VADOA FE KJ@VE@GFJ pán. 1. CAKVJTE[ FE E]XA@[GÛ@..........................................................................; 1.1. KAOKUOJ FE CAKVJTE[ FE E]XA[GJ@.................................................; 1.1.1 Eleipoj Caktjr fe expa`sgû` \j`a 1..........................................................; 1.4. CAKVJTE[ FE E]XA@[GÛ@.......................................................................6 4. IAVTG\ JTGNE@/FE[VG@J............................................................................5 ;. AKVUAOG\AKGJ@ FE IAVTG\ JTGNE@/FE[
[email protected] ;.1. IEVJFJ ‛ KTEKGIGE@VJ U@GCJTIE KU...............................................3 ;.4. IEVJFJ ‛ CAKVJT XTJIEFGJ CX..........................................................> ;.;. IEVJFJ ‛ CUT@E[[ C..............................................................................7 ;.6. IEVJFJ ‛ FEVTJGV F.............................................................................14 ;.5. IEVJFJ ‛ CTAVAT CT.............................................................................1; 6. AKVUAOG\AKGJ@ FE IAVTG\ J/F KJ@ IJFEOJ[ NTASGVAKGJ@AOE[ ............................................................................................................................1> 6.1. IÇVJFJ XJVE@KGAO X............................................................................1= 6.4. IÇVJFJ E]XJ@E@KGAO E.......................................................................48 5. A@E]J[.........................................................................................................4;
OG[VA FE VADOA[ pán. Vadoa 1. G`cjriakgû` fe e`kuesta fjigkgogarga fe ijvgogfaf \j`a 1...................; Vadoa 4. Caktjres fe expa`sgû` \j`as fe Vu`la.................................................6 Vadoa ;. Iatrgz fesaktuaogzafa.............................................................................3 Vadoa 6. Caktjres fe krekgige`tj para kafa zj`a...............................................3 Vadoa 5. Káokuojs reaogzafjs 1¸ gterakgû` KU.......................................................> Vadoa 3. Iatrgz J/F aktuaogzafa 1¸ gterakgû` KU..................................................> Vadoa >. Káokuojs g`gkgaoes CX..............................................................................> Vadoa =. Káokuojs 1¸ gterakgû` CX.........................................................................= Vadoa 7. Káokuojs 4¸ gterakgû` CX.........................................................................= Vadoa 18. Káokuojs ;¸ gterakgû` CX.......................................................................7 Vadoa 11. Káokuojs g`gkgaoes C...............................................................................7 Vadoa 14. Káokuojs 1¸ gterakgû` C........................................................................18 Vadoa 1;. Kj`tg`uakgû` káokuojs 1¸ gterakgû` C..................................................18 Vadoa 16. Káokuojs 4¸ gterakgû` C........................................................................18 Vadoa 15. Kj`tg`uakgû` káokuojs 4¸ gterakgû` C..................................................11 Vadoa 13. Káokuojs ;¸ gterakgû` C........................................................................11 Vadoa 1>. Kj`tg`uakgû` káokuojs ;¸ gterakgû` C..................................................11 Vadoa 1=. Káokuojs g`gkgaoes F............................................................................14 Vadoa 17. Káokuojs 1¸ gterakgû` F.......................................................................14 Vadoa 48. Káokuojs 4¸ gterakgû` F.......................................................................1; Vadoa 41. Káokuojs ;¸ gterakgû` F.......................................................................1; Vadoa 44. Káokuojs g`gkgaoes CT..........................................................................16 Vadoa 4;. Caktjres g`gkgaoes CT..........................................................................16
Vadoa 46. Káokuojs 1¸ gterakgû` CT.....................................................................16 Vadoa 45. Caktjres 1¸ gterakgû` CT.....................................................................15 Vadoa 43. Káokuojs 4¸ gterakgû` CT.....................................................................15 Vadoa 4>. Caktjres 4¸ gterakgû` CT.....................................................................15 Vadoa 4=. Káokuojs ;¸ gterakgû` CT.....................................................................13 Vadoa 47. Caktjres ;¸ gterakgû` CT.....................................................................13 Vadoa ;8. Iatrgz fe fgsta`kgas e`tre zj`as........................................................1> Vadoa ;1. Iatrgz a alustar...................................................................................1= Vadoa ;4. Káokuojs 1¸ gterakgû` X.......................................................................1= Vadoa ;;. Káokuojs 4¸ gterakgû` X.......................................................................1= Vadoa ;6. Káokuojs ;¸ gterakgû` X.......................................................................17 Vadoa ;5. Káokuojs 6¸ gterakgû` X.......................................................................17 Vadoa ;3. Iatrgz jrgne`/festg`j kaogdrafa X.......................................................48 Vadoa ;>. Káokuojs 1¸ gterakgû` E.......................................................................48 Vadoa ;=. Káokuojs 4¸ gterakgû` E.......................................................................48 Vadoa ;7. Káokuojs ;¸ gterakgû` E.......................................................................41 Vadoa 68. Káokuojs 6¸ gterakgû` E.......................................................................41 Vadoa 61. Iatrgz jrgne`/festg`j kaogdrafa E.......................................................44
OG[VA FE CGNUTA[ pán. Cgnura 1. Tef vgao................................................................................................1>
1. CAKVJTE[ FE E]XA@[GÛ@ E` eo prese prese`te `te kapgt kapgtuoj uoj se pre prese` se`ta ta fe ia` ia`era era fet fetaoo aooafa afa oa ietjfj ietjfjojn ojnéa éa eipoeafa y caktjres fe expa`sgû` para kafa zj`a fe oa kgufaf fe Vu`la.
1.1. KAOKUOJ FE CAKVJTE[ FE E]XA[GJ@ Oa expresgû` utgogzafa para eo káokuoj fe ojs caktjres fe expa`sgû` fe oas 34 zj`as fe oa kgufaf fe Vu`la se e`kue`tra a kj`tg`uakgû`2
A ∔ Ce 9
)
(
K ∞ F A ∞ K + D D D ∔K ∔ F
Fj`fe2 Ce es eo caktjr fe expa`sgû` fe oa zj`a g , A es oa pjdoakgû` fe mjnares, D oa iuestra seoekkgj`afa, K oa oa iuestra `j eoengdoe y F oa iuestra `j ojnrafa. o jnrafa.
1.1.1 Eleipoj Caktjr fe expa`sgû` \j`a 1 Xara oa zj`a 1 se tge`e oa g`cjriakgû` ijstrafa e` oa sgnuge`te tadoa. Vadoa 1. G`cjriakgû` fe e`kuesta fjigkgogarga fe ijvgogfaf \j`a 1 \j`a
Xjdoakgû` fe Mjnares A
Iuestra seoekkgj`afa D
Iuestra `j eoengdoe K
Iuestra `j ojnrafa F
1
467
14
1
5
Cue`te< Afaptafj fe VTADALJ G@FGSGFUAO FG[VTGDUKGJ@ NEJNTACGKA FE SGALE[ Teeipoaza`fj ojs a`tergjres vaojres e` oa ekuakgû` ijstrafa prevgaie`te se jdtge`e oj sgnuge`te.
