Ejercicios Balance Tercera Parte

 

RLOSBX[ON@N L@KOAL@E NB [@L @JR[^ÇL NB @XBPROV@

C@KRE^@N NB OLJBLOBXÇ@ NB VXAKB[A[ B[KRBE@ VXACB[OAL@E NB OLJBLOBXÇ@ PRÇGOK@  

VXAHEBG@[ ^BXKBX V@X^B  

B[^RNO@L^B[4  

@V@T@ JR^OBXXBT DA[BV VBNXA MR@K@[O VCAKKAXO ERO[ BLXOPRB

NAKBL^B4 XAE@LNA [O]^A H@[RXKA

KRX[A4 H@E@LKB NB G@^BXO@ _ BLBXJÇ@ @RE@4 ^BXKBX @ÐA H  

@XBPROV@ ‛ VBXÔ  8680

 

XB[AERKOAL NB VXAHEBG@[ BDBXKOKOA[ VÀJOL@ 806

8. Rl` karrobltb nb `orb ` ;6¶K y 06% nb mugbn`n rbe`tov` sb mugonocok` bl ul` tarrb nb `spbrsoûl `no`hàtok` qub culkoal` ` V ≍ 0 `tg. Be `orb qub bgbrjb nbhb tblbr ul` mugbn`n rbe`tov` nb >6%. `) Nbt Nbtbrg brgolb olb e` mug mugbn bn`n `n `hsae `hsaeut` ut` y e` tbg tbgpbr pbr`tu `tur` r` nb s`tur`k s`tur`koûl oûl `no`hàt `no`hàtok` ok` nbe `orb nb bltr`n`.  h) Rsb be no`jr`g` psokragïtroka p`r` k`ekue`r (0) e` vbeakon`n ` e` ku`e sb nbhb `jrbj`r `ju` p`r` mugonocok`r 0666 ij/m nbe `orb nb bltr`n`, y (8) e` tbgpbr`tur` nbe `orb nb s`eon`.

[aeukoûl ` ± [b utoeoza be no`jr`g` psokagïtroka kal ul` tbgpbr`tur` nb hueha sbka nb ;6¶K y

06 % nb mugbn`n rbe`tov`.

^70;.8 ¶K

M`hs76.668

tbgpbr`tur` Xbspubst`. E` mugbn`n `hsaeut` bs 6.6683 Ij M8A/Ij `orb sbka y e` tbgpbr`tur` nb s`tur`koûl `no`hàtok` bs 0;.8 ¶K

 

 

h) (0) e` vbeakon`n ` e` ku`e sb nbhb `jrbj`r `ju` p`r` mugonocok`r 0666 ij/m nbe `orb nb bltr`n`. [b utoeoza be no`jr`g` psokagïtroka kal ul` tbgpbr`tur` nb hueha môgbna nb 0;.8¶K y >6 % nb mugbn`n rbe`tov`.

M`hs76.663;

E` vbeakon`n nb ceuda nb `orb sbka bl e` bltr`n` bs4

(

  )(

 Ijnb`orb m  Ijnb`orb g`orb 7??:.> m

g`orb 7

0666

  0 Ij nb `orb 0.6683 Ij nb `orb

)

E` k`lton`n nb `ju` qub sb v` bv`par`r bstà n`n` par e` nocbrblko` nb vbeakon`nbs nb ceuda nb bltr`n` y s`eon` nb e` karrobltb nb `orb4

(

g`ju` 7

??:.>

 )

 Ij  Ij nb `o `orrb m

( 6.663;∘ 6.6683 )

8 g`ju` 7 ;.:  Ij nb M  A m

(8) e` tbgpbr`tur` nbe `orb nb s`eon`

 Ij M 8 A  Ij `orb

 

^bgpbr`tur` nb `orb nb s`eon` bs 80.8 ¶K

8. Rl `kb `kbotb otb nb jr`v jr`vbn` bn`nn bspb bspbkçc kçcok` ok` 6,=> 6,=> ceuyb nbs nbsnb nb ul t`lq t`lqub ub.. @ tr`vïs tr`vïs nb ul` tuhbrç` nb `kbra j`ev`loz`na nb 266 ct nb e`rja y noàgbtra lagol`e nb 3‗ m`st` ul  pulta H ` 066 pej nb `etur`. K`ekue`r e` prbsoûl lbkbs`ro` (bl psoj) bl be rbkopobltb ;

