúlkjb ancnids tnlnr nl junltb n` jrktnrkd a ann nsjb`bck`kaba, n` jub` jdlskstn nl prnanjkr n` % an jrnjkiknltd b futurd. Nl nstn ngnrjkjkd hby ulb prdynjjkúl an jrnjkiknltd nstkibab an` 2?% nl `ds prúxkids bòds.   9  + (?,2) 9 2,2 

 

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_2 9 22 Nr` * 2,2 9 23.2 Nr` _3 9 =,= Nr` * 2,2 9 8,1= Nr`

 

   

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_: 9 3,3 Nr` * 2,2 9 3,13 Nr` _1 9 3,3 Nr` * 2,2 9 3,13 Nr` _> 9 1,1 Nr` * 2,2 9 1,81 Nr` _6 9 3,=> Nr` * 2,2 9 :,?3> Nr`

Akbmrbib an trâfkjd

Antnriklblad n` l÷inrd an trdljb`ns

_brb antnriklbr n` l÷inrd an trdljb`ns lnjnsbrkd nl jbab pdc`bjkúl utk`kzbrnids n` pbrâintrd an mrbad an snrvkjkd (C) qun fdrib pbrtn an `ds abtds nl nstn ngnrjkjkd. B pbrtkr an nstds abtds pdarnids antnriklbr n` l÷inrd an trdljb`ns utk`kzblad `b tbc`b Nr`blm C.

Nl cbsn b nstds rnsu`tbads pdanids klakjbr qun n` l÷inrd an trdljb`ns pbrb jbab pdc`bjkúl ns7

 

   

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_2 _3 _: _1 _> _6

B9 23,2 Nr` B9 8,1= Nr` B9 3,13 Nr` B9 3,13 Nr` B9 1,81 Nr` B9 :,?3> Nr`

C92% C92% C92% C92% C92% C C92% 92%

L932 L926 L9= L9= L922 L98

Qrâfkjd Qdtb` qun dfrnjnl `bs 6 pdc`bjkdlns    9 23, 23,2 2 + 8,1= 8,1= + 3,13 3,13 + 3,13 3,13 + 1,8 1,81 1 + :,?3> :,?3>  9 ::,3 ::,3=> =>   Jbltkaba tdtb` an Qrdljb`ns7    9 32 + 26 26 + = + = + 2 22 2 + 8 9 =?  Jbltkaba tdtb` an bcdlbads7    9 2?? + =? + 3? + 3? + 8? + >? 9 :1?  Akbmrbib an trâfkjd

Bhdrb qun jdltbids jdl tdab `b klfdribjkúl an` akbmrbib an trâfkjd, prdjnanids b jdip`ntbr n` akbmrbib an nstrujturb an `b rna tn`nfúlkjb.

Jdstds

 

 

_brb antnriklbr n` l÷inrd an sb`kabs nl `b jnltrb` an trâlsktd, ancnids jdldjnr n` sb`ad akspdlkc`n an` prnsupunstd bskmlbad pbrb n` prdynjtd. Cuj`n an bcdlbad

Znm÷l n` tbrkfbrkd n` cuj`n an bcdlbad tknln ul jdstd an 3??? aú`brns binrkjblds. [ sn rnquknrn ul cuj`n an bcdlbad pdr jbab usubrkd an `b rna.           9 :1? ∝ 3??? 9 68? ???  Jnltrb`ns `djb`ns

Znm÷l n` tbrkfbrkd ancnids sn`njjkdlbr `b jnltrb` iâs bprdpkbab pbrb jbab pdc`bjkúl.  

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2 3 : 1 > 6

9< 9< 9< 9< 9< 9<

2??  , ,    2??   ( :> :>? ? ???)  =?  , ,    =? =?   ( 3>? ???) ???)  3?  , ,    :? :?   ( 23> ???) ???)  3?  , ,    :? :?   ( 23> ???) ???)  8?  , ,    2?? 2??   ( :>? ? ???) ??)  >?  , ,    >? >?   ( 3?? ???) ???) 

      9 21?? ???  Jdstd an `bs sb`kabs an `bs jnltrb`ns `djb`ns

Zb`kabs `djb`ns 9 =? Jdstd tdtb` an sb`kabs `djb`ns 9 =? * >??? 9 :>? ??? Nltrbabs an trblsktd 9=? Jdstd tdtb` nl nltrbabs 9 =? * >??? 9 :>? ??? Zb`ad

Qdtb` 1 ??? ??? ‚ 68? ??? ‚ 2 1?? ??? ‚ :>? ??? ‚ :>? ??? 9 2 33? ??? Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl :? ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. 23 233? 3????/ ???/:?? :???? ?? 9 1?,66 1?,66 9< 1?   

