Incerteza de Medição - Entre Erros e Incertezas

 

 

 

 

Tuaårfm  Eprcsclteâäm .............................................................................................. ..................................................................................................................................................... ....................................................... 4 5.

Crrms nc acnfâäm ...................................................................... ....................................................................................................................................... ................................................................. > 5.5. 5.?.

Crrm Tfstcaåtfdm c ^clnëldfe Flstruacltei ...................................................................................... ...................................................................................... 0 Crrm `fnudfei.............................................................................................................................. ........................................................................................................................................ .......... 0

5.4.

Crrm nc Jfstcrcsc ............................................................................................................................... ............................................................................................................................... 2

5.>.

Crrm aåxfam enafssávci.............................................................. ..................................................................................................................... ....................................................... 2

?.

Fldcrtcze nc acnfâäm .............................................................. ................................................................................................................................ .................................................................. :

4.

Eiberfsams Tfblf`fdetfvms ........................................................................................................................... ........................................................................................................................... 6

>.

Errcnmlneacltm ..................................................................................................................................... ..................................................................................................................................... 57

3.

Mpcreâócs Aetcaåtfdes c Eiberfsams Tfblf`fdetfvms ........................................................... .............................................................................. ................... 55

0.

@mltcs nc fldcrtcze ................................................................................................................................. ................................................................................................................................. 5?

2.

Diessf`fdeâäm nes `mltcs nc fldcrtcze ...................................................................................................... ...................................................................................................... 5> 2.5. 2.?.

Fldcrtcze ^fpm E ............................................................... ............................................................................................................................... ................................................................ 5> Fldcrtcze tfpm O................................................................................................................................ ................................................................................................................................ 52

 

 

Eprcsclteâäm

Miå! Tcke auftm oca-vflnm ç tcrdcfre euie nm dursm nc Fldcrtcze ne Acnfâäm. Le euie nc jmkc veams `eier smorc Crrms c Fldcrtcze ne Acnfâäm, frcams nc`flfr m quc säm c dmam mdmrrca ms crrms nc acnfâäm, frcams csteocicdcr ms dmldcftms nc crrm sfstcaåtfdm c tclnëldfe flstruacltei, crrm `fnudfei, crrm nc jfstcrcsc, crrm aåxfam enafssávci c nc`flfr m quc säm `mltcs nc fldcrtcze, eiæa nc fltrmnuzfr ms dmldcftms nc fldcrtczes ^fpm E c ^fpm O. Em `flei ncsse euie, scräm nfspmlfofifzenms cxcrdádfms pere `fxeâäm, icaorc-sc nc `ezë-ims, pmfs essfa vmdë pmncrå vcrf`fder sc rceiacltc dmaprcclncu m essultm treoeijenm lcsse euie.

Omls cstunms!

 

 

5 Crrms nc acnfâäm Pmdë kå ncvc tcr pcrdcofnm, ncsnc lmsse prfacfre euie, dmam æ dmapicxm rceifzer uae acnfâäm dma ua aálfam nc dml`feofifnenc. Le vcrnenc, acsam quc m mpcrenmr scke cxpcrfcltc, m cqufpeacltm cstcke oca deiforenm c es dmlnfâócs eaofcltefs cstckea dmltrmienes, mu scke, acsam quc tmnms ms dufnenms pmssávcfs sckea tmaenms, eflne essfa, queiqucr acnfâäm rceifzene tcrå uae fldcrtcze nc acnfâäm essmdfene e cie. Ca mutres peievres, æ fapmssávci `ubfr ne fldcrtcze nc acnfâäm, aes æ pmssávci dmrrfbfr m crrm!

Essfa, e flvcstfbeâäm smorc ms crrms clvmivfnms lm prmdcssm nc acnfâäm æ `ulneacltei. M prmdcssm nc deiforeâäm pcraftc e fncltf`fdeâäm nms crrms nc acnfâäm c nes fldcrtczes cxfstcltcs.

Deiforeâäm  Tcbulnm m ftca ?.46 nm PFA, Deiforeâäm æ e ’Mpcreâäm quc csteocicdc, smo dmlnfâócs cspcdf`fdenes, luae prfacfre

ctepe, uae rcieâäm cltrc ms veimrcs c es fldcrtczes nc acnfâäm `mrlcdfnms pmr penrócs c es flnfdeâócs dmrrcspmlncltcs dma es fldcrtczes essmdfenes8 luae scbulne ctepe, utfifze cste fl`mraeâäm pere csteocicdcr uae rcieâäm vfselnm e motclâäm nua rcsuitenm nc acnfâäm e pertfr nuae flnfdeâäm‑.   Ca mutres peievres, e deiforeâäm æ m dmlkultm nc mpcreâócs quc csteocicdc, smo dmlnfâócs cspcdf`fdenes, e rcieâäm cltrc ms veimrcs flnfdenms lm prmdcssm nc acnfâäm c ms veimrcs dmrrcspmlncltcs nes brelnczes csteocicdfnms pmr  penrócs. Æ fapmrteltc läm dml`ulnframs deiforeâäm dma ekustc. Uuelnm deiforeams ua cqufpeacltm läm sfblf`fde quc cic  pesserå e ’acnfr dmrrctm‑ epôs e deiforeâäm. M quc pmncams e`fraer æ quc scus crrms c e sue fldcrtcze scräm

dmljcdfnms, pmfs, e deiforeâäm æ rceifzene pmr acfm nc ua prmdcssm quc dmapere ms veimrcs acnfnms pcim cqufpeacltm, dma veimrcs nc ua penräm.

Eflne lcsse euie, vcrcams dmam restrcer es `mltcs nc crrm, aes pmr clqueltm, `fqucams dma e nc`flfâäm nc crrm;

Nc edmrnm dma m ftca ?.50 nm Pmdeouiårfm Fltcrledfmlei nc Actrmimbfe -  -  PFA, PFA, e nc`flfâäm nc crrm nc acnfâäm æ; ’Nf`crclâe ’Nf`crclâe cltrc m veimr acnfnm nuae brelncze c ua veimr nc rc`crëldfe‑. rc`crëldfe ‑. 

M veimr acnfnm cqufveic em rcsuitenm ne acnfâäm, c m veimr nc rc`crëldfe æ m veimr tcmrfdeacltc dmrrctm, mu scke, ’m veimr quc ncvcrfe ner‑. 