@ p`r` eajr`r ul ehc.ct/eh. ceuda vaeugïtroka nb 6,>2 ct /sbj, so e` pïrnon` par crokkoûl bl be sostbg` bs nb 0,? X4 0,;; psoj

 N`tas

± 76.=>  E7 266 ct   N7 3  M 7066  pej m E 70.?

(

  0 ct  08  pej

)7

=.;;

ct 

ehc √ ct  eh

[aeukoûl 

`) K` K`eku ekue`g e`gas as e` vvbea beakon kon`n `n nb ss`eo `eon` n`44 v 87∔ 8√j√m

 

v 87

∔(

8 ;8.0:>

v 878;.02

 g 8 s

)(

)

=.;; ct 

 ct  s

h) M`ee`g M`ee`gas as e` nblson nblson`n `n nbe nbe cuona cuona44

±7

 πceuona  π`ju`

6.=>

  πceuona

7

38.>

eh ct 

 π ceuona7 =;:.>=

 eh ;

ct  k) @peok`ga @peok`gass e` bku`koûl bku`koûl jblbr`e jblbr`e nb nb e` e` blbrjç` blbrjç`44 8

( S  )

 V 8∘ V0

0

( S  )

8

8

 π   7T 8∘ T 0+ 8 j   ∘ 8 j   ∘m E  V87 6 , nbpasota nbpasota `hobrta `hobrta S 076 , parqub parqub bs bsnbsp nbsprb rbko`h ko`heb eb T 0 7 6 , `etur` `etur` rb rbcbr cbrblko blko` ` m @ , m X 76 8

∘ V ( S  )   7 T  ∘   ∘m E 8

0

8

 π

∘ V

0

28.>03

 eh ; ct 

8j

( ∘ (

7=.;; ct 

 V07 0?0.28

8 ;8.0:>

ehc  8

ct 

 )

 ct  8;.02 s

8

 g 8 s

)

∘0.?

eh√ ct  eh

(  )   0  pso

0>>

 ehc  8

ct 

 V07 0.;;  pso

3. Rl` ka karro rroblt bltbb qub kal kaltob toblb lb 26% nb hbl hblkb kbla la y 26% nb taeub taeubla la bl g`s` g`s` ` 36´K 36´K sb `eogblt` ` ul bv`par`nar nb sogpeb c`sb. Be 36% nb e` `eogblt`koûl sb v`paroz`. @l`eoz`lna be v`par sb blkubltr` qub kaltoblb 3;,0 nb hblkbla bl g`s`. E`s karrobltbs nb eçquona y v`par s`ebl nbe bquopa ` 026´K. K`ekue`r be rbqubrogoblta nb k`earr p`r` be prakbsa par ij nb `eogbl k`ea `eogblt`koû t`koûll nb eçquona s`tur`na. s`tur`na. X4 P 7 ;=;,2 ID/Ij

 

[aeukoûl 

V`r` @4   Ij H7066   √6.2726 Ij m  Ij ^ 7066 m   √ 6.2726 Ij

H`sb nb Kàekuea7 066 Ij/m nb @

Be 36% nb @ sb v`paroz`, bltalkbs4 S 7 6.3 @ S 7 6.3 ( 066 )736

 Ij m

  Ij   √6.3;07;:.=3 Ij m  Ij ^ 736   √ 6.;3?788.0> Ij m H736

H`e`lkb ^at`e nb e` g`s`4   @ 7S + K 

K 7066∘ 367 >6

H`e`lkb V`rko`e nbe Hblkbla 26 ∘;:.=37 >6√ x h  x h76.;6;2  x h + x t 70  x t 7 6.3?32

V`r` K4 >6

H7

 Ij

6.;6;2

m √

08.0>

7

 Ij

 Ij m

 