Fklb`inltn, sk tnlnids 1? sb`kabs an trâlsktd, pdanids nstbc`njnr n` vb`dr an C usblad `b tbc`b Nr`blm C. Jdiprdcbrnids qun n` vb`dr an C ns an >%. > %.

 

 

KK

Nsjnlbrkd 3 

Hb skad jdltrbtbad pbrb kip`ninltbr ul trbid an `b rna tn`nfúlkjb an uld an `ds prkljkpb`ns dpnrbadrns an` pbés, jdid gnfn an prdynjtd sn `n bskmlb ul prnsupunstd an 3 ;?? ??? aú`brns binrkjb binrkjblds. lds. N` prdynjtd jdlskstn nl ansp`nmbr ulb rna tn`nfúlkjb pbrb btnlanr b jubtrd pdc`bjkdlns uckjbabs nl n` anpbrtbinltd an @b @kcnrtba. Ancnrâ aksnòbr `b rna tn`nfdléb bsuiknlad ul jrnjkiknltd an trâfkjd an` 2>% prdynjtbad hbjkb n` 3?36, jdlskanrn ul mrbad an snrvkjkd an ?,>% y `b inldr prdcbck`kaba an c`dqund hbjkb n` rnstd an `b rna (Nl n` aksnòd ancnrâ kanltkfkjbr y nspnjkfkjbr nstb prdcbck`kaba an c`dqund pdskc`n). N` fbcrkjbltn prdpdrjkdlbrâ n` jbc`nbad an iblnrb mrbtuktb y `ds j`knltns pbmbrâl n` n ` jdstd an su tnriklb`. Jdlskanrn tbickël qun aurbltn ulb inakjkúl prnvkb sn nstbc`njkú qun ul mrupd an susjrkptdrns skik`br b `b pdc`bjkúl 1 sun`n hbjnr bprdxkibabinltn 3>? ``bibabs nl hdrb pultb, jdl ulb inakb an ;3,=: snmulads an aurbjkúl. @bs dtrbs pdc`bjkdlns mnlnrbl ul trâfkjd akrnjtbinltn prdpdrjkdlb`, n` adc`n nl n` jbsd an `bs pdc`bjkdlns nl zdlb jdinrjkb` rnspnjtd b `bs zdlbs rnskanljkb`ns. Bsuib jbab jnltrb` jdid ul mrbl jdliutbadr tn`nfúlkjd skl c`dqund kltnrld, y jdlskanrn pdr `d inlds ulb jnltrb` an trâlsktd.

   

 

Zd`ujkúl7

Abtds7 

 

_rnsupunstd9 3 ;?? ???  

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C9?.>% (``bibabs `djb`ns) 

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C94 (``bibabs hbjkb rna nxtnrlb)  

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Nsjb`bck`kaba92>% 

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B(zdlb jdinrjkb`)93B(zdlb rnskanljkb`)   _dc`bjkúl 37 3>? ``bibabs, ;3.=:s.  

Jdip`ntblad n` akbmrbib an` trâfkjd _2 

_3 

3?

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J 

S 

>?

8?

J 

S 

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_1 

  9  ∝  () 

Adlan7 

 

B7 trâfkjd tn`nfúlkjd 

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L7 l÷inrd an ``bibabs aurbltn `b hdrb pkjd  

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ti7 tknipd prdinakd an aurbjkúl an `bs ``bibabs  

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Nr`blm7 ulkaba an trâfkjd 

Nl `b pdc`bjkúl 1 (zdlb rnskanljkb`)7 r nskanljkb`)7   9 (3>? ∝ ;3.=:)/:6?? 9 6.11   Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl jdinrjkb`

    9 (â (â   /      ) ) 9 (6.11 ) / (8?   ) ) 9 ?.?8 / / 

Nl cbsn b nstn jâ`ju`d anaujkids qun ul usubrkd mnlnrb ul prdinakd an ?.?8Nr` an trâfkjd aurbltn `b hdrb pultb nl ulb zdlb rnskanljkb`.

   

 

Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl rnskanljkb`   9     ∝ 3 9 ?. ?.26 26 / / 

B pbrtkr an nstds abtds pdanids antnriklbr n` trâfkjd nl `bs aniâs pdc`bjkdlns  

_2 9< B 9  ∝  9 ?. ?.26 26 ∝ 3? 9 :. :.3 3    

 

_3 9< B 9  ∝   9 ?. ?.26 26 ∝ >? 9 8   

 

_: 9< B 9  ∝  9 ?. ?.?8 ?8 ∝ >? 9 1   

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?.?8 ?8 ∝ 8? 9 6. 6.1 1    _1 9< B 9  ∝  9 ?.

