Kuí` ld Dstulhb O. 8
0. Ibs shkuhdot shkuhdotds ds v`ibrds v`ibrds fbrrdspbo fbrrdspboldo ldo ` i`s dst`tu dst`tur`s r`s ld uo krupb krupb ld `iumobs `iumobs ld uo` uo` hostufhöo ’JKN”, dxprds`l` do fm. 06.>< >6 .>< >1.>: >:.44 >:.4 4 67.78 >8.04 >8. 04 >8.07 >:.8> >8.87 >8. 87 67.6< 6>.0.7;+>6.>1.>:+>:.44+>:.8>+>8.07+>8.04+>8.87+67.78+67.6.:.78 00 00 >8.07
Ohokuob (\blbs dodo hku`i fbolhfhöo ob sd rdphtdo màs ld uo` vdz)
8. Di Mhohstdrhb ld Dluf`fhöo hobrmö qud lur`otd ibs óimbs `ðbs rdfhnhdrbo kr`lbs ld ihfdofh`tur` do Fhdofh`s M`tdmàf`s d Hobrmàf` Hobrmàf` @lmhohstr`v` di shkuhdotd oómdrb ld pdrsbo`s3 4766 414> 170 :;08 0004< 040>0 ²Fuài ds di prbmdlhb `ou`i ld ibs kr`lu`lbs2²Ds uo` mdlh` mudstr`i b pbni`fhbo`i2 = ´ = 4766+414>+170+:;08+00040 = 48>:; = :7.< >7.7 >>.> >6.: >0.6 >4.0 >0.> >>.8 >:.> >>.7 >4.; >>.; >6.1 >6.> >0.7 To dmpb prbmdlhb pbr pi`f` mdobr ` ibs >6 sdkuolbs holhf` uo` prblufvhl`l s`s`ftbrh`. ²Ldndrí` ld dst`r prdbfup`lb di Kdrdotd ld Wrbluffhöo2 = >7.7+>7.0.7+>0.>+>0.6+>>.7+>>.>+>>.;+>>.8+>6.>+>6.1+>6.:+>:.> = 6.>84 >7 >7 = \hdod qud rdlufhr di dmpb pbrqud ib holhf`lb sdrí` mdobr ` >6 sdkuolbs. Ldnd nusf`r dstr`tdkh`s.
06. I` fbmp`ðí` ZXS dod uo fbotr`tb ld frèlhtb rbt`vb fbo N`ofb @tiàol`. Di frèlhtb dod ibs shkuhdotds s`ilbs mdosu`ids. D A M L 0>067 00>67 ;>:7 :7
;>:7
4;67
4:;7
1007
47:7
7
7
7
7
7
7
7
7
7
I` fbmp`ðí` ds didkhnid p`r` btbrk`rid uo` t`s` ld hotdrès n`c`, sh su s`ilb prbmdlhb ds m`ybr ld I. 14,777.77. ²I` fbmp`ðí` bndod i` t`s` ld hotdrès n`c`2 ` = 0>0677+00>677+;>:77+;>:77+;>:77+4;677+4:;77+10077+47:77+ 77 + ;177 = 1:,811.1; 0> 0> n = Vh i` bndod.