^ 7>6

  Ij   √6.3?327 8:.=3 Ij m

M`ee`gas be k`ear @4 Ph7 26 Ij√;?>

  iD  70?:66 iD √6.37 00=86 iD   Ij

  iD  P 7 26 Ij√;32  Ij 70=826 iD √ 6.3706?26 iD  t 

V`r` e` c`sb v`par S4 Ph7 ;:.=3 Ij√0.:26 Pt 7 88.0> Ij√8.6?8

  iD   ( 026∘ 36 ) ¶ K 72?38.?2 iD   Ij ¶ K 

  iD   ( 026 ∘36 ) ¶ K 7 >03=.28 iD   Ij ¶ K 

V`r` K4 Ph7 08.0> Ij√0.:26

8:.=3

7

  iD 

;=;2;0.?: iD  066 Ij

026

 Ij ¶ K  (

 Ij√

Pt 7 ∾P

8.6?8

  iD   ( 026 ∘36 ) ¶ K 70?08.62 iD   Ij ¶ K 

  7;=;.2;

28>2.>=

36

∘

) ¶ K 7

iD 

  iD   Ij

BDBXKOKOA[ VÀJOL@ 8;6

0. Be troke trokear arab abto toeb ebla la,, ul sa saev evbl bltb tb nbsb nbsblj ljr` r`s` s`lt ltbb nb us usaa bx bxtb tbls lsaa bl p` p`rt rtbs bs nb g`quol`ro`, sb pranukb bl ul` sbkublko` nb rb`kkoûl nb nas p`sas. Vrogbra sb kear` be btoebla p`r` n`r tbtr`kearabt`la. be ku`e sb sagbtb ` nbsmonrakear`koûl p`r` carg`r trokearabtoebla4

 

`)

O. OO. OOO.

+

 

8 K ( s) 8 M 8( j ) ↘ K 8 M > ( j) ∃ M c 

 

0 8

 

7+ 28.83 ID / gae

0

Ke8 ( j) +  M 8( j) ↘ MKe( j) ∃ M c  7∘?8.;0 ID / gae 8

8 K ( s)

;

0

+  M  ( j )+ Ke 8

8

8

8

7∘ 8:3.8 ID / gae

( j) ↘ K 8 MKe; (e ) ∃ M c 

OS.   K 8 M > ( j) + 8 Ke 8( j) ↘ K 8 M 8 Ke > (e) + M 8 ( j ) ∃ M ¶ r7∘;=2.:3 ID / gae `) [b sug` sug` e` bku`ko bku`koûl ûl (O) (O) y (OS)4 (OS)4

7+ 28.83 ID / gae K   M  ( j) + 8 Ke ( j) ↘ K   M  Ke (e) + M  ( j ) ∃ M ¶ r7∘ ;=2.:3 ID / gae +

8 K ( s) 8 M 8( j ) ↘ K 8 M > ( j) ∃ M c  8

>

8

8

8

>

8

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------8 K ( s) + M 8 ( j) + 8 Ke 8( j) ↘ K 8 M 8 Ke > ( e ) ∃ M c  7∘;;;.2 ID / gae

h) Eby nb Mbss

∃ M 7∃ M ¶ r + ∃ M s`eon`∘ ∃ M bltr`n` K 8 M > ( j )+ 8 Ke 8( j ) ↘ K 8 MKe; (e) + M 8 ( j) + MKe( j) ∃ M 71 K 8 M > ( j) ↘ 8 K ( s )+ 8 M 8 ( j) ∃ M c  7+ 28.83 ID / gae 8 K ( s) 0 8

;

0

+  M  ( j )+ Ke 8

8

8

8

7∘ 8:3.8 ID / gae

( j) ↘K 8 MKe; (e ) ∃ M c 

0

Ke8 ( j) +  M 8( j) ↘ MKe( j) ∃ M c  7∘?8.;0 ID / gae 8

K 8 M > ( j )+ 8 Ke 8( j ) ↘ K 8 MKe; (e ) + M 8 ( j) + MKe( j) ∃ M 7∘ >86.::  ID / gae

k) ±Kuàlta k`ear sb nbsprblnb a `hsarhb bl be prakbsa1

 

