Tema 4: MSE. Fernando González

 

]CID =

8/;0/7045

I[C. Ocrjdjmn Hnjzälcz

4

 

[BIPL [BIP L BOBKDKBÛJ MC CUPW CUPWC[BNJ C[BNJC[ C[ WDKBNJD WDKBNJDL L C[

;0/08/7045

 

7

 

[BIPL [BIP L BOBKDKBÛJ MC CUPW CUPWC[BNJ C[BNJC[ C[ WDKBNJD WDKBNJDL L C[

;0/08/7045

 

;

 

[BIPL [BIP L BOBKDKBÛJ MC CUPW CUPWC[BNJ C[BNJC[ C[ WDKBNJD WDKBNJDL L C[

;0/08/7045

 

=

 

[BIPL [BIP L BOBKDKBÛJ MC CUPW CUPWC[BNJ C[BNJC[ C[ WDKBNJD WDKBNJDL L C[

;0/08/7045

 

3

 

[BIPL [BIP L BOBKDKBÛJ MC CUPW CUPWC[BNJ C[BNJC[ C[ WDKBNJD WDKBNJDL L C[

;0/08/7045

 

?

 

ISL]BPLBKDKBÛJ R MB_B[BÛJ Mbvbsbûj Mbvbsb ûj mc cxprcsbnjcs cxprcsbnj cs rdkbn rdkbnjdlcs jdlcs ▦

Kdigbdjmn ld mbvbsbûj pnr iultbplbkdkbûj mc ordkkbnjcs.

▦

Sjd vcz quc sc ed inm nmbobobbkdmn cl cfcr fcrkbkbn sc prnkcmc d mcsdrrnlldr bhudl quc ld iultbplbkdkbûj, edkbcjmn odktnrbzdkbnjcs n prnmuktns jntdglcs, n lns dfustcs jckcsdrbns.

;0/08/7045

 

8

 

ISL]BPLBKDKBÛJ R MB_B[BÛJ

;0/08/7045

 

5

 

]CID 3

8/;0/7045

I[C. Ocrjdjmn Hnjzälcz

2

 

]CID 40. [B[]CID[ [B[]CID[ LBJCDLC[

Lds idtciätbkds snj ld iösbkd mc ld rdzûj. Fdics Fnscpe [ylvcstcr 

;0/08/7045

40

 

CKSDKBNJC[ LBJCDLC[ MC SJD BJKÛHJB]D ▦

Sjd ckudkbûj knjstd mc mns pdrtcs lldidmds ibcigrns   y cl sbhjn mc bhudlmdm   “9’. Cfcipln6

;0/08/7045

44

 

]BPN MC [NLSKBNJC[ MC [B[]CID[ LBJCDLC[

;0/08/7045

 

47

 

IÂ]NMN[ MC [NLSKBÛJ ;0/08/7045

4;

 

[NLSKBÛJ PNW [SID[ R WC[]D[ ▦

Wcknrmcins quc kudjmn guskdins snlukbnjcs mc uj sbstcid mc ckud kudkbnjc kbnjcss lbjc lbjcdlcs, lcs,  jns rcocrbins d uj pdr nrmcjdmn mc vdl dlnr nrcs cs (n iäs iäs) quc quc sdtbs dtbsod odkc kcjj tnmd tnmdss lds lds ckud ckudkb kbnj njcs cs mcl mcl sbstcid.

▦

Cstc iâtnmn mc s u i ds y r cs t ds , quc cs cl iäs scjkblln, tbcjc kni ninn ngfct gfctbbvn rcmukbr d ujd snld ckudkbûj bûj knj ujd snld bjkûhjbtd.

;0/08/7045

 

4=

 

;0/08/7045

 

43

 

[NLSKBÛJ PNW [SID[ R WC[]D[ ▦

Wcsnlvcr 

x-7y9? ;x+7y97

;0/08/7045

 

4?

 

[NLSKBÛJ PNW [SID[ R WC[]D[ ▦

[b suidins cl ldmn bzqubcrmn mc lds mns ckudkbnjcs tcjcins x - 7y 9 ? ;x + 7y 9 7 =x 9 5

▦

Mc deé quc R luchn sustbtuycjmn x 9 7 cj x-7y9? 7 - 7y 9? y 9 -7

▦

Ld snlukbûj pdrd cl sbstcid cs (7, -7), cstc pdr nrmcjdmn (cl prbicr vdlnr cs pdrd x, cl schujmn cs pdrd y) sdtbsodkc digds ckudkbnjcs.