Kuí` ld Dstulhb O. 07 F`ifui`r di v`ibr ld3 `. I` Mdlh`, n. I` Mdlh`o`, f. I` Mbl` ld i`s shkuhdotds lhstrhnufhbods ld rdfudofh`. 0. Z A Ax A` 0
6
6
6
6
>
1
4
4
:
;
>0
00
0
00
>>
ƨ
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0>>
Z = ƨ o = 0>> = 4.4> W = o + 0 = >> + 0 = 00.4 Md = 4 > > f. Mbl` 4
6. Z
A
Ax
A`
06.>
6
68.1
6
04.6
4
;1.4
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0;.>
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01
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60
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Z = ƨ o = 441.0 = 0;.8< o 60 W = o + 0 = 60 + 0 = 01 Md = 0;.> > > f. Mbl` 08.>
4. Z
A
Ax
A`
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4
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4
>6.1
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*To didv`lbr ld uo jbtdi dstà lhsdð`lb p`r` sbpbrt`r uo pdsb màxhmb ld >777 ihnr`s. ²Vd sbnrdf`rk` sh do uo vh`cd tr`ospbrt` : mucdrds qud pds`o 0>6 ihnr`s y ` 4 jbmnrds qud pds`o 0;< ihnr`s f`l` uob. Z A Ax Mucdrds 0>6 ins
:
8:<
Jbmnrds 0;< ins
4
:;7
ƨ
06
0:4<
8. I`s puotu`fhbods ao`ids do hokids, fbmput`fhöo, fbot`nhihl`l, m`tdmàf` y dsp`ðbi ld uo dstulh`otd udrbo3 ;:% :4% 16% ;7% :7% rdspdfv`mdotd. rdspdfv`mdotd. Vh tdoí`o 7 ` 477 ld sus sbfhbs do 0886, I. 14.6> ` 4;4 sbfhbs do 0887 ` 17: sbfhbs do 0884, I. :;.6> ` 117 sbfhbs dm 0881. ²Fuài ds i` mdlh` pboldr`l` ldi lhvhldolb2 Zw = 46.>(477) + 14.6>(4;4) + ;6.>(17:) + :;.6>(117) = >1177+6;448+684.:7 = ;7.8: >64< mhiibods ld ihnr`s ld idoku`lb, 66 rdspdfv`mdotd mhiibods ld ihnr`s ld n`f`i`b, 06 mhiibods ld ihnr`s ld pdrf`, 00> mhiibods ld ihnr`s ld `n`ldcb, >;8 mhiibods ld ihnr`s ld `tóo. ²Fuài ds di prbmdlhb kdodr`i ld ibs prdfhbs pbr ihnr` qud rdfhndo ibs pdsf`lbrds2 Zw = 7.44)+ 7.101(>;8) = 618,40:,777 180 mhiibods ld ihnr`s 180 = 7.46 = 4.71> 07 07 4.0; + 4.>< = 07. > Mbl` ob dod
;. Do fu`trb ldp`rt`mdotbs ld uo` fbmp`ðí`, 087 tr`n`c`lbrds rdfhndo do prbmdlhb uo s`i`rhb ld I. .14 pbr jbr` y >7 rdfhndo uo` p`k` do prbmdlhb ld I. 07 (0 + 48 + >>;; + >:> = 087 + 107 + 0:7 + >7 0777
:877 = :.87 0777 *Lur`otd i` f`mp`ð` ld vdot`s ld `nrhf`otds ld fhdrtb dquhpb, ibs >7 tr`n`c`lbrds ldi fdotrb prbmdlh`rbo 047 oudvbs fbot`ftbs ld fbmpr`, ibs >4 ldi obrtd prbmdlh`rbo 0:7 y ibs 04 ldi sur prbmdlh`rbo 017. ²Fuài ud di prbmdlhb tbt`i ld ibs oudvbs fbot`ftbs ld fbmpr` ibkr`lbs pbr dsbs vdoldlbrds2 Zw = >7(047) >7(047) + >4(0:7) + 04(017) = 6777+7 + >4 + 04 17 17
Kuí` ld Dstulhb O. 00 Ldtdrmho`r3
`. I` mdlh` n. I` mdlh`o` f. I` mbl`
0. Z
A
A`
I^
Zm
Axm
4 -
8
4
4
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08.4 ‖ >>
>>7
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>8
1
66
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>;
01>
Zm
Axm
ƨ
66
4:0
Z = ƨxm = 4:0 = 0;.10 o 66 Md = Irh + f (o/> - ƨ 0) = 0 ‖ 06) = 0.4 0 - > 1+< 6. Z
A
A`
;
0
0
1
1
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07
4
1
8
7
04
047
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6
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06.4 ‖ 01.4
46<
Z = ƨxm = 46< = 04.;0 o 6< Md = Irh + f (o/> - ƨ 0) = 06.4 + 6 (6 ‖ 07) = 06.4 + >.0 = 04.1 md 07 Mb = Irh + f (
0 ) = 06.4 + 6 ( 1 ) = 06.4 +0.:6 = 04.6 0 - > 1+<
4. Z
A
A`
I^
Zm
Axm
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4
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8.4 ‖ 06.4
1 ‖ >>) = 8.4 + 0.> Mb = Irh + f (
0 ) = 8.4 + < ( 0 - >
; ) = 8.4 + 0.:; = 00.6; ;+ : 1.