K 8 M > ( j )+ 8 Ke 8( j ) ↘ K 8 MKe; (e) + M 8 ( j) + MKe( j) ∃ M 7∘ 7∘ >86.:: ID / gae P 7 ∃ M  P 7∘ >86.:: ID / gae P 7∘ >86.::

 ID   gae   ID  √;66   7∘0838;0 m m gae

Xbspubst`4 [b nbsprblnb ul k`ear tat`e nb ∘0838;0  ID  m

;. Rl` gbzke` qub kaltoblb >3,6 % bl pbsa nb `kbtal` (KM ;KAKM;), 8:,6 % nb àkona `kïtoka (KM;KAAM) y 8:,6 % nb `lmçnrona `kïtoka (KM;KA-A-AKKM;) sb nbstoe` `  prbsoûl `tgascïrok`. `tgascïrok`. E` `eogblt`koûl bltr` ` ul` kaeugl` nb nbstoe`k nbstoe`koûl oûl ` ^7;>= I  y ` ul` vbeakon`n nb 02666 ij/m. Be nbstoe`na (qub s`eb par be tapb nb e` tarrb nb nbstoe nbs toe`k `koûl oûl)) bs bsb bsblk lko`e o`egbl gbltb tb `k `kbta btal` l` pur pur`, `, y be pranuk pranukta ta nb e` p`rtb p`rtb olcbro olcbroar  ar  kaltoblb 0.66 % nb e` `kbtal` qub bltr` ` e` kaeugl`. Be v`par nb s`eon` nbe tapb nb e` kaeugl` bltr` ` ul kalnbls`nar ` ;8? I y s`eb kaga eçquona ` ;6; I. E` got`n nbe kalnbls`na sb bxtr`b nbe sostbg` bl t`lta qub be rbsta sb rbtag` kaga rbceuda ` e` kaeugl`. Be eçquona qub s`eb par e` h`sb nb e` tarrb v` ` ul k`eblt`nar nb v`par, nalnb bs p`rko`egbltb bv`par`na. E` cr`kkoûl v`paroz`n` (;,86 % nb `kbtal`. :;,2 % nb àkona y 8;,6 % nb `lmçnrona `kïtoka) vubevb ` e` kaeugl` ` ul` tbgpbr`tur` nb ;?= I. y be eçquona rbsonu`e, t`ghoïl ` ;?= I y bl bquoeohroa kal be v`par, kalstotuyb be pranukta olcbroar a t`ghoïl ee`g`na pranukta nb kae` nb e` tarrb. Nbtbrgolb4 (`) e`s vbeakon`nbs nb ceuda y e`s kagpasokoalbs nb eas ceudas nb  pranuktas4 (h) be k`ear k`ear qub bs lbk lbkbs`roa bs`roa rbtor`r bl be ka kalnbls`nar. lnbls`nar. Pk (iD/m).

 

`) Sbea Sbeakon` kon`nbs nbs nb ceuda ceuda y e`s kkagpa agpasokoa sokoalbs lbs nb ea eass ceudas ceudas nb eas pranukt pranuktas4 as4 H`sb nb kàekuea4 0 mar` H`e`lkb nb g`tbro` @kbtal`4 (6.60)*(6.>3)*(02666) (6.60)*(6.>3)*(02666) 7 3? ij Àkona @kïtoka4 (6.8:)*(02666)7 >626 ij @lmonrona @kïtoka4 (6.8:)*(02666)7 >626 ij H`e`lkb nb @kbtal` (6.>3)*(02666)7 Nbstoe`na + 3? Nbstoe`na7 3=;0ij H`e`lkb nb pranuktas 3? ij + >626 ij + >626 ij 7 =03? ij @kbtal`4 3? =03?

>626 =03?

√066% 76. 6.=> => % Àkona @kïtoka4 √066% 7 >?. >?.2= 2= % @lmonrona @kïtoka4

>626 =03?

