curs 2 : despre masurare
TRANSCRIPT
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Lursu` 9
EC\_YC MJ\SYJYC
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Mjsurjrc
Mctrg`gbkj- egmcaku` stkkatck sk tcnaklkk ljrc sc glupj lujspcltc`c tcgrctklc sk prjltklc j`c prglcsu`uk ecmjsurjrc!
Mctrg`gbkj - mctrga - mjsurj, `gbgs stkkatj!
Grklc jltkvktjtc umjaj6
ljrc utk`kzcjzj mkf`gjlc tcnaklc,
ljrc sc rcj`kzcjzj lu g prclkzkc kmpusj,
prcsupuac mjsurjtgrk ljrc lcrtkdklj rcj`kzjrcj prclkzkcklcrutc!
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Mjsurjrc
\lncmj bcacrj`j j prglcsu`uk ec mjsurjrc
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Mjsurjrc
Mctgej ec mjsurjrc- jasjmi`u` ec prkalkpkk sk prglceccutk`kzjtc pcatru gitkacrcj kadgrmjtkk`gr ec mjsurjrc =\GDU!
Mkf`glu` ec mjsurjrc- jasjmi`u` mkf`gjlc`gr tcnaklc
utk`kzjtc a prglcsu` ec mjsurjrc = NJYE!
C`cmcatc`c prglcsu`uk ec mjsurjrc6
mjsurjaeu` sju mjrkmcj ec mjsurjt8 mctgej ec mjsurjrc8
mkf`glu` ec mjsurjt8
ctj`gau`!
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Mjrkmc
Mrkmc- prgprkctjtc j gikcltc`gr, dcagmcac`gr sju skstcmc`grljrc cstc cvkecatkjtjlj`ktjtkv sk mjsurjtj ljatktjtkv!
Mrkmc dkzklj - mjrkmc ecslrksj lu prgprkctjtk`c dkzklc j`c
gikcltc`gr, dcagmcac`gr sju skstcmc`gr!
Lj`ktjtkv - sc rcdcrj `j ajturj mrkmkk, ec cx6 `uabkmcj,mjsj, cacrbkj!
\pclkk ec mjrkmk - mjrkmk lj`ktjtkvc ec jlccjsk ajturj, ec cx6ekstjatj, ecp`jsjrcj, brgskmcj, kaj`tkmcj, `uabkmcj ec uaejka mctrg`gbkc rcprczkatj g skaburj mjrkmc6 `uabkmcj!
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Mjrkmc
Eupj skstcmc`c ec uaktjtk ec mjsurj6
Mrkmk duaejmcatj`c - mrkmk j`c lrgr uaktjkec msur sc utk`kzcjzj `j lgastrultkj uauk
skstcm ec uaktjtk ec mjsurj8 suatkaecpcaecatc katrc c`c!
Mrkmk ecrkvjtc - mrkmk j`c lrgr uaktjk ec
msurrczu`t a mge uakvgl eka rc`jtkk`c ececdkaktkc ka ljrc s-ju utk`kzjt mjrkmk sk uaktjtk ecmjsurj duaejmcatj`c!
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Mjrkmc
Mrkmc dkzklsc ljrjltcrkzcjz prka6 ajturj,
vj`gjrc!
Tj`gjrcj sc cxprkm prka msurj!
Msurjlgrcspuaec uack ekmcaskuak!Ekmcaskuacj jrc g uaktjtc ec mjsurj!
Mjsurjrcj cstc gpcrjtkj ljrc stjik`cstc cxpcrkmcatj` rjpgrtu` aumcrkl
katrc vj`gjrc sk uaktjtcj sj ec mjsurj!
Msurjrcj prcsupuac6
g rc`jkc ec clnkvj`ca k gregajrc,
stjik`krcj uack slrk lgavcakgaj`c lu grkbkakc luagslutj!
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Cxprcskj mjtcmjtkl j msurrkk uack mrkmk cstc6
M = m XM]
M cstc msurjk cxprkm vj`gjrcj mrkmkk,
XM] cstc uaktjtcj ec msur lu vj`gjrc rkburgs
luagslut,
mcstc ua aumrj ljruk vj`gjrc aumcrkl
rczu`t eka msurjrc!