M crrm nc acnfâäm,dmam; mu crrm eosmiutm, pmnc, cltäm, scr nc`flfnm aetcaetfdeacltc

>

 

 

 1  ∟     Crrm eosmiutm

Crrm eosmiutm æ fbuei ç nf`crclâe cltrc m veimr flnfdenm lm flstruacltm c m veimr nc rc`crëldfe.

Mlnc C æ m veimr eosmiutm nm crrm, Z  æ  æ m veimr flnfdenm lm flstruacltm c P _ æ m veimr nc rc`crëldfe. . 

Moscrvc e faebca em ienm; M rcsuitenm eprcscltenm pcie oeielâe æ nc 7,677 hb, kå m veimr vcrnencfrm (pcsm-penräm) æ nc 5,777 hb. Dma oesc lcsses fl`mraeâócs, dmam deiduieams m crrm nc acnfâäm nm cqufpeacltm= Tfapics;  C 1 7,677 - 5,777 1 - 7,577 hb

Imbm, C 1 - 7,577 hb (icaorc-sc quc m Crrm scaprc tca e acsae ulfnenc ne acnfne quc vmdë rceifzmu). Moscrvc quc m sflei aetcaåtfdm ncvc scr dmlsfncrenm le cstfaetfve nm crrm nc acnfâäm (lm cxcapim edfae m crrm æ aclms zcrm várbuie ua qufimbreae), pmfs ua sflei pmsftfvm flnfde quc e acnfâäm nm flstruacltm æ aefmr quc m veimr nc rc`crëldfe c ua sflei lcbetfvm nclmte quc e acnfâäm æ aclmr quc m veimr nc rc`crëldfe. Uuelnm rceifzeams vårfes acnfâócs pmncams cldmltrer vårfms veimrcs pere m crrm nc acnfâäm. Lcstc desm dmam prmdcncr= Ncvcams enmter m aefmr veimr dmam m crrm nc acnfâäm. Cxcapim; @mrea rceifzenes quetrm acnfâócs ca uae oeielâe c cldmltrenms ms scbufltcs veimrcs; 5?2 5?2,3ab8 ,3ab8 5?2,0ab8 5?2,3ab c 5?2,>ab. Teoclnm quc m veimr nc rc`crëldfe æ 5?2,0:ab, quei m crrm nc acnfâäm ne oeielâe= M crrm nc acnfâäm æ nenm pcie cxprcssäm;  1  ∟  . Imbm tcrcams; C5 1 5?2,3 — 5?2,0: 1 - 7,5:ab C? 1 5?2,0 — 5?2,0: 1 - 7,7:ab C4 1 5?2,3 — 5?2,0: 1 - 7,5:ab C> 1 5?2,> — 5?2,0: 1 - 7,?:ab Dmam tcams quetrm veimrcs utfifzercams m veimr nm aefmr crrm nc acnfâäm (ca tcrams eosmiutms). C 1 - 7,?:ab Dmltfluelnm; 

3

 

 

5 5 Crrm Tfstcaåtfdm c ^clnëldfe Flstruacltei Nc edmrnm dma m ftca ?.52 nm  nm  PFA, PFA, m crrm sfstcaåtfdm æ e ’Dmapmlcltc nm crrm nc acnfâäm quc, ca acnfâócs rcpctfnes, pcraelcdc dmlsteltc mu verfe nc aelcfre prcvfsávci‑ . 

Läm cltclncu= Oma, quelnm m crrm enmte ua dmapmrteacltm prcvfsávci c rcpctftfvm, cic æ djeaenm nc crrm sfstcaåtfdm. Sa cxcapim nc crrm sfstcaåtfdm scrfe uae oeielâe quc crre scaprc ca 5hb ca queiqucr acnfâäm quc sc `eâe lcie. Cssc tfpm nc crrm, quelnm nctcdtenm, æ `edfiacltc dmrrfbfnm c rcprcsclte pmude fl`iuëldfe lm rcsuitenm ne acnfâäm. Le vcrnenc, quelnm ua sfstcae nc acnfâäm tclnc e rcpctfr ua dcrtm crrm, nfzcams quc jå uae tclnëldfe flstruacltei flstruacltei, quc pmnc scr deiduiene.

Cssc dåiduim æ rcprcscltenm ne scbufltc `mrae;

 1 ̃ ∟   

^clnëldfe flstruacltei

^clnëldfe æ fbuei ç nf`crclâe cltrc e aænfe nc rcpctfnes flnfdeâócs c ua veimr nc rc`crëldfe.

 æ e aænfe nc ua lûacrm `flftm nc acnfâócs, c P r æ m veimr nc rc`crëldfe pere m Mlnc ^  æ  æ e tclnëldfe,  tclnëldfe,  aclsurelnm. Cssc veimr pmnc scr ncsdmltenm mu edrcsdfnm em veimr acnfnm, pere eprmxfaer m rcsuitenm ne acnfâäm nm veimr dmlvcldfmlenm dmam dcrtm. Djeaeams csse mpcreâäm nc dmrrcâäm. Ebmre veams em prôxfam tfpm nc crrm;

5 ? Crrm `fnudfei Auftes vczcs läm æ dmlvclfcltc user nfrcteacltc m veimr eosmiutm nm crrm nc acnfâäm. Cxcapim; 7,5a nc crrm ca ?7a dmrrcspmlnca e 7,3% nc crrm nc acnfâäm8 7,5a nc crrm ca ?a dmrrcspmlnca e 3% nc crrm nc acnfâäm c8 7,5a nc crrm ca 7,?a dmrrcspmlnca e 37% nc crrm nc acnfâäm. M crrm `fnudfei æ ua pcrdcltuei nc ua veimr nc rc`crëldfe, teaoæa djeaenm nc veimr `fnudfei. Le brelnc aefmrfe nes sftueâócs ms veimrcs `fnudfefs säm csteocicdfnms ca rcieâäm ç eapiftunc ne flnfdeâäm nc acnfâäm (cxcapim nc aelþactrms c vmitáactrms), aes æ pmssávci cldmltrer flstruacltms dukm crrm `fnudfei æ deiduienm dmlsfncrelnm m veimr ne icfture dmam m veimr nc rc`crëldfe.