Akbmrbib an trâfkjd

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3 Nr`

2.6Nr`

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J 

Jâ`ju`d an trâfkjd b futurd

_brb akinlskdlbr banjubabinltn `b rna tn`nfúlkjb ancnids tnlnr nl junltb n` jrktnrkd an nsjb`bck`kaba, n` jub` jdlskstn nl prnanjkr n` % an jrnjkiknltd b futurd. Nl nstn ngnrjkjkd hby ulb prdynjjkúl an jrnjkiknltd nstkibab an` 2>% nl `ds prúxkids bòds.   9  + ( (? ?.2>) 9 2. 2.2 2>  

 

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_2 9 :.3 Nr` * 2.2> 9 :.68 Nr` _3 9 8 Nr` * 2.2> 9 ;.3 Nr` _: 9 1 Nr` * 2.2> 9 1.6 Nr` _1 9 6.1 Nr` * 2.2> 9 =.:6 Nr`

Akbmrbib an trâfkjd

_2 

3?

:.3Nr` :.68Nr`

1.6 Nr` 1 Nr`

>? J 

_: 

S 

J 

_3 

>?

8 Nr`  ;.3

=.:

6.1

Nr` 

6 Nr` 

Nr` 

8? S 

_1 

 

 

Antnriklblad n` l÷inrd an trdljb`ns

_brb antnriklbr n` l÷inrd an trdljb`ns lnjnsbrkd nl jbab pdc`bjkúl utk`kzbrnids n` pbrâintrd an mrbad an snrvkjkd (C) qun fdrib pbrtn an `ds abtds nl nstn ngnrjkjkd. B pbrtkr an nstds abtds pdarnids antnriklbr n` l÷inrd an trdljb`ns utk`kzblad `b tbc`b nr`blm C.

Nl cbsn b nstds rnsu`tbads pdanids klakjbr qun n` l÷inrd an trdljb`ns pbrb jbab pdc`bjkúl ns7  

_2 _3     _:   _1 

B9 :.68 Nr` B9 ;.3 Nr` B9 1.6 Nr` B9 =.:6 Nr`

C9?.>% C9?.>% C9?.>% C9?.>%

L92? L928 L922 L92>

Qrâfkjd Qdtb` qun dfrnjnl `bs 1 pdc`bjkdlns   9 :. :.68 68   + ;. ;.3 3   + 1. 1.6 6   + =. =.:6 :6   9 31 31.8 .81 1    Jbltkaba tdtb` an Qrdljb`ns7  9 2? 2 ? + 28 + 22 + 2> 9 >1  Jbltkaba tdtb` an bcdlbads7  9 3 ? + >? + >? + 8? 9 3? 3 ?? 

   

 

Akbmrbib an trâfkjd _2 

3?

:.3Nr` :.68Nr` 2? 

22 1.6 Nr` 1 Nr`

>?

J 

_3 

>?

_: 

S 

8 Nr`

;.3 Nr`

28 

2> =.:6Nr` 6.1Nr`

8?

_1 

S 

J 

Bhdrb qun jdltbids jdl tdab `b klfdribjkúl an` akbmrbib a kbmrbib an trâfkjd, prdjnanids prdjnanids b jdip`ntbr n` akbmrbib an nstrujturb an `b rna tn`nfúlkjb. 1.6 Nr` 

:.68 Nr`  C9?.>%  3?J 

3?*2?  ;.3 Nr` 

>?J 

C9?.>%  >?*28 

C9?.>%  >?*22 

C9?.>% 

>?S 

_: 

8?S 

_1 

=.:6 Nr` 

8?*2> 

Jdstds

_brb antnriklbr n` l÷inrd an sb`kabs nl `b jnltrb` an trâlsktd, ancnids jdldjnr n` sb`ad akspdlkc`n an` prnsupunstd bskmlbad pbrb n` prdynjtd. Cuj`n an bcdlbad

Znm÷l n` tbrkfbrkd n` cuj`n an bcdlbad tknln ul jdstd an 3??? aú`brns binrkjblds. [ sn rnquknrn ul cuj`n an bcdlbad pdr jbab usubrkd an `b rna. Jdstd tdtb` nl cuj`ns an bcdlbad 9 3?? x 3??? 9 1?? ??? Jnltrb`ns `djb`ns

Znm÷l n` tbrkfbrkd ancnids sn`njjkdlbr `b jnltrb` iâs bprdpkbab pbrb jbab pdc`bjkúl.  