467 ∔
Ce 9
467 14
(
∞
1+
)
1∞5 14
14 ∔1∔ 5
Ce 9;3,38 vgales
;
E` dase a oj a`tergjr se tge`e que 1 vgale reaogzafj pjr u`a persj`a que resgfe e` oa zj`a 1 equgvaoe a ;3,38 vgales.
1.4. CAKVJTE[ FE E]XA@[GÛ@
E`oas oa 31 sgnuge`te tadoa se e`kue`tra` ojs caktjres fe expa`sgû` kjrrespj`fge`tes a zj`as fe o a kgufaf oa fe Vu`la. Vadoa 4. Caktjres fe expa`sgû` \j`as fe Vu`la \j`a 1 4 ; 6 5 3 =
Caktjr fe ;3,38 48,>6 1>,85 17,45 45,== 68,51 ;6,5>
\j`a ;; ;6 ;5 ;3 ;= ;7 68
Caktjr fe 41,47 ;,55 44,>1 15,64 11,71 11,36 17,=8
7 18 11 14 1; 16 15 13 1> 1= 17 48 41 44 4; 45 43 4> 4= 47 ;8 ;1 ;4
4 17 =,,8 ;7 8 4;,4= 14,;7 17,5; 16,3> 1=,4; ;4,>3 13,38 4;,63 13,5= 44,;= 16,57 1=,84 41,=4 41,31 15,>3 15,;1 >,=5 48,65 ;,>1 47,88 3>,11
6 61 4 6; 66 65 63 6> 6= 67 58 51 54 5; 56 55 53 5> 5= 57 38 31 34
4 1; 7,,; ;> ; 15,54 1;,16 1;,>7 6=,37 16,45 1;,16 11,63 11,3> 1=,>8 4;,=6 1=,7; 41,88 16,63 1>,76 ;8,48 1;,3> =,51 1;,;= 15,55 1;,5=
Cue`te< eoadjrakgû` prjpga
6
4. IAVTG\ JTGNE@/FE[VG@J Oa iatrgz jrgne`/festg`j expa`fgfa para oa kgufaf fe Vu`la, se e`kue`tra e` oa mjla mj la IJF E fe feoo a`e a`exj xj V;IVEATC , esta cue reaogzafa kj` oa jpkgû` tadoa fg`áigka feo sjctware Exkeo. E` dase a oj rengstrafj e` oa iatrgz, se jdserva que oa zj`a 1 es oa iayjr prjfuktjra fe vgales kj` u` tjtao fe ;5;18 vgales, y que oa zj`a ;> es oa ie`jr prjfuktjra fe estjs, kj` u` tjtao fe 1;7 vgales. Afgkgj`ao a estj, se e`kj`trû que oas zj`as `jidrafas a`tergjrie`te sj` oas iayjres/ie`jres atraktjras fe vgales respektgvaie`te. E` tjtao se tge`e` que se reaogza` u` tjtao fe ;55636 vgales.
5
;. AKVUAOG\AKGJ@ FE IAVTG\ JTGNE@/FE[VG@J E` eo prese`te kapgtuoj se e`kue`tra` ojs fgcere`tes içtjfjs eipoeafjs para oa aktuaogzakgû` fe oa iatrgz jrgne`/festg`j fafa.
Oa iatrgz ae`aktuaogzar y ojstadoas. caktjres kjrrespj`fge`tes para kafa zj`a se e`kue`tra` oas sgnuge`tes Vadoa ;. Iatrgz fesaktuaogzafa J /F 1 4 ; 6 5
1 8 1= 1= ;1 ;1 ;= ;= 43
4 48 8 65 58 ;5
; ;8 66 8 13 56
6 68 54 15 8 57
5 45 ;; 55 38 8
Cue`te< afaptafj Cue`te< afaptafj fe VTAD VTADALJ ALJ G@FGSGFUAO G@FGSGFUAO FG[VTGDUK FG[VTGDUKGJ@ GJ@ NEJN NEJNTACGK TACGKA A FE SGALE[ Vadoa 6. Caktjres fe krekgige`tj para kafa zj`a Caktjres fe Krekgige`tj pjr \j`a 1 4 ; 6 5 1,88 1,86 1,8; 8,75 1,88
Cue`te< afaptafj fe VTADALJ G@FGSGFUAO FG[VTGDUKGJ@ NEJNTACGKA FE SGALE[
;.1. IEVJFJ ‛ KTEKGIGE@VJ U@GCJTIE KU Eo caktjr fe krekgige`tj para tjfas oas zj`as, cue kaokuoafj kjij u` prjiefgj fe ojs caktjres g`fgvgfuaoes prese`tafjs e` oa tadoa 6 Caktjres fe krekgige`tj para kafa zj`a, jdte`gfj asé u` caktjr gnuao a 1,886. E` oas sgnuge`tes tadoas se prese`ta oa ü`gka gterakgû` reaogzafa para este. Kjij se puefe jdservar e` oa tadoa 3, ojs vgales ne`erafjs y atraéfjs sj` gnua gnuaoe oess ya que que ojs ojs vgal vgales es se vger vgerj` j` acek acekta tafj fjss pj pjrr eo igsi igsij j cakt caktjr jr fe krekgige`tj, g`fepe`fge`te fe oa zj`a.