0

 

  M crrm `fnudfei æ deiduienm ne scbufltc `mrae;  C  `fnudfei

 C    

Pr 

 

Mlnc, C 1 crrm nc acnfâäm P rr  1    1 veimr nc rc`crëldfe

5 4 Crrm nc Jfstcrcsc  M crrm nc jfstcrcsc nc ua flstruacltm nc acnfâäm rcprcsclte e aefmr nf`crclâe cltrc ms veimrcs le derbe, c`ctuenm quelnm ne epifdeâäm nc ua sflei drcsdcltc ca veimr, c le ncsderbe, c`ctuenm quelnm ne epifdeâäm nc ua sflei ncdrcsdcltc ca veimr. Pcke m cxcapim. Cxcapim; Deiforeâäm nc ua aelþactrm, epifdelnm prcssäm (derbe) c eifvfelnm e prcssäm (ncsderbe).

(Peimr nm penräm) oer

Flnfdeâäm nm Flstruacltm le derbe (oer)

Flnfdeâäm nm Flstruacltm le ncsderbe (oer)

7

7

7

57

55

57

>7 37 07

46

>5

>6

37

07

07

Tflei cltrene

?7 47

56 47

56 47

Wcrdcocams quc lms pmltms nc 57 oer, >7 oer c 37 oer cxfstc uae nf`crclâe cltrc ms veimrcs le derbe c le ncsderbe, e seocr;   5 oer pere ms pmltms nc 57 oer c 37 oer c   ? oer pere m pmltm nc >7 oer Lcstc desm enmtercams dmam crrm nc jfstcrcsc nm aelþactrm m veimr nc ? oer. M `clþaclm ne jfstcrcsc æ oesteltc tápfdm ca flstruacltms acdïlfdms, tclnm es `mibes c nc`mraeâócs essmdfenes em etrftm dmam es prfldfpefs `mltcs nc crrm. Flstruacltms quc pmnca eprcsclter jfstcrcsc säm oeielâes, nfleaþactrms c aelþactrms eleiôbfdms.

5 > Crrm aåxfam enafssávci Tcbulnm m ftca >.?0 nm PFA, m crrm aåxfam enafssávci æ m ’v eimr cxtrcam nm crrm nc acnfâäm, dma

rcspcftm e ua veimr nc rc`crëldfe dmljcdfnm, edcftm pmr cspcdf`fdeâócs mu rcbuieacltms pere uae nene acnfâäm, flstruacltm nc acnfâäm mu sfstcae nc acnfâäm.‑   E lmrae oresficfre LO_ 5>573, pmr cxcapim, csteocicdc ms scbufltcs crrms aåxfams enafssávcfs pere aelþactrms tfpm Omuroml ca `ulâäm ne sue Diessc;

2

 

   

 

 

 

Diessc E>, crrm aåxfam nc 7,57%8 Diessc E4, crrm aåxfam nc 7,?3%8 Diessc E?, crrm aåxfam nc 7,37%8 Diessc E5, crrm aåxfam nc 5,7%.

Peams cxcapif`fder! Ncvcams deiforer ua aelþactrm ne Diessc E? c csdeie 7 e 07 oer. Uuei m crrm aåxfam enafssávci pere cssc flstruacltm=

@fbure 5; Aelþactrm eleiôbfdm. @mltc; m eutmr

_cspmste; pcie lmrae LO_ 5>573, e Diessc E? enaftc ua crrm aåxfam nc 7,3%. Dmlsfncrelnm m veimr aåxfam ne csdeie nc 07 oer c deiduielnm 7,3% ncssc veimr cldmltrercams 7,4 oer. Mu scke, sc nureltc e deiforeâäm cldmltrerams, pere queiqucr pmltm ne csdeie, ua crrm aefmr quc 7,4oer cssc flstruacltm ncvcrå scr rctfrenm nc usm, pmfs läm etclnc ms rcqufsftms lmraetfvms lmraetfvms..

? Fldcrtcze nc acnfâäm Eltcs ncua cltrer lm tôpfdm prfldfpei, æ e Fldcrtcze nc Acnfâäm prmprfeacltc nfte, æ fapmrteltc eomrner dmldcftm oåsfdm, quc æ mquc nc Eiberfsams Tfblf`fdetfvms. C pmr quc fssm æ fapmrteltc= Cxfstc ua nmduacltm nc rc`crëldfe fltcrledfmlei CE>/7?  —  Cxprcssäm ne Fldcrtcze nc Acnfâäm ca Deiforeâäm — quc csteocicdc quc ’M veimr luaærfdm ne fldcrtcze cxpelnfne ncvc scr eprcscltenm dma lm aåxfam nmfs eiberfsams sfblf`fdetfvms.  M veimr luaærfdm nm rcsuitenm ne acnfâäm, ca sue `mrae `flei, ncvc scr errcnmlnenm pere m ûitfam eiberfsam sfblf`fdetfvm nm veimr ne fldcrtcze cxpelnfne, etrfouáne em rcsuitenm ne acnfâäm.‑   Mre, sc läm dmljcdcams eiberfsams sfblf`fdetfvms, errcnmlneacltm, c es mpcreâócs aetcaåtfdes clvmivclnm csscs eiberfsams, dmam cxprcsser dmrrcteacltc m veimr ne fldcrtcze nc acnfâäm c m veimr luaærfdm nm rcsuitenm ne acnfâäm= Cltäm veams iå!

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4.  Eiberfsams Tfblf`fdetfvms  Tfblf`fdetfvms  M rcsuitenm nc uae acnfâäm motfne e pertfr nc dåiduims aetcaåtfdms ncvc icver ca dmlte quc ms lûacrms usenms tëa ua veimr aåxfam nc eiberfsams quc pmnca scr caprcbenms. Fssm pmrquc clvmivc ms dmldcftms nc fldcrtcze, cxetfnäm c rcsmiuâäm nc icfture. Tupmlnm, pmr cxcapim, quc :?,3>4 da rcprcscltc m veimr aefs prmvåvci nc uae acnfâäm, c quc e verfeâäm motfne le særfc nc acnfâócs `mf nc µ 7,?3 da. Ncvcams, cltäm, cxprcsser m rcsuitenm ne acnfâäm ne scbufltc `mrae;

(:?,3>4  7,?3) da Wcrdcoc-sc quc e scbulne dese ncdfaei nm veimr aefs prmvåvci kå æ e`ctene pmr uae dcrte nûvfne. Ncsse `mrae, e cxprcssäm dmrrcte nm rcsuitenm ne acnfâäm æ;