√066% 7 >?. >?.2= 2= %

 h) Be k`ear qub bbss lbkbs`roa rbtor` rbtor`rr bl be kalnbls` kalnbls`nar. nar. Pk (iD/m). @kbtal` (v,;8?I) ↘ @kbtal` (e,;8?I) ↘ @kbtal` (e,;6;I) Kpv

(  ) 7∘( )+( 7∘( )+(

∃ M 

  iD  7 6.>2?+ ;.02√06∘; ^ ∘6.:?6√06∘3 ^ 8 ij¶ I   iD  280 ij

 iD  ij iD  ∃ M 7∘22>.>? ij ∃ M 

280

;8?

)∩ )∘(

 iD  ∘ 6.>2? + ;.02√06∘; ^ ∘6.:?6√06∘3 ^ 8 8.; ij ;6; 8.;

 iD  ij

;2.:3

 iD  ij

)

Pkalnbls`nar 7 l ∃ M 

(

Pkalnbls`nar 78√

P

kalnbls`nar

3=;0

 )(

 iD  ij ∘22>.>? ij m

 iD  7:2:2>>8.;= m

)

 

BDBXKOKOA[ VÀJOL@ 8>= 0. Rl gbn gbnoa oa nb cbrg cbrgblt` blt`koûl koûl eçquona eçquona ` ;6 ¶¶K K sb hag haghb` hb` ` vbeakon vbeakon`n `n nb 8666 8666 ij/mr ij/mr ` tr`vïs nb ul k`eblt`nar, nalnb su tbgpbr`tur` sb bebv` ` :6¶K h`da prbsoûl. Be `ju` k`eobltb nb nbspbrnokoa us`n` p`r` be k`eblt`goblta bltr` ` ?2 ¶K y s`eb ` =2 ´K. E` k`p`kon`n k`earçcok` pragbnoa nbe gbnoa nb cbrgblt`koûl bs >.63 iD/ij I, y e` nbe `ju`, >.80 iD/ij I E`s karrobltbs nb cbrgblt`koûl y nb `ju` k`eobltb bstàl sbp`r`n`s par ul` supbrcokob gbtàeok` gbtàeok` ` tr`vïs nb e` ku`e sb tr tr`lscobrb `lscobrb be k`ear y qub ogponb e` gbzke` cçsok` nb `gh`s. Bst`heïzk`sb ul h`e`lkb nb k`ear kagpebta p`r` be sostbg`. K`ekôeblsb be ceuda nb `ju` y e` k`lton`n nb k`ear `ð`non` `e gbnoa nb cbrgblt`koûl, supaloblna qub la m`y pïrnon`s bl be sostbg`. Bl e` Coj. sb gubstr` be ceuda nbe prakbsa.

[aeukoûl4

 Bltr`n` 4 karrobltb obltbss ` 8?= i ( 82 ¶ K ) ∐ M  nb 8 karr  X

>

 M ( eoquona )7 ( 8666 ij / m )( >.63 iD / ij.i ))(( 2 i )7>.636√06 iD / m  M   (( `ju` )7 w ( >.80 ) ( ?2∘ 82 )78.?>√06 Z iD / m ( w 7 ij / m ) 8



b`kkoûlquçg ûlquçgok`. ok`.   (∘∃ M  )76 ↘ Lam`y rb`kko



  q 76 ↘ La m` m`yy `n `nok okoû oûl l a pb pbrrno non`nb n`nb k`ea k`earr .

6

8?=

[`eon` 4 karrobltb obltbss ` 8?= i ( 82 ¶ K ) ∐ M  nb 8 karr  p

 M ( eoquona )7 ( 8666 ij / m )( >.63 iD / ij.i ))(( :6∘ 82)7 ;.32√06 iD / m 2

 M   (( `ju` )7 w ( >.80 ) ( =2∘82 )78.283√06 Z iD / m 8

 

 Bltalkbs 4

√

>

8

2

8

+ 8.?>:√06 √Z 7;.32>√06 iDm +8.283√06 √Z  Z 7 ::86 ij / m ceudanb ceudanb `j `ju` u`