;. Wdsbs do ek ld uo` mudstr` ld p`qudtds mds ld cuohb
Z
A
A`
I^
Zm
Axm
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07.8
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88.4 >88.84 ‖ 6;.7: = 6>;.76 md ;> Mb = Irh + f (
0 ) = >88.84 + 47 (
0<
) = >88.84 +67. 0< + 8 00. I`s dl`lds ld ibs rdshldotds ld i` Fbiboh` C`rlhods ld Ib`rqud ldi nibqud 08, dstào ldsfrht`s do i` shkuhdotd lhstrhnufhöo ld rdfudofh`s. F`ifui`r `. I` mdlh` n. I` mdlh`o` f. I` mbl`
Z
A
0;.7 - >>.8 67 >6.7 - >:.8 64 >8.7 - 64.84 87:.>4 >:.84 - 6 04 046 6
Zm
Axm
6;.8 6;.84 4
0>0< 0>0 - ƨ 0) = >:.84 + 1 (>01/> ‖ 14) = >:.84 + :.84 + 1 (
>0
) = >:.84 + >.: = 60.;4
0 - >
>0 + ><
06. To` màquho` `utbmàf` iido` i`t`s ld cukb ld o`r`oc`. To` vdrhaf`fhöo ld ibs pdsbs ldi fbotdohlb ld uo fhdrtb oómdrb ld i`t`s rdvdib ib shkuhdotd3 F`ifui`r `. I` mdlh` n. I` mdlh`o` f. I` mbl` Z A A` I^ Zm Axm 067 -
068
>
>
0618
0;, >1 >> phsbs. F`ifui`r i` ldsvh`fhöo dstàol`r ld dst` mudstr` ld dlhafhbs. O=01 ∐x=4, 6>, >;, >;, >1 >> phsbs. O=0> ∐x=6;0
V= V= V= V= V= =( =
>7.<
F`ifui`r i` ldsvh`fhöo dstàol`r y v`rh`oz` ld i` shkuhdotd lhstrhnufhöo do rdfudofh` shmpid.
x 4 1 ; : 8 07 00 O= 6< O=6<
A > 4 : ; 6 < 4
x 4 1 ; : 8 07 00
x > 4 : ; 6 < 4
O= 6< >;< >60:
V= V= V= V= =( =
6.60
07 67 41 41 >; 4->4
A
: 04 6: 07 : 1 :4
Zm
AZm
A(xm)>
00 0< 0; >7 06 >1
:: >07 >77 0:< 041 0,,8 ;,0;:
´>= (0;.=67;.0;:-67.8 67- 1 0> 47
0.84 6.84 4.8: ;.84
6.8 >6.; ;0.< 48.;4
;.10 86.1> 8 067-04 18.;4
6,,0.7< 8;6.70
0,786.;4
07,>11.66
0>4
Q`rh`oz` ∎>=608.;<
*ibsLdrdfbrrhlbs ibs dmpid`lbs uo`dotrd dmprds`, sd bntuvb i` shkuhdotd lhstrhnufhöo do ibsld vh`cds di jbk`r y i` bafho`. Di rdfbrrhlb Z sd l`ld dordfudofh` Em. J`ii`rsbnrd i`
mdlh`, i` ldsvh`fhöo dstàol`r y i` v`rh`oz` ld i` lhstrhnufhöo. Fboshldrd fbmb pbni`fhöo (O) prhmdrb y ldspuès fbmb mudstr` (o) dxpihqud i` lhdrdofh` sh i` j`y.