(:?,3>  7,?3) da Æ ncslcdcssårfm csdrcvcr e tcrdcfre dese ncdfaei kå quc e scbulne æ nuvfnmse. Essfa, eiberfsams sfblf`fdetfvms nc uae acnfne säm ’ms ’ms eiberfsams dmlsfncrenms dmrrctms, e dmlter nm  prfacfrm nf`crcltc nc zcrm, c m ûitfam ûitfam eiberfsam, eiberfsam, quc æ m nuvfnmsm nuvfnmsm‑  ‑ . Cltäm, queltms eiberfsams sfblf`fdetfvms pmssuf e acnfne :?,3> da= Wmssuf quetrm eiberfsams sfblf`fdetfvms; :, ? c 3 dmrrctms c m > nuvfnmsm. Pckeams e `fbure ne ræbue brenuene nc 7,3 ca 7,3 da eoefxm; e oefxm;

Mijelnm e pmsfâäm ne aerdeâäm nfráeams quc m veimr æ nc 0,3 da. M eiberfsam 3 æ m nuvfnmsm, pmfs läm pmncams e`fraer quc m pmsfdfmleacltm ne scte æ nc `etm 0,3 da. Tc e ræbue `mssc brenuene nc 5 ca 5 aa teivcz punæsscams icr 0,> da, 0,3 da mu 0,0 da. Acsam essfa, m eiberfsam >, m eiberfsam 3 c m scbulnm 0 ne acnfne 0,0 da scrfea nuvfnmsms.

Mutrms cxcapims;

5?4,37a dfldm sfblf`fdetfvms 7,7>:a nmfs sfblf`fdetfvms ?4a nmfs sfblf`fdetfvms 62,0a trës sfblf`fdetfvms

Ms zcrms läm säm sfblf`fdetfvms sc sftuenms ç csqucrne nm prfacfrm eiberfsam nf`crcltc nc zcrm, pmfs sô ncamlstrea quc m rcsuitenm ne acnfâäm æ fl`crfmr ç ulfnenc. Æ pmr fssm quc 7,7>: a sô pmssuf ? eiberfsams sfblf`fdetfvms.

6

 

  Ncvcams etclter pere m usm nm eiberfsam zcrm lm `flei nms lûacrms. Tc utfifzenms nc `mrae dmrrcte, cltäm 5?4,37 pmssuf dfldm eiberfsams sfblf`fdetfvms c 5?4,377 pmssuf scfs. Tc ms zcrms ç nfrcfte läm `mrca lcdcsserfeacltc sfblf`fdetfvms ncvc scr utfifzene e lmteâäm penräm cxpmlcldfei, mu "dfcltá`fde". Cxcapim; sc m lûacrm nc eiberfsams sfblf`fdetfvms `mr >, 3 mu 0 pmncams csdrcvcr 5?4.377 deimrfes dmam; 5?4,3 Ò 574 deimrfes (> eiberfsams sfblf`fdetfvms) 5?4,37 Ò 574deimrfes (3 eiberfsams sfblf`fdetfvms) 5?4,377 Ò 574 deimrfes (0 eiberfsams sfblf`fdetfvms)

>.  Errcnmlneacltm Errcnmlneacltm   Uuelnm m rcsuitenm nc uae acnfâäm eprcsclter ua lûacrm nc eiberfsams sfblf`fdetfvms supcrfmr em quc sc prcdfse ncvcams dmlscrver epcles ms lcdcssårfms. Wmr cxcapim, >3,206 a pmssuf dfldm sfblf`fdetfvms. Tc ncsckerams cxprcsser dma epcles trës ncvcams csdrcvcr >3,: a. Lmtc quc mdmactclnm eiberfsam ua ne crrm prfacfre desea. ncdfaei pessmu nc 2 pere :. Tc tfvæsscams usenm >3,2 a csteráeams nc 7,706 (>3,206 — >3,2) a 1 7,706a Em userams >3,: a dmactcams ua crrm aclmr nc 7,745 a. (>3,: — >3,206) a 1 7,745a Cxfstc uae lmrae oresficfre EOL^ LO_ 3:65;?75>  — _cbres nc errcnmlneacltm le luacreâäm ncdfaei rceif zer errcnmlneacltms;  — quc ncvc scr scbufne pere rceifzer   ’Uuelnm m eiberfsam e scr dmlscrvenm `mr scbufnm nc eiberfsam fl`crfmr e 3, pcraelcdc m

eiberfsam dmlscrvenm c rctfrea-sc rctfrea-sc ms pmstcrfmrcs.‑  pmstcrfmrcs.‑  

Cxcapim; 2,>4? errcnmlnenm pere uae dese ncdfaei `fde 2,>   ’Uuelnm m eiberfsam e scr dmlscrvenm `mr scbufnm nc eiberfsam supcrfmr e 3, mu fbuei e 3 scbufnm

nc lm aálfam ua eiberfsam nf`crcltc nc zcrm, smae-sc uae ulfnenc em eiberfsam dmlscrvenm c rctfrea-sc ms pmstcrfmrcs. pmstcrfmrcs.‑ 

Cxcapims; 2,>0 errcnmlnenm pere uae dese ncdfaei `fde 2,3 2,>370 errcnmlnenm pere uae dese ncdfaei `fde 2,3   ’Uuelnm m eiberfsam e scr dmlscrvenm `mr áaper, scbufnm nc dfldm c pmstcrfmracltc nc zcrms,

smae-sc uae ulfnenc em eiberfsam dmlscrvenm c rctfrea-sc rctfrea- sc ms pmstcrfmrcs pmstcrfmrcs.‑  .‑  

Cxcapim; 2,437 errcnmlnenm pere uae dese ncdfaei `fde 2,>   ’Uuelnm m eiberfsam e scr dmlscrvenm `mr per, scbufnm nc dfldm c pmstcrfmracltc nc zcrms,

57

 

   pcraelcdc e scr dmlscr dmlscrvenm venm c rctfrearctfrea-sc sc ms pmstcrfmrcs.‑  pmstcrfmrcs.‑  