Mjrkmc
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Mjrkmc
Tj`gjrc aumcrklj cstc6
ua c`cmcat eka mu`tkmcj aumcrc`gr rcj`c ljrclgrcspuaec uack stjrk eka mu`tkmcj stjrk`gr uack
mjrkmk8
cstc ua aumjr, pgzktkv sju acbjtkv, ljrc ecpkaec ecsljrj ec rcdcrkatj jegptjtj pcatru mjsurjrc!
Saktjtcj ec mjsurj cstc6 c`cmcatu` eka mu`tkmcj stjrk`gr mjrkmkk ljrc lgrcspuaec
vj`grkk aumcrklc uau8
sc kecatkdklj prka ecaumkrc6 mctru, hk`gbrjm, ctl!
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Mjrkmc
Tj`gjrcj mrkmkkcstc cxprkmjrc aumcrklj j mrkmkk6
Ec cx6 9:2,9m
_catru g mjrkmc dkzklj, uaktjtcj ec msur sc spclkdklj
gi`kbjtgrku ka vj`gjrcj mrkmkk!
uaktjtc ec mjsurjaumjr
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L`jskdkljrcj mjrkmk`gr mjsurjik`c a dualtkc ec tkmp
Mjrkmc
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Mkf`gjlc ec mjsurjrc
Ctj`ga6
mjrkmc jllcptjtj gdklkj` ka stkkatj, ka tcnaklj sju ka rc`jtkk`cclgagmklc ljrc scrvcstc lj uaktjtc ec ijzj katr-ua skstcm ec
mjsurjrc8
mgec` pcrdclt j` uack mjsurk-tkp, lgadcltkgajt lu mjrc prclkzkc skutk`kzjt lj ijzj ec lgmpjrjtkc!
mjsurj lu prclkzkj mjxkmj pcrmksj ec tcnaklj mjsurjrkk katr-uajaumkt stjeku j` eczvg`tjrkk, ecstkajtj6
pjstrjrkk sk rcprgeulcrkk uack uaktjtk ec mjsurj,
vcrkdkljrkk sk brjejrkk ekdcrktc`gr mjsurk sk kastrumcatc ec mjsurj!
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L`jskdkljrc ctj`gjac`gr prgprku-zksc6
Ctj`gjac ec ijzj- j`ltukcsl ijzj `cbj`j sk
stkkatkdklj ka tcnaklj mjsurjrkk katr-g tjrj,
Ctj`gjac ecrkvjtcrcprczkatj rcprgeulcrcjlgalrctj j uaktjtk`gr ecrkvjtc8
Ctj`gjac ec `ulru - utk`kzjtc `j cxclutjrcj
`ulrrk`gr lurcatc ec mctrg`gbkc!
Mkf`gjlc ec mjsurjrc
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L`jskdkljrc ctj`gjac eupj ecstkajtkc6
Ctj`gjac jisg`utc ekspgzktkvc utk`kzjtc `j ecdkakrcjuaktjtk`gr ec mjsurj duaejmcatj`c6 mctru`, hk`gbrjmu`,scluaej, jmpcru`8
Ctj`gjac ec lgascrvjrc ekspgzktkvc prclksc sk stjik`cka tkmp ljrc durakzcjzj uaktjtcj ec mjsurjlgrcspuazjtgjrc sk aclcsktj lj`kirjrc ka rjpgrt lu
ctj`gjac`c jisg`utc8
Ctj`gjac ec trjasdcr ekspgzktkvc ljrc pcrmkt trjasdcru`uaktjtk`gr ec mjsurj katrc egmcakk sju rcbkuak ec
dualtkgajrc!