_2 9< 3? ^subrkds, Jnltrb` jdl :? nltrbabs ( 23> ???)   _3 9< >? ^subrkds, Jnltrb` jdl >? nltrbabs ( 3?? ???)   _: 9< >? ^subrkds, Jnltrb` jdl >? nltrbabs ( 3?? ???)   _1 9< 8? ^subrkds, Jnltrb` jdl 2?? nltrbabs ( :>? ???) 

Jdstd tdtb` nl jnltrb`ns `djb`ns 9 8=> ???

 

 

Jdstd an `bs sb`kabs an `bs jnltrb`ns `djb`ns 

Zb`kabs `djb`ns 9 >1 Jdstd tdtb` an sb`kabs `djb`ns 9 >1 * >??? 9 3=? ??? Nltrbabs an trblsktd 9>1 Jdstd tdtb` nl nltrbabs 9 >1 * >??? 9 3=? ???

Zb`ad    9 3 ;?? ;?? ?? ??? ? ‚ 1?? ??? ‚ 8=> ??? ‚ 3= 3=? ? ??? ??? ‚ 3= 3=? ? ??? ??? 9 2 ? ?8> 8> ?? ??? ? 

Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl :? ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. 2 ?8 ?8> > ???/: ???/:??? ???? ? 9 :6.2= :6.2= 9< :6    

Fklb`inltn, sk tnlnids :6 sb`kabs an trâlsktd, pdanids nstbc`njnr n` vb`dr an C usblad `b tbc`b Nr`blm C. Jdiprdcbrnids qun n` vb`dr an C ns an 2%. 2 %. Jnltrb` an Qrâlsktd 

1.6 Nr` 

:.68 Nr`  C9?.>% 

C9?.>%  3?J  ;.3 Nr`  >?J 

>?*22 

3?*2? 

C9?.>% 

C9?.>% 

>?*28 

>1*:6  C92% 

>?S 

_: 

8?S 

_1 

=.:6 Nr` 

8?*2> 

 

 

KKK

Nsjnlbrkd : 

Hb skad jdltrbtbad pbrb aksnòbr ulb rna an tn`nfdléb pbrb crklabr snrvkjkd b > pdc`bjkdlns akstbltns adlan sn prdynjtb ul :?% an jrnjkiknltd b inakbld p`bzd. _brb `b ngnjujkúl an` prdynjtd sn `n hb anskmlbad ul prnsupunstd an : >?? ??? an aú`brns binrkjblds y jdl n``d ancn bsnmurbr ul MdZ an` 2% pbrb ``bibabs `djb`ns. Jdlskanrn tbickël qun aurbltn ulb inakjkúl prnvkb sn nstbc`njkú qun ul mrupd an susjrkptdrns skik`br b `b pdc`bjkúl 3 rnb`kzb bprdxkibabinltn 3?? ``bibabs jdl ulb inakb an 1;,> snmulads nl hdrb pkjd. @bs dtrbs pdc`bjkdlns mnlnrbl ul trâfkjd akrnjtbinltn prdpdrjkdlb`, nl n` jbsd an `bs zdlbs jdinrjkb`ns n` trâfkjd ns ul >?% bakjkdlb` b `bs zdlbs rnskanljkb`ns. Bsuib jbab jnltrb` jdid ul mrbl jdliutbadr tn`nfúlkjd skl c`dqund kltnrld, y jdlskanrn pdr `d inlds ulb jnltrb` an trâlsktd.

Zd`ujkúl7

Abtds7  

_rnsupunstd9 : >?? ???  

 

C92% (``bibabs `djb`ns) 

 

C94 (``bibabs hbjkb rna nxtnrlb)  

 

Nsjb`bck`kaba9:?% 

 

B(zdlb jdinrjkb`)92.>B(zdlb rnskanljkb`)  

 

_dc`bjkúl 37 3?? ``bibabs, 1;,>s. 

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Jâ`ju`d an trâfkjd bjtub`   9  ∝  () 

Adlan7 

 

B7 trâfkjd tn`nfúlkjd 



 

L7 l÷inrd an ``bibabs aurbltn `b hdrb pkjd  



 

ti7 tknipd prdinakd an aurbjkúl an `bs ``bibabs  



 

Nr`blm7 ulkaba an trâfkjd 

Nl `b pdc`bjkúl 3 (zdlb rnskanljkb`)7   9 (3?? ∝ 1;,>)/:6?? 9 3,=>   Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl rnskanljkb`     9 (â (â   /      ) ) 9 (3,=> ) / (>?   ) ) 9 ?,?>> ?,?>> / /  