´ = 0786.;4 = :.;4 0>4 > ´ = (:.;4)> = ;1.41 ∎
Ldsvh`fhöo Dstàol`r Wbni`fhbo`i 07.>11.66 ‖ ;1-4 ;1-41 1
∎ :>.06 -; -;1 1.41 4.4; ∎ ∎ =>.61
0>4
Q`rh`oz` Wbni`fhbo`i ∎>= :>.06-;1.41 ∎>= 4.4;
Ldsvh`fhöo Dstàol`r mudstr`i Z = 0786.;4 = :.;4 0>4 R Z > = ;1.41
07 ,>11 ,>11.6 .66 6
- 0>4( 0>4(;1 ;1.4 .41) 1)
= :>.;8 -84 -84;7
V= 0>4 -0
0>4-0
0>4-0
=
:>.;8 -;; -;;.0: = = >.6;
4.10
* Z
A
Zm
Axm
A(xm)>
6-4 1-: 8-00 0>-0< 04-0;
> 07 0> 8 :
< ; 07 06 01
;7 ;7 0>7 00; 0>:
4> 77 0400 >77 >0->6
< >
08 >>
;1 0 sd ids hmp`rö di di mhsmb fursb ld ld f`p`fht`fhöo. Di krupb 0 `lhdstr`lb `lhdstr`lb fbo di p`qudtd @ rdquhrhdrbo do prbmdlhb 6>.00 jbr`s jbr`s y uo` v`rh`oz` ld 1:.78 jbr`s y di krupb > fbo di p`qudtd N quhdods quhdods rdquhrhdrbo uo prbmdlhb prbmdlhb ld 08.;4 jbr`s y uo` v`rh`oz v`rh`oz`` ld ;0.0< jbr`s. ²Fuài prbkr`m` mbstrb i` mdobr v`rh`nhihl`l rdi`v`2 ²Wbr què2 Lds`rrbiib Krupb ’@” L`tbs3 F.Q= Krupb ’N” L`tbs
Krupb ’@”
F.Q=
L.Vt`ol`r
F.Q= ^/. Di krupb ’@” mbströ mdobr v`rh`nhihl`l, pbrqud dod mdobr pbrfdot`cd ld lhspdrshöo.
*Do ibs 6 óimbs `ðbs i` fbmp`ðí` @ `if`ozb uo prbmdlhb ld rdolhmhdotb sbnrd i` hovdrshöo ldi >:% fbo uo` ldsvh`fhöo dstàol`r 4.6% y i` fbmp`ðí` N, uo rd rdolhmhdotb olhmhdotb prbmdlhb ldi 6;.:% fbo uo` ldsvh`fhöo dstàol`r ld > FF. Btr` prblufd 0:7 ff fbmb prb prbmdlhb mdlhb fbo uo` ldsvh`fhöo dstàol`r dstàol`r ld :.1 :.1 FF. ²Fuài ld i`s lbs màquho`s dodo i` mdobr dx`ftul ldsld di puotb ld vhst` ld i` lhspdrshöo rdi`v`2 ²Wbr què2 L`tbs3 @= N= Màquho`3 F.Q= F.Q= I` màquho` ’@” dod mdobr dx`ftul pbrqud prdsdot` m`ybr pbrfdot`cd ld lhspdrshöo.
;. Di ludðb ld uo supdrmdrf`lb dmpid` lbs örmui`s örmui`s lhdrdotds lhdrdotds p`r` prdldfhr i`s vdot`s mdosu`ids. I` prhmdr` örmui` dod uo` `ii` prbmdlhb ld ;77 lhsfbs fbo uo` v`rh`oz` ld 0,>>4. I` sdkuol` ld 677 lhsfbs fbo uo` uo` ldsvh`fhöo dstàol`r ld 01. ²fuài brmui` ds rdi`v`mdotd mdobs prdfhs`2 Aörmui` ’0” F.Q.= Aörmui` ’>” F.Q.= ^/. I` Aörmui` ’>” ds i` mdobs prdfhs`.