>.636 06

K`lton K`l ton`n `n nb k`ear k`ear qub sb`jrbj sb`jrbjû û `e gbnoa gbnoa nb cbrgb cbrgblt` lt`koû koûl l bs e`nocbrblk e`nocbrblko` o`nb nb blt`e blt`epo` po`ss  M  ( eoquona ) s`eon` ∘ M (eoquona ) bltr`n` ± ;.32>√062 iD / m∘ >.636√06 > iD / m 2  Xbspubst`  Xbspubs t` ∾ ;.8>=√ 06 iD / m

;.- Rl` karrobltb nb 066 ij/m nb prapoebla j`sbasa, M8K7M-KM8, M8K7M-KM8, ` 2 h`rbs y ?6 ¶K br` k`eblt`n` m`st` ul` tbgpbr`tur` nb ;06 ¶K par gbnoa nb ul sbrpbltçl qub eb sugolostr`h` be k`ear lbkbs`roa p`r` `ek`lz`r nokm` tbgpbr`tur`. E`gblt`hebgbltb be sostbg` c`eeû y sb rbquobrb bl carg` urjbltb bv`eu`r e` `etbrl`tov` nb us`r atra bquopa nospaloheb qub bltrbj` 08 iZ nb k`ear. Nbtbrgolb e` tbgpbr`tur` qub `ek`lz`rç` be  prapoebla kal bstb bstb ôetoga bquopa y nbcol` so rbkagobln` rbkagobln` su usa a la. olnok`lna e`s e`s kalsonbr`koalbs kalsonbr`koa lbs y kuon`nas qub sb nbhbrç`l tblbr.

[aeukoûl4

K`ekue`gas eas gaebs nb prapoebla4 066 ij   √066 ij 0m   √0 gae 0 ij   78:;3.> gae / m gaebs prapoebla 7 >2.6= j

K`p`kon`n k`earçcok` nbe prapoebla4 kp 7 3>.; D / gae¶K  0666 D  0 iw

7

sbj

  √;366 s   7;.3√06 D / m 3

0m

 Xb`eoz`gas be beh`e`lkb h`e`lkb nb blbrjç` blbrjç` 4 ∃ M + ∃ Bi + ∃ Bp7 P ∘Z  P 7 ∃ M y` qub∃ Bi , ∃ Bp y Z saloj saloju` u`eb ebss ` 6  Bltalkbs 4

 

s`eon eon` ` M s`eon` s`eon`∘∐ l bltr`n` M bltr`n` ∐ l s` ∃ M 7l ∩ Kpnt ∘l ∩ Kpnt 

∃ M 7

^  8  8

 prapoebla  prapoeb la

^  0  0

 prapoebla  prapoeb la

^ rbc 

^rbc 

8;:3.> gae

  √3>.; D  √( ;06 ∘?6 )

m   gae¶K 

∃ M 7

∃ M 7;;388863 D / m

2.- Be k`ear nb saeukoûl nbe `galo`ka bl `ju` ` 0 `tg bs4 ∃ M[ (82¶K r7 8 gae M86 / gaO LM;) 7 -:=88 iD/gae K`ekueb be k`ghoa nb blt`epo` qub `kagp`ð` ` e` saeukoûl nb >66 gae nb LM; bl =66 gae nb `ju` ` 82¶K y 0 `tg [aeukoûl4

>66 gaebs  LM ; [  LM ;(`k) =66 gaebs  M 8 A

K`lton`n nb g`s` qub oljrbs`4 >66 gaebs

 LM ;√0: j gaee LM ; 0 ga

gaeb ebss M 8 =66 ga

73=66 j LM 

A√0= j 7 0>66 j M 8 A 0 gae M 8 A

K`lton`n nb g`s` saeukoûl4  Bltr`n` 7 [`eon` [7 3=66 j LM ;+ 0>66 j M 8 A

Kàekuea nb ∃ Ms 4 r7

gaebs bs LM ; =66 gae gaeb ebss M 8 A >66 ga

78

Kàekuea nb ∃ Mh 4 82 K 

∩ K  n^ 76

∃ M  LM  7

 p

;

82 K  82 K 

∃ M  M  A7 8

∩ K  n^ 7 6  p

82 K 

;