Cxcapim; 2,>37 errcnmlnenm pere uae dese ncdfaei `fde 2,>

3.  Mpcreâócs Aetcaåtfdes c Eiberfsams Tfblf`fdetfvms  Tfblf`fdetfvms    c Tuotreâäm; m rcsuitenm `flei ncvc tcr m acsam lûacrm nc deses ncdfaefs ne perdcie quc e) Tmaepmssufr m aclmr lûacrm nc deses ncdfaefs. Cxcapim; 4:3,?0 a - 0,3 a + :,?43 a 1 = M rcsuitenm ncvc dmltcr epcles 5 dese ncdfaei, quc æ m lûacrm nc deses ncdfaefs ne perdcie 0,3 a. 4:3,?0 a + 0,3 a + :,?43 a 1 4:0,663 a Sselnm e rcbre ne smae c suotreâäm m rcsuitenm `flei scrå 4:2,7 a. o)  o)  Auitfpifdeâä Auitfpifdeâäm m c Nfvfsäm; m rcsuitenm `flei ncvc tcr m acsam lûacrm nc eiberfsams sfblf`fdetfvms ne perdcie quc pmssufr m aclmr lûacrm nc eiberfsams sfblf`fdetfvms. Cxcapim; 2:0,2> a? ò 4,02 a 1 = M rcsuitenm ncvc dmltcr epcles 4 eiberfsams sfblf`fdetfvms, quc æ m lûacrm nc eiberfsams sfblf`fdetfvms ne perdcie 4,02 a.

Sselnm e rcbre ne auitfpifdeâäm c nfvfsäm m rcsuitenm `flei scrå ??7 a. d) d)  

_efz Uuenrene; ua lûacrm dma l  eiberfsams sfblf`fdetfvms pmnc tcr l  mu l - 5  eiberfsams

sfblf`fdetfvms, ncpclnclnm ne lcdcssfnenc nm dåiduim. Cxcapim; 2?,3  + 4,2 1 :,3 + 4,2 1 5?,?

 2?,3 pmssuf 4 eiberfsams c

2?,3 + 4,20 1 :,35 + 4,20 1 5?,?2

:,3 pmssuf ? eiberfsams

 2?,3 pmssuf 4 eiberfsams c

:,35 pmssuf 4 eiberfsams

Dmljcdfnm m dmldcftm nc eiberfsam sfblf`fdetfvm c sues mpcreâócs, vmitcams em tôpfdm prfldfpei. Peams rcicaorer m dmldcftm nc Fldcrtcze nc Acnfâäm=

PFA ?75?    - Fldcrtcze ne Dml`mracænc`flfnm lm ftcaläm ?.?0lcbetfvm nm Pmdeouiårfm Fltcrledfmlei Actrmimbfe ?75? acnfâäm m; ’Werïactrm quc deredtcrfze e nfspcrsäm nms- veimrcs etrfouánm etrfouánms s e ua aclsurelnm, dma oesc les fl`mraeâócs utfifzenes‑ .

55

 

 

Tcbulnm m ftca ?.?.4 nm Bufe pere e cxprcssäm nc fldcrtcze nc acnfâäm -BSA BSA,, Fldcrtcze ne acnfâäm æ m; ’Werïactrm, essmdfenm em rcsuitenm nc uae acnfâäm, quc deredtcrfze e nfspcrsäm nms veimrcs quc  pmnca scr `ulneaclteiacltc `ulneaclteiacltc etrfouánms e ua aclsurelnm aclsurelnm‑  ‑ . Cstc perïactrm pmnc scr, pmr cxcapim, ua ncsvfm penräm (mu ua aûitfpim ncic), mu e actenc nc ua fltcrveim dmrrcspmlncltc e ua lávci ne dml`felâe ncdierenm. ncdierenm. Pmdë kå seoc quc m rcsuitenm nc uae acnfâäm æ smacltc uae eprmxfaeâäm mu uae cstfaetfve nm veimr nm aclsurelnm, ncste `mrae, e eprcsclteâäm nm rcsuitenm sô æ dmapictm quelnm edmapeljenm pmr uae queltfnenc quc ncdiere sue fldcrtcze c nc sue ulfnenc nc acnfâäm. Essfa, m rcsuitenm ne acnfâäm A pmnc scr cxprcssm le `mrae;

A 1 Z µ S X  âäQ âäQ  Mlnc Z æ m veimr ne acnfâäm c S æ e fldcrtcze `flei, mu

A 1̃xµ S X  âäQ âäQ  Mlnc̃x æ e aænfe nms rcsuitenms motfnms nc ua dmlkultm nc acnfâócs c S æ e fldcrtcze `flei. Essfa, e fldcrtcze æ ua perïactrm quc useams pere rculfr, ca ua ûlfdm veimr luaærfdm, S, tmnes es nfspcrsócs quc e acnfâäm ca qucstäm pmsse eprcsclter. Dene ua nms `etmrcs quc fl`iucldfea lm rcsuitenm nc uae acnfâäm ncvc scr eleifsenm nc `mrae sfstcaåtfde pere quc sue fl`iuëldfe scke nctcraflene c queltf`fdene. Wmr fltcr`crfrca le dml`feofifnenc ne acnfâäm, csscs `etmrcs quc pmnca scr e actmnmimbfe, m flstruacltm, m mpcrenmr, es dmlnfâócs eaofcltefs c ctd., säm nclmaflenms `mltcs nc fldcrtcze.

0 @mltcs nc fldcrtcze Ca lmsse prfacfre euie, quelnm tclteams acnfr m nfïactrm nc uae cs`cre actåifde e `fa nc deiduier scu vmiuac, vfams quc teltm m flstruacltm utfifzenm (pequáactrm dma fl`flftes deses ncdfaefs), dmam m lûacrm nc acnfâócs, e tcapcreture tcapcreture eaofcltc c ctd., ctd., e`cterea m rcsuitenm ne acnfâäm. Csscs `etmrcs quc säm flcrcltcs em prmdcssm nc acnfâäm dmltrfouca, ca aefmr mu aclmr breu, pere e queifnenc nm rcsuitenm, c säm djeaenms nc @mltcs @m ltcs nc fldcrtcze nc acnfâäm. M aepceacltm ncsses `mltcs nc fldcrtcze tmrle-sc lcdcssårfm läm sô pere seocr m queltm dene uae ncies fltcr`crc le acnfâäm, aes teaoæa pere `edfifter eâócs nc dmltrmic c nc acijmrfe nm prmdcssm nc acnfâäm. M nfebreae nc deuse c c`cftm (Fsjfhewe) Fsjfhewe) æ uae nes `crreacltes aefs usenes pere `ezcr m aepceacltm nes `mltcs nc fldcrtcze. Eoefxm tcams ua cxcapim nc nfebreae nc deuse c c`cftm, dukes `mltcs nc fldcrtcze säm es scbufltcs; e nc`flfâäm nm aclsurelnm, m prmdcssm nc acnfâäm, m flstruacltm nc acnfâäm, es dmlnfâócs eaofcltefs, m `etmr juaelm c m sfstcae nc acnfâäm utfifzenm. Dene uae ncies ncpclnc, pmr sue vcz, nc uae særfc nc `etmrcs, c, queltm aefmr `mr m lávci nc ncteijeacltm ncsscs `etmrcs, acijmr scrå m cltclnfacltm nm prmdcssm nc acnfâäm.