8. To `o`ihst` ld hovdsk`fhöo p`r` uo` Dmprds` ld fbrrdt`cd ld `ffhbods, ldsd` fbmp`r`r i` lhspdrshöo do i`s r`zbods prdfhb- rdolhmhdotb.
^dolhmhdotb #0 F.Q. = ^dolhmhdotb #>
FQ = ^/. Di fbdafhdotd ld v`rh`fhöo obs pdrmhtd vhsu`ihz`r i` lhspdrshöo. *@ uo krupb ld `sphr`otds ` i`
[email protected]. sd id `pihf`rbo lbs prudn`s dxpdrhmdot`ids3 uo` ld `ftulds mdfàohf`s mdfàohf`s @M) y btr` ld ldstrdz` ldstrdz` m`ou`i LM). i` mdlh` ld i` prhmdr` prhmdr` prudn` ud ld >77 y i` ldsvh`fhöo dstàol`r dstàol`r ld 07. Do i` sdkuol`, i` mdlh` mdlh` ud ld 677 y i` v`rh`oz` ld 61. Fbmp`r`r i` lhspdrshöo rdi`v` ld `mnbs krupbs y dxpihf`r fu`iquhdr lhdrdofh`. Wrudn` (@M) F.Q. = Wrudn` (LM) F.Q. = Do i` prudn` (@M) ibs `sphr`otds prdsdot`rbo m`ybr rdolhmhdotb. ²Fuài ds di v`ibr ld Z dod i` m`ybr fboouhl`l rdi`v` `i fbocuotb ld l`tbs ldi fu`i prbfdld2 @3 Z=:4 lbold N3 Z=86 lbold Z=:4 lbold S= Z=86 lbold F. S= Di Z=:4 ldi fbocuotb ’@” dod m`ybr m`kohtul rdi`v`.
*Di oómdrb ld `fhdrtbs do uo dx`mdo ld `ptul, `pihf`lb ` ohvdi o`fhbo`i, dod uo` mdlh` y uo` ldsvh`fhöo dstàol`r ld 477 y 077 rdspdfv`mdotd, f`ifui`r di oómdrb ld `fhdrtbs p`r` f`l` v`ibr ld z3 S=0.: n) S=->.76 f) z=-0.> l) z=0.>> d) S=6.7> y @). S=0.:= S=S=-0.>= S=0.>>= S=6.7>=
*To` pbni`fhöo dod uo` mdlh` y ldsvh`fhöo dstàol`r ld 47 y 1 F) Z=47 L) Z=48 D) Z=;7 S= N=
S=
F=
S=
L=
S=
L=
S=
*Do uo` fbmp`ðí`, i` `ffhöo F dod uo prdfhb obrm`i mdlhb ld I.4:.77 fbo uo` ldsvh`fhöo dstàol`r ld I.00.77 y sd vdold `ftu`imdotd do I.;1.77. i` `ffhöo L sd vdold ` uo prdfhb mdlhb ld I.6:.77 fm fbo uo` ldsvh`fhöo dstàol`r ld I.0.< fbo ldsvh`fhöo dstàol`r ld 6.0, mhdotr`s qud ibs sbihfht`otds ` hokrds`r ` TOH\DF dod uo` f`ihaf`fhöo ld m`tdmàf` @F\ prbmdlhb ld >>.0 fbo ldsvh`fhöo dstàol`r ld >.: ²Fbo rdspdftb ` fuài ld dst`s > uohvdrshl`lds dstà uo dstulh`otd do uo` pbshfhöo rdi`v`mdotd mdcbr, sh bndod3 `) >1 do su dx`mdo n) 60 do su dx`mdo2
TWO pbrqud (0.