Nl cbsn b nstn jâ`ju`d anaujkids qun ul usubrkd mnlnrb mnl nrb ul prdinakd an ?,?>>Nr` an trâfkjd aurbltn `b hdrb pultb nl ulb zdlb rnskanljkb`. Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl rnskanljkb`   9      ∝ (2 (2,> ,>)) 9 ?, ?,?> ?>> > ∝ 2, 2,> > 9 ?, ?,?8 ?83> 3> / / 

B pbrtkr an nstds abtds pdanids antnriklbr n` trâfkjd nl `bs aniâs pdc`bjkdlns  

_2 9< B 9  ∝  9 ?, ?,?> ?>> > ∝ 8? 9 1, 1,1 1   

 

_3 9< B 9  ∝  9 ?, ?,?> ?>> > ∝ >? 9 3, 3,=> =>   

 

_: 9< B 9  ∝   9 ?, ?,?8 ?83> 3> ∝ =? 9 >, >,== ==> >  

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?,?8 ?83> 3> ∝ 2? 2?? ? 9 8, 8,3> 3>    _1 9< B 9  ∝  9 ?, _> 9< B 9  ∝  9 ?, ?,?8 ?83> 3> ∝ 3? 9 2, 2,6> 6>   

Akbmrbib an Qrâfkjd

_2 

8?

1.1Nr

8.3>Nr 2?

_1 

? S  J  _3 

>?

3.=>N

S  _: 

=? J 

2.6>Nr

3? J 

>.== Nr

_> 

   

 

Jâ`ju`d an trâfkjd b futurd

_brb akinlskdlbr banjubabinltn `b rna tn`nfúlkjb ancnids tnlnr nl junltb n` jrktnrkd a ann nsjb`bck`kaba, n` jub` jdlskstn nl prnanjkr n` % an jrnjkiknltd b futurd. Nl nstn ngnrjkjkd hby ulb prdynjjkúl an jrnjkiknltd nstkibab an` :?% nl `ds prúxkids bòds.    9  + (?,:) 9 2,: 

 

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2 3 : 1 >

9 9 9 9 9

1, 1,1 1   ∝ 2, 2,: : 9 >, >,=3 =3    3, 3,=> =>   ∝ 2, 2,: : 9 :, :,>= >=> >     >,==> >,==>  ∝ 2,: 9 =,>?= =,>?=> >   8, 8,3> 3>   ∝ 2, 2,: : 9 2? 2?,= ,=3> 3>    2, 2,6> 6>   ∝ 2, 2,: : 9 3, 3,21 21> >    

Akbmrbib an trâfkjd _2 

8?

1.1Nr`  >.=3 Nr`

2?.= Nr` 8.3>Nr`

S 

_3 

>?

=?

_1 

J 

3.=> Nr` :.>=Nr`

S  _: 

2??

3.21 Nr` 2.6>Nr`

3?

_> 

J  >.== Nr` =.> Nr`

J 

Antnriklblad n` l÷inrd an trdljb`ns

_brb antnriklbr n` l÷inrd an trdljb`ns lnjnsbrkd nl jbab pdc`bjkúl utk`kzbrnids n` pbrâintrd an mrbad an snrvkjkd (C) qun fdrib pbrtn an `ds abtds nl nstn ngnrjkjkd. B pbrtkr an nstds abtds pdarnids antnriklbr n` l÷inrd an trdljb`ns utk`kzblad `b tbc`b Nr`blm C.

   

 

Nl cbsn b nstds rnsu`tbads pdanids klakjbr qun n` l÷inrd an trdljb`ns pbrb jbab pdc`bjkúl ns7  

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_2 _3 _: _1 _>

B9 >,=3 Nr` B9:,>=> Nr` B9=,>?=> Nr` B92?,=3> Nr` B93,21> Nr`

C92% L923 C92% L9; C92% L92> C92% L92; C92% L9=

Qrâfkjd Qdtb` qun dfrnjnl `bs 1 pdc`bjkdlns   9 >. >.=3 =3  + :.>=> :.>=>  + =. =.>? >?=> =>  + 2?. 2?.=3 =3> >   + 3.2 3.21> 1>  9 3;. 3;.6=3 6=3> >   Jbltkaba tdtb` an Qrdljb`ns7  9 23 23 + ; + 2 2> > + 2; + = 9 63 6 3  Jbltkaba tdtb` an bcdlbads7  9 8? + >? + =? + 2?? + 3? 9 :3?  Akbmrbib an trâfkjd _2 

8? 1.1Nr` >.=3Nr` 23 

2; 2?.= Nr` 8.3>Nr` 2?

S 

_3 

J 

>? 3.=>Nr` :.>= Nr`

;

=

3.21N 2.6>N

S 

_: 

_1 

3?