Mkf`gjlc ec mjsurjrc
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L`jskdkljrc ctj`gjac eupj prclkzkc6
Ctj`gjac katcrajtkgaj`c sc pjstrcjzj `j Ikrgu` Katcrajtkgaj` ec
mjsurk sk Brcutjtk IKMB ec `j \cvrcs, Drjatj8
Ctj`gjac prkmjrc.ajtkgaj`c+ sc pjstrcjzj `j Ikrgu` Ajtkgaj` ecMctrg`gbkc @cbj`j,IAM@ j tjrkk sk scrvcsl `j vcrkdkljrcj ctj`gjac`gr
scluaejrc8 suat lc`c mjk prclksc ctj`gjac eka tjrj rcspcltkvj sk sc
vcrkdklj pcrkgekl lu ctj`gjac`c katcrajtkgaj`c8
Ctj`gjac scluaejrc scrvcsl `j vcrkdkljrcj ctj`gjac`gr ec `ulru sksuat pjstrjtc `j dk`kj`c`c rcbkgaj`c j`c IAM@8
Ctj`gjac tcrtkjrc.ec `ulru+ sc pjstrcjzj ka `jigrjtgjrc`c
mctrg`gbklc sk sc utk`kzcjzj `j vcrkdkljrcj jpjrjtc`gr ec mjsurj ec
prclkzkc!
Mkf`gjlc ec mjsurjrc
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Lj`ktjtcj ejtc`gr mjsurjtc ecpkaec ec prclkzkj jpjrjtc`gr ecmsurjrc!
Jpjrjtc`c ec msur ju urmjtgjrc`c ljrjltcrkstklk mctrg`gbklc6
dkec`ktjtc - `j msurjrcj jlc`cjk mrkmk, a lgaekkk kecatklc jpjrjtu`
ej kaekljkk lu vjrkjkk mkakmc, scaskik`ktjtcj - jpjrjtu` cvkecakjz lc`c mjk mklk vjrkjkk j`c
mrkmkk lc sc msgjr,
fustccj6
mjsurj ka ljrc kaekljtkk`c jpjrjtu`uk suat jprgpkjtc ec vj`gjrcjrcj`j jmrkmkk8
egu jpjrjtc ju jlccjsk fustcc, ejl mcekk`c jrktmctklc j`cuauk kr ec mjsurjtgrk suat jlc`cjk,
ctj`gajrcj uauk jpjrjt cstc cscatkj`j pcatrufustccjmjsurjtgrkk!
Mkf`gjlc ec mjsurjrc
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Yc`jtkj ekatrc vj`gjrcj jecvjrjtj j mrkmkkm
k kaekljkj jpjrjtu`uk x8 : lurij ec ctj`gajrc
Lurij ec ctj`gajrc .:+ cstc6
g dualkc katrc m sk x,
g dualkc jdcltjt ec crgrkj`cjtgrkk!
J?I? cstc zgaj ec kalcrtktuekac jmprtkcrkk kaekljkk`grx!
Kaekljkk`c j`cjtgrkk j`c jpjrjtu`uksuat lcatrjtc pc vj`gjrcj x!
Ejl rcpjrtkkj crgrk`gr cstcagrmj`j sk sc `kmktcjz `j
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Giscrvjtkk6 Mjsurjtgrk`c lgaka crgrkecgjrclcsc gitka vj`grk ekdcrktc `j
rcpctjrcj msurrkk!
@kmktc`c ec mjsurjrc sc stjik`csl eka kmprjstkcrcj msurtgrk`grrcpctjtc!
Jpjrjtc`c ec mjsurj ejuvj`grk jprgxkmjtkvc pcatru mrkmk luvj`gjrc acluagslutj!
Lj`lu`c`c ec prc`ulrjrc j`c ejtc`gr mjsurjtc katrgeul crgrk!
Crgrk`c ec mjsurjrck ec lj`lu` pgt jdcltj vj`grk`c k katcrprctjrcjejtc`gr!
Msurtgrk`c k lj`lu`c sc djl lu g prclkzkc sudklkcat, ljrclgrcspuaec cdgrturk`gr cxpcrkmcatj`c sk ec lj`lu`!
Mkf`gjlc ec mjsurjrc
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Ugtj`ktjtcj mkf`gjlc`gr tcnaklc utk`kzjtc `j msurjrc!