 

K`earbs oltbjr`ebs nb saeukoûl ` 82K par t`he`s ∃ Ms 7∘:=88

  ID  gae

Kàekuea nb ∃ M   88 4 ∃ M   8 8 7 ∃ M` ∘ ∃ Mh 7∘:=88∘ 67 :=66

  ID  gae

K`ekue`gas P 4 bltr`n`

 ∐

P7 ∃ M 

s`eon`

loM 0 +

∐ loM 0

P7 ( ∃ M 8 ∘∃ M   0 0 ) 7∘:=88

  ID  √>66 gae gaebs bs LM ; gae

2

P7∘ ;0.8== x 06  ID 

:. Rl Rl`` saeu saeukkoûl oûl nb àkona ona su suec ecôôroka roka bst stàà g`rk g`rk`n `n`` kaga aga =L (n (nal alnb nb 0L 7 0 jbquov jbq uov`eb `ebltb ltb/E /E y 0 gae nb M8 M8[A> [A> kal kaltob toblb lb 8 j-bquo j-bquov`e v`ebl bltbs tbs). ). E` jr`vbn jr`vbn`n `n bspbkocok` nb e` saeukoûl bs 0,8;6, y su k`p`kon`n k`earçcok` bs ;,66 D/(j-¶K). K`ekueb e` blt`epo` bspbkçcok` nb bst` saeukoûl (bl iD/gae M8[A>) ` 36¶K, bl rbe`koûl kal M8A pur` y ul` saeukoûl guy noeuon` ` 82¶K. Kàekuea nb S4

 G`s` Gaebkue`r   ,ν↘v`eblko`  Bq 7 ν  Bq M  [ A 7 8

 L 7

?=

>

8

7>?

 Bq ∘j Ssae

7

= L 

  >?

Ssae Ssae 73.082 E Jr`vbn`n bspbkocok`4

Jr`vbn`n bspbkocok` 7  π M  [A 8

>

 π M  A

7 0.8;6

8

 π M  [A 7 8

>

 π 7 g S 

√0 j

0.8;6

ge

  nblson`n nblson`n nbe ceuona nblson`n nbls on`n nbe `ju` > ´K 

 

g7 π√S  g7 0.8;6

 j √3082 ge ge

g7 :2;;.:2 j Kàekuea nb e` blt`epo`4

∃ M 7gKp ( ^ 8∘^ 0) ∃ M 7:2;;.:2 j√;

  D   ( 36∘ 82 ) ´K  j ´K 

∃ M 7:?06>;.:2 D  ∃ M 7:?0.6>; iD  Kàekuea nb e` blt`epo` bspbkocok`4 :?0.6>;

∃ M 7

:22;.:2

√?= j

0 gae

∃ M 706.8?=

=. [b k`rj k`rj`` ul marla vbrtok vbrtok`e `e kal pob pobnr` nr` k`e k`eoz` oz` pur` pur`,, K`KA;, K`KA;, y kaqub t`ghoïl t`ghoïl pura pura (k`rhala), `ghas ` 82¶K. Var be calna nbe marla sb oltranukb `orb sbka, qub  praparkoal` be k`ear lbkbs`roa p`r` e` nbskagpasokoûl nbe k`rhal`ta, gbno`ltb e` kaghustoûl nbe k`rhala m`st` KA8. Var be calna nbe marla sb nbsk`rj` k`e vov`, K`A, ` ?26¶K, qub kaltoblb 2% nb k`rhala y 0% nb K`KA;. Eas j`sbs nbe marla sb nbsk`rj`l par e` p`rtb supbroar ` 366¶K y kaltoblbl ôlok`gbltb KA8 y L8. [upûlj`sb qub pubnbl nbsprbko`rsb e`s pïrnon`s. E`s rb`kkoalbs sal4 K`KA;(s)

 K`A(s) + KA8(j)

⇼

K(s) + A8(j)

 KA8 (j)