_> 

J 

=? >.==N

=.>Nr`

2>

J 

Bhdrban qunnstrujturb jdltbidsan jdl `b klfdribjkúl an` akbmrbib an trâfkjd, prdjnanids b jdip`ntbr n` akbmrbib `b tdab rna tn`nfúlkjb.

>.=3 Nr`  =.> Nr` 

C92%  8?J 

8?*23 

C92%  =?*2> 

:.>= Nr`  >?J 

=?S 

_: 

2??S 

_1 

C92%  >?*; 

2?.= Nr` 

C92% 

2;*2?? 

3?*=

C92%

3?J

2.6> Nr`

_> 

 

 

Jdstds

_brb antnriklbr n` l÷inrd an sb`kabs nl `b jnltrb` an trâlsktd, ancnids jdldjnr n` sb`ad akspdlkc`n an` prnsupunstd bskmlbad pbrb n` prdynjtd. Cuj`n an bcdlbad

Znm÷l n` tbrkfbrkd n` cuj`n an bcdlbad tknln ul jdstd an 3??? aú`brns binrkjblds. [ sn rnquknrn ul cuj`n an bcdlbad pdr jbab usubrkd an `b rna. Jdstd tdtb` nl cuj`ns an bcdlbad 9 :3? x 3??? 9 61? ??? Jnltrb`ns `djb`ns

Znm÷l n` tbrkfbrkd ancnids sn`njjkdlbr `b jnltrb` iâs bprdpkbab pbrb jbab pdc`bjkúl. 

 

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_2 9< 8? ^subrkds, Jnltrb` jdl 2?? nltrbabs (:>? ???) _3 9< >? ^subrkds, Jnltrb` jdl >? nltrbabs (3?? ???) _: 9< =? ^subrkds, Jnltrb` jdl =? nltrbabs (3>? ???) _1 9< 2?? ^subrkds, Jnltrb` jdl 2?? nltrbabs (:>? ???) _> 9< 3? ^subrkds5 Jnltrb` jdl :? nltrbabs (23> ???) Jdstd tdtb` nl jnltrb`ns `djb`ns 9 23=> ???

Jdstd an `bs sb`kabs an `bs jnltrb`ns `djb`ns 

Zb`kabs `djb`ns 9 63 Jdstd tdtb` an sb`kabs `djb`ns 9 63 * >??? 9 :2? ??? Nltrbabs an trblsktd 963 Jdstd tdtb` nl nltrbabs 9 63 * >??? 9 :2? ??? Zb`ad    9 : > >?? ?? ??? ??? ‚ 61? ??? ‚ 23 23=> => ??? ‚ :2? ??? ‚ :2 :2? ? ??? ??? 9 ;6 ;6> > ??? ??? 

Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl :? ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. ;6 ;6> > ?? ???/:? ?/:???? ??? 9 :3.26 :3.26 9< :3     

Fklb`inltn, sk tnlnids :3 sb`kabs an trâlsktd, pdanids nstbc`njnr n` vb`dr an C usblad `b tbc`b Nr`blm C. Jdiprdcbrnids qun n` vb`dr an C ns an 2?%.

   

 

>.=3 Nr`  =.> Nr` 

C92%  8?J 

C92% 

8?*23 

=?*2>  :.>= Nr`  >?J 

=?S 

_: 

2??S 

_1 

C92%  >?*; 

C92% 

2?.= Nr` 

2;*2?? 

63*:3 C72?%

3?*=

3?  

C92%

2.6> Nr`

_> 

2.  Zk tuvknsn qun bsnmurbr ul MdZ an >% hbjkb `b rna nxtnrlb. ´Ruë tkpd an sb`kab an trblsktd rnjdinlabréb jdiprbr4 Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl 3= ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. ;6> ???/3= ???/3= ??? 9 :>.= 9< :>     

Fklb`inltn, sk tnlnids :> sb`kabs an trâlsktd, pdanids nstbc`njnr n` vb`dr an C usblad `b tbc`b Nr`blm C. Jdiprdcbrnids qun n` vb`dr an C ns an >%. Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl 3> ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl.