3
Vadoa 5. Káokuojs reaogzafjs 1¸ gterakgû` KU J /F 1 4 ; 6 5
1
8 1= ;1 ;= 43 11; 1,886 11;,654
Fl Cl F' l
4
;
6
48 ;8 68 8 66 54 65 8 15 58 13 8 ;5 56 57 158 166 133 1,886 1,886 1,886 158,3 166,5>3 133,336
5 Jg 45 ;; 55 38 8 1>; 1,886 1>;,374
Cg 115 16> 163 136 1>6
1,886 1,886 1,886 1,886 1,886
J 'g 115,63 16>,5== 163,5=6 136,353 1>6,373
>6=,7=6 >6=,7=6 9
Cue`te< eoadjrakgû` prjpga Vadoa 3. Iatrgz J/F aktuaogzafa 1¸ gterakgû` KU J /F 1 4 ; 6 5 Fl Fl9F 9F'l'l
1 8,88 1=,8> ;1,14 ;=,15 43,18 11;,65 ,65
4 48,8= 8,88 65,1= 58,48 ;5,16 158,38 ,38
; ;8,14 66,1= 8,88 13,83 56,44 166,5=
6 68,13 54,41 15,83 8,88 57,46 133,33
5 Jg9J'g 45,18 115,63 ;;,1; 16>,57 55,44 163,5= 38,46 8,88 136,33 1>6,>8 1>;,37 9
Cue`te< eoadjrakgû` prjpga
;.4. IEVJFJ ‛ CAKVJT XTJIEFGJ CX Ojs káokuojs g`gkgaoes para eo içtjfj fe caktjr prjiefgj se e`kue`tra` e` oa sgnuge`te tadoa. E` esta se puefe jdservar que ojs vgales ne`erafjs y atraéfjs `j sj` gnuaoes. Vadoa >. Káokuojs g`gkgaoes CX J /F 1 4 ; 6 5
Fl Cl F' l
1 8 1= ;1 ;= 43 11; 1,88 11;
4 48 8 65 58 ;5 158 1,86 153
; ;8 66 8 13 56 166 1,8; 16=,;4
6 68 54 15 8 57 133 8,75 15>,>
Cue`te< eoadjrakgû` prjpga
>
5 Jg 45 115 ;; 16> 55 163 38 136 8 1>6 1>; 9 1,88 1>;
Cg
1,,88 1 1,86 ,86 1,8; ,8; 8,75 1,88 1,
J 'g 115 154,== 158,;= 155,= 1>6
>6=,83 >6=,84 ≨
E` oa sgnuge`te tadoa se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa prgiera gterakgû` fe este içtjfj. [e jdserva que ojs caktjres fe krekgige`tj fe oas zj`as sj` fgcere`tes ta`tj e` atrakkgû` kjij e` ne`erakgû`. Vadoa =. Káokuojs 1¸ gterakgû` CX J1/F 8,1 88 4 1=,;3 ; ;1,6> 6 ;>,85 5 43,88 114,= == [Fl 114, 1,8 1,8811 811 cFl 11;, 11;,8 88 F'l
484,68 8,88 63,5= 67,>5 ;5,>8 154, 154,6 6; 1,8 1,84;5 4;5 153, 153,8 88
;8;,65 65,56 8,88 15,=6 56,=1 163,3 3,36 1,8 ,811 115 5 16=,; =,;4
;76,88 51,>6 16,=5 8,88 5>,5; 13;,14 ,14 8,7 ,733 33= = 15>,>8 ,>8
g ,=5 cJ g 5,88 455,88 [1J 16 1,g881; J1'1 ;;,33 167,;8 1, 1,8468 154 154,== 55,=; 16=,>4 1, 1,8114 158 158,;= 5=,58 131,16 8, 8,7337 155 155,=8 8,88 1>6,86 8, 8,777= 1>6 1>6,88 1>4,7 >4,77 7 9 1,8 ,888 881 1 >6=,83 1>;,8 >;,88 8 >6=, >6=,84 84 ≨
Cue`te< eoadjrakgû` prjpga E` oa sgnuge`te tadoa se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa senu`fa gterakgû` feo içtjfj. Au` `j se prese`ta oa kj`verne`kga fe ojs vgales Vadoa 7. Káokuojs 4¸ gterakgû` CX J /F 1 4 ; 6 5 [Fl cFl F' l
1
4
;
6
8,88 1=,57 ;1,33 ;3,63 43,81 114,>4 1,8845 11;,88
48,35 8,88 6>,;= 67,51 ;3,14 15;,33 1,8154 153,88
;8,36 63,;5 8,88 15,3> 55,14 16>,>= 1,88;> 16=,;4
;=,;= 51,58 16,37 8,88 53,53 131,1; 8,7>=> 15>,>8
5 [J g cJ g J 'g 116, 6,37 37 1,88 1,884> 4> 11 115, 5,88 88 45,84 11 158, 8,58 58 1,81 1,815= 5= 15 154, 4,== == ;6,8> 15 167, 7,=> => 1,88 1,88;6 ;6 15 158, 8,;= ;= 53,16 16 157, 7,1> 1> 8,7> 8,7>== == 15 155, 5,=8 =8 5>,5; 15 1>;, ;,=1 =1 1,88 1,8811 11 1> 1>6, 6,88 88 8,88 1> 1>4,>3 9 1,8816 >6=,83 1>;,88 >6=,84 ≨
C
ue`te< eoadjrakgû` prjpga E` oa sgnuge`te sgnuge`te tadoa se e`ku e`kue`tra e`tra oa g`cjri g`cjriakgû akgû` ` kjrrespj` kjrrespj`fge`t fge`te e a oa terkera terkera gterakgû` feo içtjfj. [e jdserva u`a fgcere`kga aprjxgiafa feo 8,86 % kj` ojs caktjres fe oa gterakgû` a`tergjr, a pesar fe estj, ojs vgales ne`erafjs y atraéfjs `j kj`verne`.
=
Vadoa 18. Káokuojs ;¸ gterakgû` CX J /F 1 4 ; 6 5 [Fl cFl F' l
1 8,88
4 48,=6
; ;8,>6
6 ;=,84
5 [J g cJ g J 'g 45,8> 116,3> 1,8847 115,88
1=,>3 ;1,>5 ;3,14 43,83 114,37 1,884= 11;,88
8,88 6>,=4 67,;3 ;3,61 156,6; 1,8181 153,88
63,=8 8,88 15,5; 55,45 16=,;4 1,8888 16=,;4
51,;3 16,53 8,88 55,77 157,7; 8,7=31 15>,>8
;6,;3 151,4= 53,4= 158,61 53,7> 15>,7= 8,88 1>;,>1 1>4,3> 9 1,8817 1>;,88
1, 1,8183 8, 8,777= 8, 8,7=34 1, 1,881>
154 154,== 158 158,;= 155 155,=8 1>6 1>6,88
>6=,83 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga
;.;. IEVJFJ ‛ CUT@E[[ C Ojs káokuojs g`gkgaoes para eo içtjfj fe Cur`ess se e`kue`tra` e` oa sgnuge`te tadoa. E` esta se puefe jdservar que ojs vgales ne`erafjs y atraéfjs `j sj` gnuaoes. Vadoa 11. Káokuojs g`gkgaoes C J /F 1 4 ; 6 5
Fl Cl F' l
1 8,88 1=,88 ;1,88 ;=,88 43,88 11;,88 1,88 11;,88
4 48,88 8,88 65,88 58,88 ;5,88 158,88 1,86 153,88
; ;8,88 66,88 8,88 13,88 56,88 166,88 1,8; 16=,;4
6 68,88 54,88 15,88 8,88 57,88 133,88 8,75 15>,>8
5 Jg Cg J 'g 45,88 11 115,88 1,88 115,88 ;;,88 16 16>,88 1,86 154,== 55,88 16 163,88 1,8; 158,;= 38,88 13 136,88 8,75 155,=8 8,88 1> 1>6,88 1,88 1>6,88 1>;,88 9 1,88 >6=,83 1>;,88 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga E` oas sgnuge`tes tadoas se e`kue`tra` oa g`cjriakgû` kjrrespj`fge`te a oa prgiera gterakgû` feo içtjfj, e` esta se kaogdra` ojs e` dase a ojs káokuojs g`gkgaoes.