5?

 

 

Pcke ua cxcapim; Tcu Kmequfa lmtmu quc ms päcs quc cic vclnc ca sue penerfe cstäm dma pcsm eoefxm nm penräm. Cic seoc quc läm jmuvc queiqucr aunelâe lm quenrm nc pcssmei, les aåqufles pelf`fdenmres, lca lms `mrlcdcnmrcs nc `erflje, mvms c ctd. Cic vcrf`fdmu teaoæa quc läm jå queiqucr prmoicae dma m `mrlm mu dma es `mraes nms päcs, c teaoæa läm jå aunelâe moscrvåvci lm eaofcltc quc kustf`fquc e aunelâe lm penräm nc queifnenc nc scus päcs. Lm clteltm, scu Kmequfa sc csqucdcu nc vcrf`fder sc e oeielâe csteve acnflnm dmrrcteacltc, c quelnm e vcrf`fdmu, vfu quc cie csteve aerdelnm ua pcsm oca eoefxm nm cspcrenm. Cltäm, cic pcrbultmu ems scus `uldfmlårfms sc jmuvc eibuae mdmrrëldfe cstrelje lm `fa nc scaele c cics nfsscrea quc läm jmuvc lene `mre nm lmraei, e läm scr m `etm nm pcssmei nm eâmubuc vfzfljm tcr utfifzenm e oeielâe ne penerfe caprcstene pere pcser eibuaes pcâes nc derlc... Pmdë pcrdcocu dmam Tcu Kmequfa `mf actônfdm lm treteacltm nm prmoicae= Cic flvcstfbmu tmnes es pmssávcfs `mltcs nc crrm nm scu prmdcssm, dmam m quenrm nc `uldfmlårfm, `mrlcdcnmrcs, `mrlm, aåqufles, aetærfe-prfae, ctd. E pertfr nm amacltm quc cic vcrf`fdmu quc läm jevfe ua prmoicae lm prmdcssm nc prmnuâäm ms päcs, cic pessmu e sc pcrbulter sc jevfe eibuae `eije lm prmdcssm nc acnfâäm, c essfa, ncsdmorfu m prmoicae. Ca Actrmimbfe, e deredtcrfzeâäm nes `mltcs nc fldcrtcze cxfbc dcrtm cs`mrâm, kå quc dcrtms tfpms nc acnfâäm clvmivca uae beae auftm dmapicxe nc `etmrcs, c lca scaprc jå uae diere dmrrcspmlnëldfe cltrc dene `etmr dma m rcsuitenm ne acnfâäm. Dmltunm, e treoeijmse terc`e nc fncltf`fdeâäm nes `mltcs nc fldcrtcze æ auftm bretf`fdeltc, läm sô pmr rcsuiter ca uae cstfaetfve nc fldcrtcze aefs rc`flene, aes teaoæa pmr prmamvcr ua brelnc eprclnfzenm smorc m prmdcssm nc acnfâäm ca qucstäm.

54

 

 

2 Diessf`fdeâäm nes `mltcs nc fldcrtcze E deredtcrfzeâäm nes `mltcs nc fldcrtcze æ ua essultm oesteltc dmapicxm, c pmr fssm, tca sfnm cstunenm ç cxeustäm pmr nfvcrsms pcsqufsenmrcs, teltm quc eibuaes `mltcs nc fldcrtcze kå tëa scu dmapmrteacltm auftm oca dmljcdfnm c deteimbenm. E rcsmiuâäm nm flstruacltm, m lûacrm nc acnfâócs rceifzenes c e deiforeâäm nm flstruacltm säm eibuaes nes `mltcs nc fldcrtcze dmauls e aefmrfe nms prmdcssms nc acnfâäm c, pmr fssm, kå säm oca dmljcdfnes pmr actrmimbfstes nc nfvcrses årces. Kusteacltc pmr eprcsclterca penrócs nc dmapmrteacltm scacijeltcs, eibuaes `mltcs nc fldcrtczes säm nfvfnfnes ca tfpms, c sue dmltrfoufâäm pere e fldcrtcze æ nc`flfne pmr dmlvclâäm. dmlvc lâäm. Es `mltcs nc fldcrtcze aefs dmljcdfnes säm eveifenes nc edmrnm dma nues detcbmrfes; Fldcrtcze nm tfpm E c Fldcrtcze nm tfpm O, dml`mrac vcrcams e scbufr. 2 5 Fldcrtcze ^fpm E Tcbulnm m ftca ?.?: nm PFA, eveifeâäm nm ^fpm E ne fldcrtcze nc acnfâäm æ e ’  Eveifeâäm nuae dmapml dmapmlcltc cltc ne fldcrtcze nc acnfâäm pmr uae elåifsc cstetástfde nms veimrcs acnfnms, motfnms smo dmlnfâócs nc`flfnes nc acnfâäm‑ . 

Es fldcrtczes nm ^fpm E dmltcapiea dmapmlcltcs eveifenes pmr aætmnms cstetástfdms pere uae særfc nc nctcrafleâócs rcpctfnes. Csse cstretæbfe tca pmr `fleifnenc flnfder e rcpctfofifnenc  mu eicetmrfcnenc  nc ua prmdcssm nc acnfâäm, `cftm smo nctcraflenes dmlnfâócs. Essfa, quelnm uae `mltc nc fldcrtcze eprcsclter uae dmapmlcltc nc verfeofifnenc, fstm æ, quc pmsse scr deredtcrfzene pmr ua ncsvfm penräm, cltäm e `mltc nc fldcrtcze scrå nm ^fpm E.