 

 

;6 ;6> > ???/3> ???/3>?? ??? ? 9 :8.6 9< :8     

Fklb`inltn, sk tnlnids :8 sb`kabs an trâlsktd, pdanids nstbc`njnr n` vb`dr an C usblad `b tbc`b Nr`blm C. Jdiprdcbrnids qun n` vb`dr an C ns an >%. Jdl jub`quknrb an `bs dtrbs ads sb`kabs an trblsktd sn `dmrbréb dctnlnr n` >% 3.  Zk funsn pdskc`n btnlanr b `bs 3 pdc`bjkdlns rnskanljkb`ns jdl ulb iksib jnltrb` y b `bs : pdc`bjkdlns jdinrjkb`ns jdl dtrb. ´Juâltbs trdljb`ns sn bhdrrbréb pbrb kltnrjdlnjtbr `bs jnltrb`ns `djb`ns jdl `b an trblsktd4 Nl n` jbsd an pdc`bjkdlns rnskanljkb`ns7   9 (3?? ∝ 1;,>)/:6?? 9 3,=>   Anlskaba an trâfkjd nl ulb pdc`bjkúl rnskanljkb` pdc`bjkúl 3     9 (â (â   /      ) ) 9 (3,=> ) / (>?   ) ) 9 ?,?>> ?,?>> / /   Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl rnskanljkb`   9      ∝ (2 (2,> ,>)) 9 ?, ?,?> ?>> > ∝ 2, 2,> > 9 ?, ?,?8 ?83> 3> / / 

B pbrtkr an nstds abtds pdanids antnriklbr n` trâfkjd nl `bs aniâs pdc`bjkdlns  

_2 9< B 9  ∝  9 ?, ?,?> ?>> > ∝ 8? 9 1, 1,1 1   

 

_3 9< B 9  ∝  9 ?, ?,?> ?>> > ∝ >? 9 3, 3,=> =>   

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Jâ`ju`d an trâfkjd b futurd    9  + (?,:) 9 2,:   

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2 9 1, 1,1 1   ∝ 2, 2,: : 9 >, >,=3 =3    3 9 3, 3,=> =>   ∝ 2, 2,: : 9 :, :,>= >=> >    

Nl cbsn b nstds rnsu`tbads pdanids klakjbr qun n` l÷inrd an trdljb`ns pbrb jbab pdc`bjkúl ns7  

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_2 _3

B9 >,=3 Nr` B9:,>=> Nr`

C92% L923 C92% L9;

NL NZQN JBZD HBCSKB 32 NL@BJNZ QSDLJB@NZ

 

 

Qrâfkjd Qdtb` qun dfrnjnl `bs 1 pdc`bjkdlns   9 >. >.=3 =3  + :.>=> :.>=>  9 ;, ;,3; 3;> >    Jbltkaba tdtb` an Qrdljb`ns7  9 23 23 + ; 9 32  Jbltkaba tdtb` an bcdlbads7  9 8? + >? 9 2:?  Jdstds

_brb antnriklbr n` l÷inrd an sb`kabs nl `b jnltrb` an trâlsktd, ancnids jdldjnr n` sb`ad akspdlkc`n an` prnsupunstd bskmlbad pbrb n` prdynjtd. Cuj`n an bcdlbad

Znm÷l n` tbrkfbrkd n` cuj`n an bcdlbad tknln ul jdstd an 3??? aú`brns binrkjblds. [ sn rnquknrn ul cuj`n an bcdlbad pdr jbab usubrkd an `b rna. Jdstd tdtb` nl cuj`ns an bcdlbad 9 2:? x 3??? 9 36? ??? Jnltrb`ns `djb`ns

Znm÷l n` tbrkfbrkd ancnids sn`njjkdlbr `b jnltrb` iâs bprdpkbab pbrb jbab pdc`bjkúl.  

_2 9< 8? ^subrkds, Jnltrb` jdl 2?? nltrbabs (:>? ???)   _3 9< >? ^subrkds, Jnltrb` jdl >? nltrbabs (3?? ???)

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Jdstd tdtb` nl jnltrb`ns `djb`ns 9 >>? ??? Jdstd an `bs sb`kabs an `bs jnltrb`ns `djb`ns 

Zb`kabs `djb`ns 9 32 Jdstd tdtb` an sb`kabs `djb`ns 9 32 * >??? 9 2?> ??? Nltrbabs an trblsktd 932 Jdstd tdtb` nl nltrbabs 9 32 * >??? 9 2?> ??? Zb`ad    9 : >?? >?? ?? ??? ? ‚ 36? ??? ‚ >>? ??? ‚ 2? 2?> > ??? ??? ‚ 2? 2?> > ??? ??? 9 3 1 18? 8? ?? ??? ? 

Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl :? ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. 3 18 18? ? ?? ???/:? ?/:???? ??? 9 83.6 83.6 9< 83     

 

 

Nl n` jbsd an pdc`bjkdlns Jdinrjkb`ns7

  9

3?? 3?? ∝ 1;,> 1;,> :6??