7
Vadoa 14. Káokuojs 1¸ gterakgû` C J /F 1 4 ; 6 5 [Fl cFl F' l
1 8,88
4 48,88
; ;8,88
6 68,88
1=,>4 ;1,7; ;3,18 43,88 114,>5 1,884 11;,88
8,88 63,;5 6>,58 ;5,88 16=,=5 1,86= 153,88
65,>3 8,88 15,48 56,88 166,73 1,84; 16=,;4
56,8= 15,65 8,88 57,88 13=,5; 8,7;3 15>,>8
5 [J g 45,88 115,88 9
;6,;4 154,== 53,35 158,;= 5>,88 155,=8 8,88 1>6,88 1>4,7> 9 1,888 1>;,88
9 9 9 9
J 'g 115,88 154,== 158,;= 155,=8 1>6,88
>6=,83 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga Vadoa 1;. Kj`tg`uakgû` káokuojs 1¸ gterakgû` C J /F 1 4 ; 6 5 [F'l F'l
F' l
1 4 ; 6 5 [J'g cJ g J 'g 8,88 48,73 ;8,>8 ;>,6; 45,88 11 116,87 1,88= 11 115,88 1=,>3 8,88 63,=4 58,38 ;6,;; 15 158,51 1,813 15 154,== ;4,88 6=,5= 8,88 16,63 53,33 15 151,37 8,771 15 158,;= ;3,1= 67,>= 15,55 8,88 5>,81 15 15=,54 8,7=; 15 155,=8 43,83 ;3,3= 55,45 55,41 8,88 1> 1>;,48 1,885 1 1> >6,88 11;,88 153,88 16=,;4 15>,>8 1>;,88 9 9 9 9 9 9 >6=,83 11;,88 153,88 16=,;4 15>,>8 1>;,88 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga E` oas sgnuge`tes tadoas se e`kue`tra` oa g`cjriakgû` kjrrespj`fge`te a oa senu`fa gterakgû` feo içtjfj, e` esta se kaogdra` ojs `uevjs caktjres para kafa zj`a, tjia`fj kjij recere`kga g`gkgao oa g`cjriakgû` expuesta e` oa kaogdrakgû` @¸1. Vadoa 16. Káokuojs 4¸ gterakgû` C J /F 1 4 ; 6 5 [Fl cFl F' l
1
8,88 17,83 ;1,>4 ;5,53 43,1= 114,54 1,886 11;,88
4
41,1; 8,88 6=,13 6=,7; ;3,=5 155,83 1,883 153,88
;
;8,76 6>,53 8,88 15,47 55,51 167,47 8,776 16=,;4
6
;>,>; 51,68 16,;; 8,88 55,63 15=,74 8,774 15>,>8
Cue`te< eoadjrakgû` prjpga 18
5 [J g J 'g 45,48 115,88 9 115,88 ;6,=> 154,== 9 154,== 53,1> 158,;= 9 158,;= 53,8; 155,=8 9 155,=8 8,88 1>6,88 9 1>6,88 1>4,4> 9 1,886 >6=,83 1>;,88 >6=,84 ≨
Vadoa 15. Kj`tg`uakgû` káokuojs 4¸ gterakgû` C J /F 1 4 ; 6 5 [F'l
1 8,88
4 41,43
; ;8,>6
6 ;>,66
17,16 ;1,=3 ;5,>1 43,47 11;,88
8,88 6=,65 67,44 ;>,8> 153,88
6>,45 8,88 15,17 55,15 16=,;4
51,88 16,44 8,88 55,86 15>,>8
9 F 'l
9 11;,88
9 153,88
9 16=,;4
5 [J 'g cJ g J 'g 45,;1 11 116,>6 1,884 11 115,88
;5,81 15 154,68 53,61 15 158,76 53,4> 15 153,;7 8,88 1> 1>;,55 1>;,88 9 9
15>,>8
1>;,88
1,88; 8,773 8,773 1,88;
15 154,== 15 158,;= 15 155,=8 1> 1>6,88
>6=,83 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga E` oas sgnuge`tes tadoas se e`kue`tra` oa g`cjriakgû` kjrrespj`fge`te a oa senu`fa gterakgû` feo içtjfj, e` esta se kaogdra` ojs `uevjs caktjres para kafa zj`a, tjia`fj kjij recere`kga g`gkgao oa g`cjriakgû` expuesta e` oa kaogdrakgû` @¸4. [e jdserva afeiás que ao cg`ao fe oa terkera gterakgû` oa suiatjrga fe ojs vgales atraéfjs y ne`erafjs `j kj`verne`, es gipjrta`te festakar que ojs caktjres cFg y cJg se akerka` iás a oa u`gfaf que ojs jdte`gfjs e` oas g`terakkgj`es a`tergjres. Xjr oj que se esperaréa que ao maker iás gterakgj`es estjs vaojres cuera` u`j. Vadoa 13. Káokuojs ;¸ gterakgû` C J /F 1 4 ; 6 5
[F l cF l F 'l
1 8,88 17,48 ;1,>6 ;5,5= 43,;3
4 41,;8 8,88 6=,4> 67,86 ;>,1>
; ;8,=1 6>,68 8,88 15,1; 55,47
6 ;>,54 51,13 16,1> 8,88 55,1=
114,== 1,881 11;,88
155,>= 1,881 153,88
16=,34 8,77= 16=,;4
15=,8; 8,77= 15>,>8
5 [J g 45,;> 115,88 9 ;5,14 154,== 9 53,48 158,;= 9 53,83 155,=8 9 8,88 1>6,88 9
1>4,>5 9 1,881 1>;,88
Cue`te< eoadjrakgû` prjpga Vadoa 1>. Kj`tg`uakgû` káokuojs ;¸ gterakgû` C
11
J 'g 115,88 154,== 158,;= 155,=8 1>6,88
>6=,83 >6=,84 ≨
J/F 1 4 ; 6 5
[ F 'l F 'l
1
9
8,88 17,44 ;1,>= ;5,34 43,;7 11;,88 11;,88
9
4
;
6
41,;; 8,88 6=,;6 67,11 ;>,44
;8,>5 6>,;8 8,88 15,18 55,1=
;>,66 51,83 16,16 8,88 55,83
153,88
9
153,88
16=,;4
9
16=,;4
15>,>8
5 [J ' g cJg J 'g 45,68 1 11 16,7; 1,881 1 11 15,88 ;5,1> 1 15 54,>5 1,881 1 15 54,== 53,4= 1 15 58,56 8,777 1 15 58,;= 53,16 1 15 55,73 8,777 1 15 55,=8 8,88 1 1> >;,=5 1,881 1 1> >6,88
9
15>,>8
1>;,88 9 1>;,88
>6=,83 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga
;.6. IEVJFJ ‛ FEVTJGV F Ojs káokuojs g`gkgaoes para eo içtjfj fe Fetrjgt se e`kue`tra` e` oa sgnuge`te tadoa. E` esta se puefe jdservar que ojs vgales ne`erafjs y atraéfjs `j sj` gnuaoes.