;0/08/7045

 

48

 

[NLSKBÛJ PNW [SID[ R WC[]D[ ▦

▦

 Cfcipln 46  Wcsuclvc pnr suids y rcstds 7x + y 9 ; (ckudkbûj 4) =x + 7y 9 47(ckudkbûj 7)

▦

▦

 Pnmcins clbibjdr ld vdrbdglc y dl iultbplbkdr ld ckudkbûj 4 pnr -7 y pnstcrbnricjtc suidr lds mns ckudkbnjcs. Knin sc iucstrd d knjtbjudkbûj6

 Knin yd sdgcins, jn tnmns lns sbstcids tbcjcj snlukbûj, sb ngtcjcins quc 0 9 ?, quc cs uj cjujkbdmn odlsn, cl sbstcid cs bjknjsbstcjtc y jn tbcjc snlukbûj.

;0/08/7045

 

45

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ ▦

▦

▦

[ustbtukbûj  Dqué tdigbâj cl ngfctbvn ngfctbvn cs rcmukb rcmukbrr cl sbstcid d ujd snld ckudk ckudkbûj bûj y ujd bjkûhjbtd. bjkûhjbtd. Cs bipnr bipnrtdjtc tdjtc rckdlkdr quc jn bipnrtd kudl iâtnmn mc snlukbûj sc ciplcc, sc llchd d ld ibsid knjklusbûj. Pdsns

4.

[c mcspcfd mcspcfd uujd jd bjkûhjbtd bjkûhjbtd cj ujd mc lds ckud ckudkbnjc kbnjcs. s.

7.

[c sus sustbtuy tbtuycc ld cxp cxprcsbû rcsbûjj mc cstd bjkûh bjkûhjbtd jbtd cj ld ntrd cckudkb kudkbûj, ûj, ngtcjbcjm ngtcjbcjmnn ujd ckudkbûj ckudkbûj knj knj ujd snld bjkûhjbtd.

;.

[c rcsucl rcsuclvc vc ld cku ckudkb dkbûj. ûj.

=.

Cl vvdlnr dlnr ngtcj ngtcjbmn bmn sc sustbtuyc cj ld ckudkbûj cj ld quc dpdrck dpdrckéd éd ld bjkûhjbtd mcspcfdmd.

3.

Lns mns vdln vdlnrcs rcs nngtcjb gtcjbmns mns knjst knjstbtuy btuycj cj ld snluk snlukbûj bûj mcl ssbstci bstcid. d.

Wcvbsd cl ibsin cfcipln rcsucltn pnr suids y rcstds denrd pnr sustbtukbûj pdrd kniprngdrln.

;0/08/7045

 

42

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ

;0/08/7045

 

70

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ ▦

Bhudldkbûj  Pdrd rcsnlvcr uj sbstcid mc ckudkbnjcs pnr cstc iâtnmn mc bhudldkbûj sc dplbkdj lns sbhubcjtcs pdsns6

▦

4. 7.

[c mcspcfd mcspcfd ld ibsid bjkûhjbtd bjkûhjbtd cj kdmd ujd mmcc lds ckudkbnjcs mcl sbstcid mdmn. [c bhudldj bhudldj cjtrc cjtrc sé lds cxprcs cxprcsbnjc bnjcss ngtcj ngtcjbmds, bmds, mc cstd cstd idjcrd idjcrd sc knjsbh knjsbhuc uc clbibjdr  clbibjdr  ujd mc lds bjkûhjbtds.

;.

Cstn md luhdr luhdr d ujd ckudkbûj ckudkbûj knj ujd bjkûhjbtd. bjkûhjbtd.

=.

[c rcsucl rcsuclvc vc ld ckudkb ckudkbûj ûj mc prbi prbicr cr hrdm hrdmnn rrcsult csultdjtc. djtc.

3.

[c sustbtuyc sustbtuyc cl vdlnr vdlnr mctcr mctcribj ibjdmn dmn cj kudlqu kudlqubcr bcrdd mc lds ckudk ckudkbnj bnjcs cs nrbhbjdl nrbhbjdlcs cs pdrd cjknjtrdr cl vdlnr mc ld ntrd bjkûhjbtd.

;0/08/7045

 

74

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ ▦

Bhudldkbûj  Pdrd rcsnlvcr uj sbstcid mc ckudkbnjcs pnr cstc iâtnmn mc bhudldkbûj sc dplbkdj lns sbhubcjtcs pdsns6

▦

4. 7.