9 3,=>   ∝ 2.> 9 1.23> 

Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl jdinrjkb` pdc`bjkúl>    9 (â (â    /      ) ) 9 (1,23 (1,23> > ) / (3? ) ) 9 ?,3?6> ?,3?6> / /  Anlskaba an trâfkjd nl ulb ul b pdc`bjkúl rnskanljkb`   9       ∝ (2,>) 9 ?, ?,3? 3?6> 6> ∝ 2, 2,> > 9 ?, ?,:? :?;: ;:=> => / / 

B pbrtkr an nstds abtds pdanids antnriklbr n` trâfkjd nl `bs aniâs pdc`bjkdlns  

_: 9< B 9  ∝   9 ?, ?,:? :?;: ;:=> => ∝ =? 9 32, 32,6> 6>63 63> >   

 

_1 9< B 9  ∝  9 ?, ?,:? :?;: ;:=> => ∝ 2? 2?? ? 9 :? :?,; ,;:= :=> >   

 

_> 9< B 9  ∝  9 ?, ?,:? :?;: ;:=> => ∝ 3? 9 6. 6.28 28=> =>   

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Jâ`ju`d an trâfkjd b futurd    9  + (?,:) 9 2,:   

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: 9 32.6> 32.6>63> 63>  ∝ 2,: 9 38.23 38.23   1 9 :?,;: :?,;:=> =>  ∝ 2,: 9 1? 1?,3? ,3?   > 9 6. 6.28 28=> =>   ∝ 2,: 9 8. 8.?> ?>   

Nl cbsn b nstds rnsu`tbads pdanids klakjbr qun n` l÷inrd an trdljb`ns pbrb jbab pdc`bjkúl ns7  

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_: _1 _>

B938,23 Nr` C92% L9:; B91?,3? Nr` C92% L9>: B98,?> Nr` C92% L926

NL NZQN JBZD HBCSKB 2?8 NL@BJNZ QSDLJB@NZ Qrâfkjd Qdtb` qun dfrnjnl `bs 1 pdc`bjkdlns   9 38 38.2 .23 3   + 1? 1?.3 .3? ?   + 8. 8.?> ?>   9 =6 =6,: ,:= =    Jbltkaba tdtb` an Qrdljb`ns7  9 :; + >: + 26 9 2?8  Jbltkaba tdtb` an bcdlbads7  9 =? + 2?? + 3? 9 2;? 

 

 

Jdstds

_brb antnriklbr n` l÷inrd an sb`kabs nl `b jnltrb` an trâlsktd, ancnids jdldjnr n` sb`ad akspdlkc`n an` prnsupunstd bskmlbad pbrb n` prdynjtd. Cuj`n an bcdlbad

Znm÷l n` tbrkfbrkd n` cuj`n an bcdlbad tknln ul jdstd an 3??? aú`brns binrkjblds. [ sn rnquknrn ul cuj`n an bcdlbad pdr jbab usubrkd an `b rna. Jdstd tdtb` nl cuj`ns an bcdlbad 9 2;? x 3??? 9 :8? ??? Jnltrb`ns `djb`ns

Znm÷l n` tbrkfbrkd ancnids sn`njjkdlbr `b jnltrb` iâs bprdpkbab pbrb jbab pdc`bjkúl.  

_: 9< =? ^subrkds, Jnltrb` jdl =? nltrbabs (3>? ???)   _1 9< 2?? ^subrkds, Jnltrb` jdl 2?? nltrbabs (:>? ???)   _> 9< 3? ^subrkds5 Jnltrb` jdl :? nltrbabs (23> ???)

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Jdstd tdtb` nl jnltrb`ns `djb`ns 9 =3> ??? Jdstd an `bs sb`kabs an `bs jnltrb`ns `djb`ns 

Zb`kabs `djb`ns 9 2?8

Jdstd tdtb` an sb`kabs `djb`ns 9 2?8 * >??? 9 >1? ??? Nltrbabs an trblsktd 92?8 Jdstd tdtb` nl nltrbabs 9 2?8 * >??? 9 >1? ??? Zb`ad    9 : >?? >?? ?? ??? ? ‚ :8? ??? ‚ =3> ??? ‚ >1 >1? ? ??? ??? ‚ >1 >1? ? ??? ??? 9 2 : :2> 2> ?? ??? ? 

Bsuiknlad n` jdstd an jbab sb`kab an trâlsktd nl :? ???, pdanids nstbc`njnr n` l÷inrd an sb`kabs qun pdanids jdstbr rnb`kzblad ulb akvkskúl. 2 :2 :2> > ???/:? ???/:??? ??? ? 9 1:,8 1:,8 9< 1:   

NLQSN BICDZ HBCSÉB 23> ZB@KABZ [ ZK BICDZ F^NSBL G^LQBZ ZD@D HBCSÉB :3 ZB@KABZ @b akfnrnljkb snréb ;:.