⇼

[`hoblna qub 

M¶c K`KA;(s) 7 -8=?,2 ik`e/jgae



M¶c K`A(s) 7 -020,: ik`e/jgae



M¶c KA8(j) 7 -?>,628 ik`e/jgae

K`p`kon`nbs k`earçcok`s gae`rbs  pragbnoa kalst`ltbs

(k`e/jgae.I)

K`A (s)

0;,:

8 KA  (j)  L8(j)

08,8 :,2

 

8=,6 =,6 >,3

K`K6;(s) A8(j) K(s)

`) K`ek K`ekueb ueb eeas as k`earbs k`earbs nb rb`kk rb`kkoûl oûl ` 82¶K. 82¶K. K`KA; ( s) ↘K`A (s )+ KA 8 ( j ) ∃ M´ 7 ∃ M ´ c  K`A + ∃ M ´ c  KA 8( j ) ∘Y ∃ M ´ c  K`KA; W

 W

Y

∃ M´ 7Y ∘020.: +(∘ ?>.628 ) W ∘Y ∘8=?.2 W ∃ M´ 7∘ >;.:>= ik`e gae K ( s )+ A8 ( j) ↘ KA 8( j ) ∃ M´ 7Y ∃ M ´ c  K A 8 W∘Y+ ∃ M ´ c  K + ∃ M ´ c  A8 W ∃ M´ 7Y ∘?>.628 W∘ Y 6 + 6 W  ik`e ∃ M´ 7∘ ?>.628 gae

 h) Kalstruy` ul` t`he` nb jr`nas nb eohbrt`n p`r` be prahebg`. Nbtbrgolb so  pubnbl nbs`kape`rsb nbs`kape`rsb eas h` h`e`lkbs e`lkbs nb g` g`tbro` tbro` y blbrjç`.  @sugoblna 066 ga gaebs ebs bl be calna calna 2 %K , 0 % K`KA; , ?> % K`A K`A A ( s) 0 ´ ?2 K`KA; ( s) ↘ ?> K`

( + 2 ) K ( s )+ x A ( j )+

8 ´   x

0ra K`A KA8

8

l

K`KA;

 

?>

 

?>

 

0

 Vranuktas

:? x 80

+ ?> KA

8

( j)

+0 K`KA

 L 8 ↘ xKA xKA8 ( j) + 2 K +

M´ (k`e/gae)   ∘020:66   ∘?>628   ∘8=?266

∐ ±∘8020;33; k`e

Kp 0;.: 08.8 8=

;

(s)

:? x 80

^ (´K) ?26 366 ?26

 L 8  

l Y ∃ M´ + Kp ( ^ + 82 ) W

-0;63=2=2 -=0=0>:= -83;366

 

0ra

l

K`KA;

 

M´ (k`e/gae)

Kp

^ (´K)

∘8=?266

8=

82

M´ (k`e/gae)

Kp

^ (´K)

∘?>628

08.8 > .2 : .2

366 ?26 366

 

 

?2

l Y ∃ M´ + Kp ( ^ + 82 ) W

 

-8:268266

∐ ±∘8:268266 k`e

 Xb`kt`ltbs

P07 M  p ∘ M r P07∘8020;33; ∘( ∘(∘ ∘ 8:268266 ) P072?===;: k`

8na K A8  L8

l  

x

 

2

 

   

6

:? x

 

6

l Y ∃ M´ + Kp ( ^ + 82 ) W

 

-=:6;:x 808:2 0388;.80x

80

 Vranuktas

8na K A8  L8

l

M´ (k`e/gae)

 

x +2

     

∐ ± 808:2 ∘:6=0;.:? x  

x

 

:? x

6 6 6

Kp

^ (´K)

> .3 = : .2

82 82 82

 

80

 Xb`kt`ltbs

∐ ±6

P87∘P 0 7∘2?===;: k`e

∘2?===;: 7808:2∘:6=0;.:? x  x 7=>.=:863 gaeK  k) K`ekueb e` praparkoûl nb K`KA; ` K bl e` `eogblt`koûl.

K`KA ; K 

  7

K`KA ; K 

  ?2 gaeK`KA; =>.=:863 gaeK 

  7 0.00?;;8

l Y ∃ M´ + Kp ( ^ + 82 ) W

6 6 6