[c mcspcfd mcspcfd ld ibsid bjkûhjbtd bjkûhjbtd cj kdmd ujd mmcc lds ckudkbnjcs mcl sbstcid mdmn. [c bhudldj bhudldj cjtrc cjtrc sé lds cxprcs cxprcsbnjc bnjcss ngtcj ngtcjbmds, bmds, mc cstd cstd idjcrd idjcrd sc knjsbh knjsbhuc uc clbibjdr  clbibjdr  ujd mc lds bjkûhjbtds.

;. =.

Cstn md luhdr luhdr d ujd ckudkbûj ckudkbûj knj ujd bjkûhjbtd. bjkûhjbtd. [c rcsucl rcsuclvc vc ld ckudkb ckudkbûj ûj mc prbi prbicr cr hrdm hrdmnn rrcsult csultdjtc. djtc.

3.

[c sustbtuyc sustbtuyc cl vdlnr vdlnr mctcr mctcribj ibjdmn dmn cj kudlqu kudlqubcr bcrdd mc lds ckudk ckudkbnj bnjcs cs nrbhbjdl nrbhbjdlcs cs pdrd cjknjtrdr cl vdlnr mc ld ntrd bjkûhjbtd.

;0/08/7045

 

77

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ

;0/08/7045

 

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ

7;

;0/08/7045

 

 

[NLSKBÛJ PNW [S[]B]SKB [S[]B]SKBÛJ ÛJ C BHSDL BHSDLD D KBÛJ

7=

;0/08/7045

 

73

 

IÂ]NMN MC KWDICW ▦

▦

Pdrd ciplcdr cstc iâtnmn cs jckcsdrbn prbicrn bjtrnmukbr ujns knjkcptns knin ln cs ujd idtrbz y cl mctcribjdjtc mc ujd idtrbz. Sjd idtrbz cs uj drrchln rcktdjhuldr mc jöicrns quc suclc rcprcscjtdrsc knj lctrds idyöskulds knin D, G, K. ctk. Cj cstc drrchln snln rcolcfdins ld bjonridkbûj kldvc n iäs rclcvdjtc mcl sbstcid.

;0/08/7045

 

7?

 

IÂ]NMN MC KWDICW ▦

▦

Pdrd ciplcdr cstc iâtnmn cs jckcsdrbn prbicrn bjtrnmukbr ujns knjkcptns knin ln cs ujd idtrbz y cl mctcribjdjtc mc ujd idtrbz. Sjd idtrbz cs uj drrchln rcktdjhuldr mc jöicrns quc suclc rcprcscjtdrsc knj lctrds idyöskulds knin D, G, K. ctk. Cj cstc drrchln snln rcolcfdins ld bjonridkbûj kldvc n iäs rclcvdjtc mcl sbstcid.

;0/08/7045

 

 

IÂ]NMN MC KWDICW ▦

Pnr cfcipln pdrd cl sbstcid lbjcdl6 ;x - 7y 9 4 x + ;y 9;

78

;0/08/7045

 

75

 

IÂ]NMN MC KWDICW  Ld idtrbz D knjscrvd lns kncobkbcjtcs kncobkbcjtcs (knj tnmn y sbhjn) mmcc lds vdrbdglcs x  c   y .  Ld idtrbz G idjtbcjc lns vdlnrcs d lns quc cstäj bhudldmds lds ckudkbnjcs.

▦

▦

 Cl tdidôn mc ujd idtrbz sc cskrbgc knin uj prnmuktn, dujquc jn sc iultbplbkd, y sc

▦

cskrbgc knin uj sugéjmbkc quc bjmbkd jöicrn mc rcjhlnjcs y knluijds, n gbcj, léjcds enrbznjtdlcs y vcrtbkdlcs.  Pnr cfcipl cfcipln, n, D cs mc tdidôn tdidôn 7x7 y G cs mc tdidôn tdidôn 7x4.

▦

▦

 Cl mctcribjdjtc mc ujd idtrbz sc ngtbcjc rcdlbzdjmn uj prnmuktn kruzdmn mc dkucrmn dl sbhubcjtc mbdhrdid.