 Ncsvfm penräm M  ncsvfm penräm  æ e acnfne nc nfspcrsäm aefs fapmrteltc pere e Actrmimbfe. Dma csse acnfne,  pmncams tcr uae  lmâäm prcdfse  ne verfeâäm nms veimrcs ca tmrlm ne aænfe. Oesfdeacltc, queltm  aclmr `mr m ncsvfm penräm, aclmr scrå e nfspcrsäm nms veimrcs, mu scke,  aefmr scrå m breu nc prcdfsäm  ncsse acnfne.

M ncsvfm penräm ncncacnfâäm (s)’æl‑utfifzenm pere eveifer e nfspcrsäm nms rcsuitenms ne acnfâäm. Tc vmdë acnfu m nfïactrm uae pcâe  (lûacrm nc acnfâócs) vczcs scbufnes, mu sc vmdë acnfu e aesse nc ’l‑  eamstres nc ua acsam imtc, cltäm vmdë pmncrå motcr e aænfe ne acnfâäm̃ , m scu ncsvfm

5>

 

  penräm

, essfa, e fldcrtcze uaænfe scrå deiduiene ne scbufltc `mrae;

uaænfe 1 µ

s   ∛ l

   Aænfe nc acnfâäm  acnfâäm 

Dmam m ncsvfm penräm kå cstå le acsae ulfnenc nm aclsurelnm, c ’l‑ æ ua lûacrm fltcfrm, pmsftfvm c sca ulfnenc, m veimr ne fldcrtcze ’u‑ kå scrå `mrlcdfnm le acsae ulfnenc nm aclsurelnm. Pcke ua cxcapim; Tc (s) cstfvcr ca actrms ( a), pmr cxcapim, c m lûacrm fltcfrm (l) läm tfvcr ulfnenc, sfblf`fde quc e nfvfsäm, mu scke, m veimr nc u teaoæa scrå `mrlcdfnm ca actrms. Lmtc quc queltm aefmr `mr m lûacrm nc rcpctfâócs (l) c`ctuenes le acnfâäm, aclmr scrå m veimr ne fldcrtcze cldmltrene.

Cxcapim; _mleinm cstå eprclnclnm smorc fldcrtcze nc acnfâäm, c rcsmivcu `ezcr ua cxpcrfacltm. Cic `cz trës særfcs nc acnfâócs nm nfïactrm nc oerres dfiálnrfdes nc ua imtc quc cic ekunmu e prmnuzfr. Le prfacfre særfc cic acnfu dfldm eamstres, le scbulne cic acnfu ?3 eamstres, c le tcrdcfre særfc cic acnfu 577 eamstres nm imtc nc oerres. Ms rcsuitenms motfnms pmr _mleinm cstäm amstrenms le teocie eoefxm;

53

 

 

Ebmre _mleinm qucr seocr queltm veic e fldcrtcze essmdfene e dene særfc nc acnfâócs, seoclnm quc trete-sc nc uae fldcrtcze nm tfpm E, cltäm cic rceifze ms scbufltcs dåiduims;

uaænfe  1 s(?7,63 ?7,63)) 1

57 1 µ> µ>,3 ,3    ∛ 3

 Fldcrtcze nc dfldm eamstres

 Fldcrtcze nc dfldm eamstres æ fbuei e ncz smorc e refz quenrene nc dfldm.  _csuitenm >3 aa.

uaænfe  1 s(?5,73 ?5,73)) 1

: 1 5, 5,00      ∛ ??33

 Fldcrtcze nc vfltc c dfldm eamstres eamstres

 Fldcrtcze nc vfltc c dfldm eamstres æ fbuei e mftm smorc e refz quenrene nc vfltc c dfldm.  _csuitenm 5,0 aa

uaænfe 1 s(?7,66 ?7,66)) 1

0 1 7, 7,00      577 ∛ 577

 Fldcrtcze nc dca eamstres

 Fldcrtcze nc dca eamstres æ fbuei scfs smorc e refz quenrene nc dca.  _csuitenm 7 0 aa 

Lmtc quc, queltm aefmr m lûacrm nc eamstres, aclmr æ m ncsvfm penräm cxpcrfacltei, c dmlscqucltcacltc, aclmr scrå m veimr ne fldcrtcze essmdfene e cssc ncsvfm. Le pråtfde, pmr nfvcrses rezócs, prfldfpeiacltc es nc mrnca cdmlþafde, m lûacrm nc rcpctfâócs nc uae acnfâäm dmstuae scr rcnuzfnm, tfpfdeacltc verfelnm cltrc trës tr ës c ncz. Mutrm pmltm fapmrteltc quc vmdë ncvc tcr ca acltc æ quc, dmam csteams treoeijelnm dma ua ncsvfm penräm eamstrei s, sfblf`fde quc e nfstrfoufâäm nc prmoeofifnenc scrå nm tfpm t-Ttunclt .

 Nfstrfoufâäm t

 E nfstrfoufâäm  t æ uae nfstrfoufâäm nc prmoeofifnenc tcôrfde. Æ sfaætrfde, ca `mrae nc sflm, c scacijeltc ç durve lmraei penräm, pmræa dma deunes aefs ierbes. ierbe s.

50

 

 

2 ? Fldcrtcze tfpm O Tcbulnm m ftca ?.?6 nm PFA, eveifeâäm nm ^fpm O ne fldcrtcze nc acnfâäm æ e ’Eveifeâäm nuae dmapmlcltc ne fldcrtcze nc acnfâäm nctcraflene pmr acfms nf`crcltcs nequcic enmtenm pere uae eveifeâäm nm ^fpm E ne fldcrtcze nc acnfâäm‑, acnfâäm‑, mu scke, ua aætmnm nc eveifeâäm ne