Vadoa 1=. Káokuojs g`gkgaoes F J /F 1 4 ; 6 5
Fl Cl F' l
1 8,88 1=,88 ;1,88 ;=,88 43,88 11;,88 1,88 11;,88
4 48,88 8,88 65,88 58,88 ;5,88 158,88 1,86 153,88
; ;8,88 66,88 8,88 13,88 56,88 166,88 1,8; 16=,;4
6 68,88 54,88 15,88 8,88 57,88 133,88 8,75 15>,>8
5 Jg Cg J 'g 45,88 11 115,88 1,88 11 115,88 ;;,88 16 16>,88 1,86 15 154,== 55,88 16 163,88 1,8; 15 158,;= 38,88 13 136,88 8,75 15 155,=8 8,88 1> 1>6,88 1,88 1 1> >6,88 1>;,88 9 1,88 >6=,83 1>;,88 >6=,84 ≨ C 1,884>
Cue`te< eoadjrakgû` prjpga E` oa sgnuge`te tadoa se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa prgiera gterakgû` fe este içtjfj. [e jdserva que eo tjtao fe ojs vgales atraéfjs y ne`e ne `era rafj fjss `j sj` sj` gn gnua uaoe oes. s. Oj igs igsij ij su suke kefe fe kj` kj` oj ojss cakt caktjr jres es cJ cJgg y cFl cFl kjrrespj`fge`tes a oas zj`as 4 y 5. Eo caktjr C fgsig`uyj e` 8,46 % kj` respektj ao káokuoj fe ojs vaojres g`gkgaoes. Vadoa 17. Káokuojs 1¸ gterakgû` F
14
J /F 1 4 ; 6 5
Fl cFl F' l
1 8,88 1=,3> ;1,=6 ;3,88 45,7;
4 48,>6 8,88 6=,8> 67,4> ;3,;8
; ;8,=4 6>,88 8,88 15,31 55,6>
6 ;>,78 51,46 16,36 8,88 55,78
114,66 1,885 11;
156,;= 1,818 153
16=,78 8,773 16=,;4
157,3> 8,7== 15>,>
5 Jg cJg J 'g 46,7; 116,;7 1,885 115 ;6,4; 15 151,16 1,814 1 15 54,== 53,58 15 151,85 8,773 1 15 58,;= 53,=6 15>,>4 8,7== 155,= 8,88 1>;,38 1,884 1>6
1>4,58 9 1,88; 1>;
>6=,83 >6=,84 ≨ C 1,8884
Cue`te< eoadjrakgû` prjpga E` oa sgnuge`te tadoa se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa senu`fa gterakgû`. Ojs caktjres cFl fe oas zj`as ; y 5 peria`eke` kj`sta`tes kj` respektj a oa prgiera gterakgû`. Eo caktjr C fgsig`uyj e` 8,84% kj` respektj a oa prgiera gterakgû`. Vadoa 48. Káokuojs 4¸ gterakgû` F J /F 1 4 ; 6 5
Fl cFl F' l
1
8,88 1=,7> ;1,=5 ;5,>; 43,11 114,3> 1,88; 11;
4
41,8> 8,88 6=,;5 67,13 ;3,>3 155,;6 1,886 153
;
;8,=5 6>,;5 8,88 15,;3 55,;> 16=,7; 8,773 16=,;4
6
;>,34 51,1= 16,;7 8,88 55,;; 15=,54 8,775 15 15>,>
5 Jg cJ g J 'g 45,1; 116,3= 1,88; 115 ;6,>4 15 154,44 1,886 15 154,== 53,68 15 158,77 8,773 15 158,;= 53,;8 15 153,53 8,775 155,= 8,88 1>;,5> 1,884 1>6 1>4,55 9 1,88; >6=,83 1>; >6=,84 ≨ C 1,8888
Cue`te< eoadjrakgû` prjpga E` oa sgnuge`te sgnuge`te tadoa se e`ku e`kue`tra e`tra oa g`cjri g`cjriakgû akgû` ` kjrrespj` kjrrespj`fge`t fge`te e a oa terkera terkera gterakgû`. Eo caktjr cJg fe oa zj`a 5 y C peria`eke` kj`sta`tes kj` respektj a oa senu senu`f `fa a gtgter erak akgû gû`. `. Ao cg`a cg`aoo fe oa oass gtgter erak akgj gj`e `ess oj ojss tjta tjtaoe oess fe oj ojss vg vgal ales es jrgng`afjs y atraéfjs `j ojnra` oa kj`verne`kga. Vadoa 41. Káokuojs ;¸ gterakgû` F
1;
J /F 1 4 ; 6 5
Fl cFl F' l
1 8,88 17,11 ;1,=4 ;5,33 43,45
4 41,44 8,88 6=,;3 67,1; ;>,81
; ;8,=1 6>,;3 8,88 15,44 55,4=
6 ;>,5; 51,1; 16,43 8,88 55,1=
114,=6 1,881 11;
155,>1 1,884 153
16=,3> 8,77= 16=,;4
15=,18 8,77> 15 15>,>
5 Jg cJ g J 'g 45,4> 116,=; 1,881 115 ;6,73 15 154,53 1,884 15 154,== 53,;1 15 158,>6 8,77= 15 158,;= 53,1> 15 153,17 8,77= 155,= 8,88 1>;,>1 1,884 1>6
1>4,>1 9 1,884 1>;
>6=,83 >6=,84 ≨ C 1,8888
Cue`te< eoadjrakgû` prjpga
;.5. IEVJFJ ‛ CTAVAT CT Ojs káokuojs g`gkgaoes para eo içtjfj fe Cratar se e`kue`tra` e` oas sgnuge`tes tadoas. E` esta se puefe jdservar que ojs vgales ne`erafjs y atraéfjs `j sj` gnuaoes.