;0/08/7045

 

IÂ]NMN MC KWDICW

 

72

;0/08/7045

 

 

DPLBKDKBNJC[ MC [B[]CID[ LBJCDLC[

;0

;0/08/7045

;4

 

PLDJ]CDIBCJ] PLD J]CDIBCJ]N N MC [B[]C [B[]CID[ ID[ MC CKSDKBNJC[ ▦

 Kdrlns bjvbrtbû $730 000, ujd pdrtc dl 8.3% y cl rcstdjtc dl ?%. [b cl bjtcrâs djudl mc lds mns

▦

bjvcrsbnjcs cs mc $4? 700 ¾kuäjtn mbjcrn bjvbrtbû d kdmd tdsd>  [nlukbûj6 0.083 x | 0.0?y 4?700 y 6 ld kdjtbmdm bjvcrtbmd dl ?%

▦

▦

▦

 Cstds mns kdjtbmdmcs (mcsknjnkbmds duj) sc rcldkbnjdj, sdgcins quc cj tntdl sc bjvbrtbcrnj $730 000.  Cjtnjkcs 0.083x | 0.0?y 4?700  R dmciäs cl bjtcrâs ngtcjbmn cs $4? 700 Knigbjdjmn digns rcjmbibcjtns, sc ngtbcjc6

;0/08/7045

 

;7

 

PLDJ]CDIBCJ] PLD J]CDIBCJ]N N MC [B[]C [B[]CID[ ID[ MC CKSDKBNJC[ ▦

Wcvbsd cl sbhubcjtc csqucid pdrd pldjtcdr y rcsnlvcr icmbdjtc uj sbstcid mc ckudkbnjcs.

;0/08/7045

 

;;

 

[NLSKBÛJ [NLSKBÛ J MC PWNGLCI PWNGL CID D [ DPLBKD DPLBKDMN[ MN[ ]bc bcjm jmd d mc mulkc mulkcss Sjd dibhd tbcjc ujd tbcjmd mc mulkcs y orutns sckns, lns kudlcs vcjmc d hrdjcl. ]digb digbâj âj qubc qubcrc rc no norc rckc kcrr uj pr prnm nmuk uktn tn knig knigbj bjdm dmnn mc kcrc kcrczd zdss kugb kugbcr crtd tdss knj knj

▦

▦

▦

▦

kenknldtc y kenknldtcs rcllcjns knj didrcttn. Lds kcrczds kugbcrtds knj kenknldtc sc vcjmcj cj $450 cl ah y cl kenknldtc knj didrcttn cj $4== pnr ah. ¾Kuäjtns ablns mc kenknldtc knj didrcttn mcgcräj iczkldrsc knj ? ablns mc kcrczds kugbcrtds, sb qubcrc vcjmcrln cj $4?0 cl abln> ¾Kuäjtns ablns edgrä mc ld iczkld> [nlukbûj6

;0/08/7045

 

[NLSKBÛJ MC PWNGLCID[  DPL  D PLBKD BKDMN[ MN[ ▦

]rdmukc

 

;=

;0/08/7045

 

[NLSKBÛJ MC PWNGLCID[  DPL  D PLBKD BKDMN[ MN[ ▦

Pldjtcd

 

;3

;0/08/7045

 

 

[NLSKBÛJ [NLSKBÛ J MC PWNGLCI PWNGL CID D [ DPLBKD DPLBKDMN[ MN[ ▦

Kdlkuld

;?

;0/08/7045

 

;8

 

[NLSKBÛJ [NLSKBÛ J MC PWNGLCI PWNGL CID D [ DPLBKD DPLBKDMN[ MN[ Pngldkbnjcs ▦

Ld pngldkbûj mc Kcrrns _crmcs tbcjc =0,000 edgbtdjtcs, y cstä krckbcjmn d ujd rdzûj mc 500 pnr dôn1 ld pngldkbûj mc Injtcs Dzulcs cs mc ??,000 edgbtdjtcs, y mckrckc d ujd rdzûj mc 300 edgbtdjtcs pnr dôn.

▦

¾Kuäjtn tbcipn pdsdrä pdrd quc digds tcjhdj ld ibsid pngldkbûj>

▦

[nlukbûj6

;0/08/7045

 

 

[NLSKBÛJ [NLSKBÛ J MC PWNGLCI PWNGL CID D [ DPLBKD DPLBKDMN[ MN[ ▦

]rdmukc

;5

;0/08/7045

 

 

[NLSKBÛJ [NLSKBÛ J MC PWNGLCI PWNGL CID D [ DPLBKD DPLBKDMN[ MN[ ▦

Pldjtcd

;2

;0/08/7045

 

[NLSKBÛJ MC PWNGLCID[  DPL  D PLBKD BKDMN[ MN[ ▦

Wcsuclvc

 

=0