fldcrtcze pmr mutrms acfms quc läm e elåifsc cstetástfde nc uae særfc nc moscrveâócs. Dml`usm= Aes æ cxeteacltc m quc percdc; es fldcrtczes nm ^fpm O  säm tmnes equcies quc läm sc cldefxea le nc`flfâäm nes fldcrtczes nm ^fpm E. Oesfdeacltc, lcssc brupm, tcams `mltcs nc fldcrtcze dukm dmapmrteacltm æ oca dmljcdfnm c, pmr fssm, läm jå amtfvm pere cstfaer e fldcrtcze pmr ua aætmnm cstetástfdm, m quc cxfbfrfe auftm tcapm c trerfe pmudm beljm ç acnfâäm. Fldcrtczes ncstc tfpm säm nctcraflenes e pertfr nc fl`mraeâócs edcssôrfes c cxtcrles em prmdcssm nc acnfâäm, dmam aeluefs nc usm c dcrtf`fdenms nc deiforeâäm. Sa dcrtf`fdenm nc deiforeâäm nc ua flstruacltm nc acnfâäm, pmr cxcapim, tca pmr `fleifnenc eprcsclter e sue fldcrtcze nc acnfâäm, pere uae nctcraflene `efxe nc acnfâäm. Cstfaer e fldcrtcze nc ua flstruacltm æ ua prmdcssm treoeijmsm c actônfdm, aes cic æ `ulneacltei pere sc tcr ua aálfam nc dml`feofifnenc le acnfâäm. Lmraeiacltc m dcrtf`fdenm flnfde e `efxe nc acnfâäm (mu scke, m fltcrveim mlnc `mf rceifzene e deiforeâäm), m veimr ne fldcrtcze cxpelnfne ( S) c m `etmr nc eorelbëldfe (h). Were vmdë cltclncr acijmr csse qucstäm ne `efxe nc acnfâäm, faebflc m scbufltc; Nfbeams quc vmdë pmssue ca sue dese uae oeielâe quc acnc nc 5 hb ç537 hb,aes scu pcsm dmrpmrei dmstuae verfer, lmraeiacltc, nc 37 hb e 33 hb c vmdë seoc quc nf`fdfiacltc frå pcser >7hb mu m u nc 5?7hb, pmfs csscs veimrcs cstäm `mre ne sue rceifnenc... Cltäm, sc vmdë qufscr deiforer sue oeielâe, em flvæs nc deiforå-ie nc 5 hb e 537 hb vmdë pmnc csteocicdcr uae `efxe nc acnfâäm nc, pmr cxcapim, >7 hb e 03 hb, m quc tmrle e deiforeâäm oca aefs edcssávci `fleldcfreacltc. Cltclnfnm= Pcke eoefxm aefs cxcapims nc `mltcs nc fldcrtcze nm tfpm O; • E`esteacltm ne tcapcreture eaofcltc ca rcieâäm ç tcapcreture nc rc`crëldfe cstfpuiene8 • _csmiuâäm nc icfture nm flnfdenmr nm flstruacltm nc acnfâäm (eleiôbfde mu nfbftei)8 •Flsteofifnenc ne rcnc ciætrfde8 •Crrm nc pereiexc8

Lmte; m crrm nc pereiexc lmraeiacltc edmltcdc ca flnfdenmrcs eleiôbfdms quelnm e icfture läm æ rceifzene nc `mrae pcrpclnfduier em amstrenmr. •Fldcrtcze nm penräm c nm flstruacltm nc acnfâäm8

52

 

 

•Flsteofifnenc nm penräm c nm flstruacltm nc acnfâäm8  •Crrms bcmaætrfdms8  •Nc`mraeâócs acdïlfdes8 •Crrm nc jfstcrcsc, ctd.

Dmam `mf nftm eltcrfmracltc, dene prmdcssm nc acnfâäm tca sues `mltcs nc fldcrtcze deredtcrástfdes c, pmrteltm, æ `ulneacltei pcsqufser smorc es `mltcs nc fldcrtcze clvmivfnes lm prmdcssm quc vmdë tca fltcrcssc. Uueltm aefmr `mr e queltfnenc nc `mltcs nc fldcrtczes fldiuánes le acnfâäm, aefmr scrå e dml`feofifnenc lm rcsuitenm ne acnfâäm. ^äm fapmrteltc queltm m tfpm ne `mltc nc fldcrtcze æ e nctcrafleâäm nm tfpm nc nfstrfoufâäm nc prmoeofifnenc quc acijmr nc`flc m scu dmapmrteacltm. Eibuaes `mltcs nc fldcrtcze säm oca dmauls ç aefmrfe nms prmdcssms nc acnfâäm, imbm tca scu dmapmrteacltm cstetástfdm oca cstunenm c dmljcdfnm, kå mutres aefs cspcdá`fdes lcdcssftea nc cstunms aefs eprm`ulnenms pere nc`flfr sue durve deredtcrástfde. Pcke e teocie dma ua rcsuam nes prfldfpefs `mltcs nc fldcrtcze, dma sue rcspcdtfve nfstrfoufâäm nc prmoeofifnenc;

@mltc nc Fldcrtcze

^fpm

Nfstrfoufâäm

_cpctfofifnenc nes acnfâócs Jcrnene nm dcrtf`fdenm nc deiforeâäm _csmiuâäm nc icfture nc flstruacltm nfbftei _csmiuâäm nc icfture nc flstruacltm eleiôbfdm Crrm aåxfam nm flstruacltm Crrm nc jfstcrcsc Perfeâäm nes dmlnfâócs eaofcltefs Crrm nc icfture (pereiexc)

E O O O O O O O

t-Ttunclt t-Ttunclt _ctelbuier _ctelbuier mu ^rfelbuier _ctelbuier _ctelbuier ^rfelbuier ^rfelbuier

Dcrtm, aes scrå quc, em caftfr m rcsuitenm nc uae acnfâäm, veams tcr quc ifster tmnes es `mltcs nc fldcrtcze dmlsfncrenes= Nc `etm, cssc ncteijeacltm läm æ usuei, e`flei, le aefmrfe nes vczcs, es pcssmes qucrca seocr epcles m rcsuitenm ne acnfâäm c e sue fldcrtcze. Aes quei scrfe e fldcrtcze nm rcsuitenm, sc edeoeams nc vcr quc säm auftes= Tcrå quc æ pmssávci smaer mu rcsuafr tmnes csses `mltcs nc fldcrtcze ca uae dmfse sô= C e rcspmste æ; ’sfa, fssm æ pmssávci!‑  pmssávci!‑ 

Le vcrnenc, pmncams dmaofler nczcles nc `mltcs nc fldcrtcze nc acnfâäm ca ua ûlfdm `etmr, quc frå ncsdrcvcr quei æ e dml`feofifnenc ne acnfâäm rceifzene. Cssc æ m dmldcftm nc fldcrtcze dmaoflene, quc pmr sflei, æ m tcae ne lmsse prôxfae euie, läm pcrde!

5:

 

 

 E euie nc jmkc `fde pmr equf! Icaorc-sc nc rceifzer ms cxcrdádfms nc `fxeâäm. Desm surke eibuae nûvfne, läm jcsftc ca qucstfmler, mh= Omls cstunms!

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