Vadoa 44. Káokuojs g`gkgaoes CT J /F 1 4 ; 6
Fl Cl F' l
5
1 8,88 1=,88 ;1,88 ;=,88
4 48,88 8,88 65,88 58,88
; ;8,88 66,88 8,88 13,88
6 68,88 54,88 15,88 8,88
43,88 11;,88 1,88 11;,88
;5,88 158,88 1,86 153,88
56,88 166,88 1,8; 16=,;4
57,88 133,88 8,75 15>,>8
Cue`te< eoadjrakgû` prjpga Vadoa 4;. Caktjres g`gkgaoes CT OJ1
1,8843 OF1
1,8844
OJ4
1,88== OF4
1,88>>
OJ;
8,7747 OF;
8,77;6
OJ6
8,7=51 OF6
8,7=58
OJ5
8,7773 OF5
1,8884
Cue`te< eoadjrakgû` prjpga 16
5 Jg Cg 45,88 11 115,88 ;;,88 16 16>,88 55,88 16 163,88 38,88 13 136,88
1,88 1,86 1,8; 8,75
J 'g 1 11 15,88 1 15 54,== 1 15 58,;= 1 15 55,=8
8,88 1> 1>6,88 1,88 1> 1>6,88 1>;,88 9 1,88 >6=,83 1>;,88 >6=,84 ≨
E` oas sgnuge`tes tadoas se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa prgiera gterakgû`, se aprekga que tjfjs ojs caktjres cJg y cFl ma` kaidgafj e` aprjxgiafaie`te iás j ie`js 8,5 % kj` respektj a ojs káokuojs g`gkgaoes, estj taidgç` ma sukefgfj kj` ojs caktjres OJ y OF. E` este kasj eo tjtao fe vgales atraéfjs y ne`erafjs (J‗g y F‗l) `j kjg`kgfe`. Vadoa 46. Káokuojs 1¸ gterakgû` CT J /F 1 4 ; 6 5
Fl cFl F' l
1
8,88 1=,=4 ;1,=5 ;5,=> 43,84 114,5> 1,88 11;
4
48,71 8,88 6=,44 67,44 ;3,5; 156,== 1,81 153
;
;8,=6 6>,1= 8,88 15,67 55,64 16=,7; 1,88 16=,;4
6
;>,>3 51,44 16,51 8,88 55,34 157,11 8,77 15>,>
5 Jg cJg J 'g 45,8; 116,56 1,886 115 ;6,6> 15 151,>8 1,88= 1 15 54,== 53,65 15 151,86 8,773 1 15 58,;= 53,5= 15>,13 8,771 155,= 8,88 1>;,38 1,884 1>6 1>4,56 9 1,88 >6=,83 1>; >6=,84 ≨
Cue`te< eoadjrakgû` prjpga
Vadoa 45. Caktjres 1¸ gterakgû` CT OJ 1 OJ 4 OJ ; OJ 6 OJ 5
1,8841 1,88;; 8,773> 8,773; 1,8817
OF1 OF4 OF; OF6 OF5
1,8844 1,88;8 8,773= 8,7734 1,8841
Cue`te< eoadjrakgû` prjpga E` oas sgnuge`tes tadoas se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa senu`fa gterakgû`, se aprekga que eo tjtao fe ojs vgales atraéfjs y ne`erafjs (Jg y Fl) kjg`kgfe`, perj aü` `j se ojnra oa kj`verne`kga fe ojs tjtaoes J‗g y F‗l. Vadoa 43. Káokuojs 4¸ gterakgû` CT
15
J /F 1 4 ; 6 5
Fl cFl F' l
1 8,88 17,87 ;1,=4 ;5,3> 43,46
4 41,48 8,88 6=,;5 67,1; ;3,7>
; ;8,=4 6>,;3 8,88 15,46 55,47
6 ;>,56 51,16 16,4> 8,88 55,48
114,=1 1,88 11;
155,35 1,88 153
16=,>8 1,88 16=,;4
15=,13 1,88 15>,>
5 Jg cJg J 'g 45,13 116,>4 1,884 115 ;6,7; 15 154,54 1,884 1 15 54,== 53,;4 15 158,>3 8,77= 1 15 58,;= 53,17 153,4; 8,77> 155,= 8,88 1>;,>8 1,884 1>6
1>4,31 9 1,88 1>;
>6=,83 >6=,84 ≨
Cue`te< eoadjrakgû` prjpga Vadoa 4>. Caktjres 4¸ gterakgû` CT OJ1 OJ4 OJ; OJ6 OJ5
1,888= 1,8818 8,77=; 8,77=; 1,888=
OF OF1 OF OF4 OF OF; OF OF6 OF OF5
1,888= 1,8887 8,77=6 8,77=; 1,8887
Cue`te< eoadjrakgû` prjpga E` oas sgnuge`tes tadoas se e`kue`tra oa g`cjriakgû` kjrrespj`fge`te a oa terkera gterakgû`, se jdserva que ojs tjtaoes fe vgales Jg y Fl kjg`kgfe`, perj que ojs vaojres J‗g y F‗l `j oj make`, pjr oj que `j se ooenû a oa kj`verne`kga fe estjs. Afeiás, ojs caktjres cFl fe oas zj`as 1,4,;,6 y 5 ma` peria`ekgfj kj`sta`tes, ojs caktjres OJ y OF ma` vargafj e` aprjxgiafaie`te 8.85 % kj` respektj a oa senu`fa gterakgû`. Xareke que ojs caktjres OJ está` prûxgijs a estadgogzarse.
Vadoa 4=. Káokuojs ;¸ gterakgû` CT J /F 1 4 ; 6 5
Fl cFl F' l
1 8,88 17,17 ;1,>> ;5,31 43,;5 114,74 1,88 11;
4 41,;1 8,88 6=,;4 67,87 ;>,15 155,=> 1,88 153
; ;8,=8 6>,;; 8,88 15,1; 55,44 16=,6= 1,88 16=,;4
6 ;>,51 51,18 16,1> 8,88 55,11 15>,=7 1,88 15>,>
Cue`te< eoadjrakgû` prjpga Vadoa 47. Caktjres ;¸ gterakgû` CT 13
5 Jg cJg J 'g 45,46 116,=3 1,881 115 ;5,14 15 154,>6 1,881 1 15 54,== 53,47 15 158,55 8,777 1 15 58,;= 53,16 155,7= 8,777 155,= 8,88 1>;,=; 1,881 1>6 1>4,>7 9 1,88 >6=,83 1>; >6=,84 ≨
OJ1 OJ4 OJ; OJ6 OJ5
1,888; 1,888; 8,7774 8,7774 1,888;
OF OF1 OF OF4 OF OF; OF OF6 OF OF5
1,888; 1,888; 8,7774 8,7774 1,8886
Cue`te< eoadjrakgû` prjpga
1>
6. AKVUAOG\AKGJ@ FE IAVTG\ J/F KJ@ IJFEOJ[ NTASGVAKGJ@AOE[ NTASGVAKGJ@AOE[ E` oa sgnuge`te cgnura se jdserva oa ref kjrrespj`fge`te a oa iatrgz fafa. Oas fgsta`kgas cuerj` jdte`gfas igfge`fj fgrektaie`te sjdre esta, kafa zj`a cue fgvgfgfa e` kuatrj partes sgnuge`fj oa dgsektrgz fe sus vçrtgkes, y kafa vez que u` arkj arkj se g` g`te ters rsek ekta tada da kj` kj` oa oass oéoé`e `eas as fe fg fgvg vgsg sgû` û` y/j y/j se dg dgcu curk rkad ada, a, se reng rengst stra rada da oa oj oj`n `ngtgtuf uf fe fgkm fgkmj j seni senie` e`tj tj,, pj pjst ster ergj gjri rie` e`te te se reao reaogz gza a u` prjiefgj kj` ojs senie`tjs jdte`gfjs, estj para kafa zj`a. Oa oj`ngtuf prjiefgj jdte`gfa es seoekkgj`afa kjij oa oj`ngtuf a rekjrrer para reaogzar vgales g`trazj`aoes, ige`tras que oa oj`ngtuf para fespoazarse fe u`a zj`a a jtra, está kj`sgferafa kjij oa oj`ngtuf prjiefgj g`trazj`ao fe oa zj`a g`gkgao, iás oas fe zj`as g`teriefgas, iás oa zj`a cg`ao, kua`fj se prese`ta` fjs jpkgj`es g`teriefgas se seoekkgj`a oa ie`jr. Cgnura 1. Tef vgao
Cue`te< afaptafj Cue`te< afaptafj fe VTAD VTADALJ ALJ G@FGSGFUAO G@FGSGFUAO FG[VTGDUKG FG[VTGDUKGJ@ J@ NEJN NEJNTACGK TACGKA A FE SGALE[ Vadoa ;8. Iatrgz fe fgsta`kgas e`tre zj`as J /F 1 4 ; 6
1 41 68 33 34
4 68 17 65 61
; 33 65 43 6=
6 34 61 6= 44
Cue`te< eoadjrakgû` prjpga
1=
Vadoa ;1. Iatrgz a alustar J /F 1 4 ; 6 F
1
4
;
6
55
38
45
;5
J 45 ;5 65 >8
Cue`te< afaptafj fe VTADALJ G@FGSGFUAO FG[VTGDUKGJ@ NEJNTACGKA FE SGALE[
6.1. IÇVJFJ XJVE@KGAO X E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs kjrrespj`fge`tes a oa prgiera gterakgû` feo içtjfj, para oa kuao es `ekesargj asuigr ojs vaojres fe D, sge`fj estjs gnuaoes a 1. E` tjfjs ojs kasjs se tradalará kj` u` vaojr fe ` gnuao a 4 . Vadoa ;4. Káokuojs 1¸ gterakgû` X D1
1 A1
7,13>3;3
D4
1 A4
5,>873>3
D;
1 A;
>,344=11
D6
1 A6
5,==4837
Cue`te< eoadjrakgû` prjpga
E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs kjrrespj`fge`tes a oa senu`fa gterakgû`, se puefe jdservar que ojs vaojres fe D para oas zj`as 1 y ; ma` auie`tafj e` aprjxgiafaie`te 13%, ige`tras que ojs vaojres fe oas zj`as 4 y 6 ma` fgsig`ugfj e` aprjxgiafaie`te 1; %. Afeiás, se gfe`tgcgka que para oas oas zj zj`a `ass kuyj kuyj va vaoj ojrr fe D ma auie auie`t `taf afj, j, eo vaoj vaojrr fe feoo pa pará ráie ietr trj j A ma fgsig`ugfj y vgkeversa. Vadoa ;;. Káokuojs 4¸ gterakgû` X D1
1,1>3=3= A1
=,67=11;
D4
8,7811=1 A4
5,71;513
D;
1,1=>;7; A;
>,88==5=
D6
8,=>6365 A6
3,;85717
Cue`te< eoadjrakgû` prjpga
E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs fe oa terkera gterakgû`, se jdserva que ojs par paráie áietrj trjss ia`tge ia`tge`e` `e` oa te` te`fe fe`kg `kga a `jidra `jidrafa fa a`terg a`tergjri jrie`t e`te, e, ojs vaojres fe D para oas zj`as 1 y ; ma` auie`tafj y ojs fe A, fgsig`ugfj. 17
Vadoa ;6. Káokuojs ;¸ gterakgû` X D1
1,446754 A1
=,;154>1
D4
8,=787>= A4
5,74;;>6
D;
1,447341 A;
3,=>76;
D6
8,=688>1 A6
3,=>76;
Cue`te< eoadjrakgû` prjpga
E` oa sgnuge`te tadoa se e`kue`tra` ojs káokuojs kjrrespj`fge`tes a oa kuarta gter gterak akgû gû`, `, e` esta esta se kj kj`s `sgf gfer era a qu que e oj ojss pa pará ráie ietr trjs js ma ma` ` ao aoka ka`z `zaf afj j oa kj`verne`k kj`ve rne`kga, ga, oa iáxgia iáxgia fgcere`kga fgcere`kga e`tre ojs vaoj vaojres res fe D, es feo 3 % oa kuao kjrrespj`fe ao vaojr fe oa zj`a 6, e` eo kasj fe ojs vaojres fe A, oa iáxgia fgcere`kga es feo ; %, taidgç` fe esta zj`a, kj` respektj a oa gterakgû` ;. Vadoa ;5. Káokuojs 6¸ gterakgû` X D1
1,44>8>3 A1
=,;76644
D4
8,=>36>5 A4
3,86>4=4
D;
1,41=171 A;
3,777183
D6
8,>=7;5= A6
Cue`te< eoadjrakgû` prjpga
3,>164;
Vjia`fj kjij recere`kga ojs vaojres kaogdrafjs e` oa kuarta gterakgû`, se feterig`a oa fgstrgdukgû` fe ojs vgales, apogka`fj oa sgnuge`te expresgû`. Sgl 9 Ag∞Jg∞Dl∞ Fl∞Kgl
∔
`
Fj`fe2 Sgl es eo `üierj fe vgales e`tre oa zj`a jrgne` g y y oa festg`j l, Jg es eo tjtao fe vgales ne`erafjs pjr oa zj`a g, Fg es eo tjtao fe vgales atraéfjs pjr oa zj`a l, A es eo caktjr kaogdrafj fe prjfukkgj`es para oa zj`a g , Dl es eo caktjr l, Kgl es oa fgsta`kga e`tre oa kaogdrafj fe lprjfukkgj`es para feo oa zj`a o a zj`a jrgne` g y y oa festg`j y, ` eo paráietrj ijfeoj.
Apogka`fj oa a`tergjr expresgû` se jdtge`e oa fgstrgdukgû` fe ojs vgales, oa iatrgz jrgne`/festg`j kaogdrafa se e`kue`tra e` oa sgnuge`te tadoa. [e jdserva que ojs vgales ne`erafjs para tjfas oas zj`as kjg`kgfe`, ya que oa fgcere`kga e`tre ojs reaoes y ojs alustafjs es feo 8 %, ige`tras que, para ojs vgales atraéfjs, se e`kue`tra` fgcere`kgas que `j supera` eo 4 %, para eo kasj fe estufgj ojs paráietrjs aü` `j ma` aoka`zafj oa kj`verne`kga gfeao, se esperaréa que e` oa sgnuge`te gterakgû` oa fgcere`kga te`fgera a ser feo 8 %. [e gfe`tgcgka taidgç` que, para tjfas oas zj`as, oa iayjr ka`tgfaf fe vgales, kjrrespj`fe` a ojs g`trazj`aoes, estj fedgfj a que prese`ta` oa ie`jr fgsta`kga e` kjiparakgû` kj` oas jtras zj`as fe festg`j. 48
Vadoa ;3. Iatrgz jrgne`/festg`j kaogdrafa X J /F 1
1 15,83
4 6,14 ; 4,45 6 ;,>6 F 45 45 Fk 45,1> 8,37 Fgc %
4 6,87
; ;,4>
6 4,5=
1>,7= 6,=8 =,61 ;5 ;5 ;5,4=
>,85 ;1,55 1;,54 55 55 55,;=
5,=5 3,68 66,;6 38 57 57,13
8,=8
8,37
J 45
Jk 45,88
;5 65 >8 1,64 -
;5,88 65,88 >8,88 -
Fgc %
8
8 8
8
-
Cue`te< eoadjrakgû` prjpga
6.4. IÇVJFJ E]XJ@E@KGAO E E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs kjrrespj`fge`tes a oa prgiera gterakgû` feo içtjfj, para oa kuao es `ekesargj asuigr ojs vaojres fe D, sge`fj estjs gnuaoes a 1. E` tjfjs ojs kasjs se tradalará kj` u` vaojr fe δ gnuao a 8,84;1, kjrrespj`fge`te ao g`versj feo prjiefgj fe oas fgsta`kgas prese`tafas e` oa tadoa ;8. Vadoa ;>. Káokuojs 1¸ gterakgû` E D1
1 A1
8,81>715
D4
1 A4
8,81;;4>
D;
1 A;
8,816>5>
D6
1 A6
8,81;3>=
Cue`te< eoadjrakgû` prjpga
E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs kjrrespj`fge`tes a oa senu`fa gterakgû`, se puefe jdservar que ojs vaojres fe D para oas zj`as 1 y ; ma` auie`tafj e` aprjxgiafaie`te 48 % y ; % respektgvaie`te, ige`tras que ojs vaojres fe oas zj`as 4 y 6 ma` fgsig`ugfj e` aprjxgiafaie`te = %. [e jdserva eo igsij kjipjrtaige`tj que para eo ijfeoj pjte`kgao. Xara oas zj`as kuyj vaojr fe D ma auie`tafj, su vaojr fe A ma fgsig`ugfj. Vadoa ;=. Káokuojs 4¸ gterakgû` E D1
1,176;=4 A1
8,81>;76
D4
8,746683 A4
8,81;;35
D;
1,8448>1 A;
8,816>6=
D6
8,73134= A6
8,81;=;3
Cue`te< eoadjrakgû` prjpga 41
E` oa sgnuge`te tadoa se e`kue`tra` ojs fatjs fe oa terkera gterakgû`, se jdserva que eo paráietrj D, fe oa zj`a 1 ma auie`tafj e` 1 %, e` esta jkasgû` eo vaojr fe D kjrrespj`fge`te a oa zj`a 4 ma auie`tafj, y que ojs fe oas zj`as ; y 6 ma` fgsig`ugfj, e` este kasj e gterakgû`, se jdtge`e` resuotafjs fgcere`tes a ojs e`kj`trafjs e` oa igsia gterakgû` feo ijfeoj pjte`kgao. Vadoa ;7. Káokuojs ;¸ gterakgû` E D1
1,48416> A1
8,81>;3>
D4
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8,75=7>1 A6
8,81;=65
Cue`te< eoadjrakgû` prjpga
E` oa sgnuge`te tadoa se e`kue`tra` ojs káokuojs kjrrespj`fge`tes a oa kuarta gter gterak akgû gû`, `, e` esta esta se kj kj`s `sgf gfer era a qu que e oj ojss pa pará ráie ietr trjs js ma ma` ` ao aoka ka`z `zaf afj j oa kj`verne`kga, se jdserva que ojs vaojres fe D para oas zj`as 1 y 4 ma` auie`tafj, ige`tras que ojs fe oas zj`as ; y 6 ma` fgsig`ugfj, afeiás, ojs paráietrjs A fe oas zj`as ; y 6 peria`eke` kj`sta`tes. Vadoa 68. Káokuojs 6¸ gterakgû` E D1
1,484576 A1
D4
8,74545; A4
D;
1,84155> A;
8,816>51
D6
8,75==4= A6
8,81;=65
8,81>;33
8,81;;3
Cue`te< eoadjrakgû` prjpga
Vjia`fj kjij recere`kga ojs vaojres kaogdrafjs e` oa kuarta gterakgû`, se feterig`a oa fgstrgdukgû` fe ojs vgales, apogka`fj oa sgnuge`te expresgû`. δ∞Kgl
∔
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Fj`fe2 δ es eo paráietrj feo ijfeoj. Apogka`fj oa a`tergjr expresgû` se jdtge`e oa fgstrgdukgû` fe ojs vgales, oa iatrgz jrgne`/festg`j kaogdrafa se e`kue`tra e` oa sgnuge`te tadoa. [e jdserva que ojs vgales ne`erafjs para tjfas oas zj`as kjg`kgfe`, ya que oa fgcere`kga e`tre ojs reaoes y ojs alustafjs es feo 8 %, ige`tras que, para ojs vgales atraéfjs, se e`kue`tra` masta feo 6 %, iayjr que oa jdte`gfa e` eo ijfeoj pjte`kgao, para eo kasj fe estufgj ojs paráietrjs aü` `j ma` aoka`zafj oa kj`verne`kga gfeao, se esperaréa que e` oa sgnuge`te gterakgû` oa fgcere`kga ta`tj para ojs vgales atraéfjs kjij ne`erafjs te`fgera a ser feo 8 %. 44
[e gfe`tgcgka taidgç` que, para tjfas oas zj`as, oa iayjr ka`tgfaf fe vgales, kjrrespj`fe` a ojs g`trazj`aoes, oj kuao kj`fgke kj` eo içtjfj pjte`kgao, perj e` este kasj oa prjpjrkgû` es ie`jr. Vadoa 61. Iatrgz jrgne`/festg`j kaogdrafa E J /F 1 4 ; 6 F Fk Fgc %
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Cue`te< eoadjrakgû` prjpga
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