Eupj prclkzkc sc l`jskdklj ka6
mkf`gjlc ec mjsurjrc ec `ulru - scrvcsl `j mjsurjrk`clurcatc eka prjltklj8
mkf`gjlc ec mjsurjrc mgec` - scrvcsl ctj`gajrkk sjuvcrkdkljrkk mjsurk`gr sk jpjrjtc`gr ec mjsurjt ec `ulru8
mkf`gjlc ec mjsurjrc ctj`ga - scrvcsl rcprgeulcrkk sjustjik`csl uaktjtcj ec mjsurj lu prclkzkc mjxkmj, scpjstrcjzj sk sc trjasmkt mkf`gjlc`gr ec mjsurjrc ecprclkzkc kadcrkgjrj!
Mkf`gjlc ec mjsurjrc
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\uat rcprczcatjtc ec6
Msurk8
Jpjrjtc`c ec msurjt8
@jaurk ec msurjrc - jasjmi`urk, kastj`jkkk skstcmc ec msurjrc
Mkf`gjlc ec mjsurjrc
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L`jskdkljrcj eupj ecstkajkc6
- ctj`ga8- ec `ulru!
L`jskdkljrcj eupj aumru` vj`grk`gr6
- msurk lu vj`gjrc uakl - suat jsglkjtc ka scrkk sjutrusc, ljrc lgatka msurk ec vj`grk ekdcrktc, j`csc eup
g jaumkt sullcskuac8
- msurk lu vj`grk mu`tkp`c ljrc pgt dk6
- msurk lu vj`grk ekslrctc,
- mjsurk lu vj`grk lgatkauc!
Mjsurj
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Jpjrjtc ec mjsurj
Jpjrjtc`c ec mjsurj suat6
mkf`gjlc ec msurjrckatcrlj`jtc atrcmrkmcj dkzkl lc au cstc jllcskik` ekrclt
gpcrjtgru`uk sk gpcrjtgr,
rcj`kzcjzlgavcrskj msurjaeu`uk atr-g
mrkmc pcrlcptkik` pcatru gpcrjtgr!
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Jasjmi`u` ec mjsurjrc
Jasjmi`u` ec mjsurjrc6
cstc g jsglkcrc skmp`j ec jpjrjtc pcatru jmjsurj g skaburj mjrkmc, cx! ua trjeultgrjsglkjt lu ua jpjrjt kaekljtgr sju karcbkstrjtgr,
rcprgeulc strulturj uauk jpjrjt ec msurjt,lu ecgscikrcj l mkf`gjlc`c lgakautc suat6
kaecpcaecatc,
lu ljrjltcrkstklk mctrg`gbklc agrmjtc scpjrjt!
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Kastj`jtkc ec mjsurjrc
Kastj`jtkj ec mjsurjrc6
cstc g jsglkcrc lgmp`cx ec jpjrjtc ec
msurjt, ekspgzktkvc sk jllcsgrkk,
msgjrj uaj sju mjk mu`tc mjrkmk ajlc`cjsk lgaektkk,
utk`kzcjzj jlccjsk mctgej ec mjsurjrc pcatrumjrkmk!
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\kstcmu` ec mjsurjrc
rcprczkatj lgmp`cxc jutgmjtkzjtc ec mjsurjrc,prc`ulrjrc sk karcbkstrjrc j rczu`tjtc`gr, cx6 skstcmc ecjlnkzktkc j ejtc`gr!
aclcsktj ua sgdtwjrc ec msurjrc bcstkgajt ec uaprglcsgr,
suat algrpgrjtc a `kakk tcnag`gbklc, suat jsglkjtc
kastj`jtkk`gr ec rcb`jrc jutgmjt j prglcsc`gr,
suat utk`kzjtc pcatru vg`umc mjrk ec mjsurjtgrkrcj`kzjtc lu drclvcatj mjrc!
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Mctgec ec mjsurjrc
Jasjmi`u` rc`jkk`gr tcgrctklc k gpcrjkk`grcxpcrkmcatj`c ec msurjrc!
\c l`jskdklj ka6
- mctgec ekrcltc,- mctgec kaekrcltc,
- mctgec lgmikajtc!
Mctgec ekrcltc6
- rczu`tjtu` sc gikac prkatr-g skabur gpcrjkc,
- vj`gjrcj mjrkmkk au cstc lgrcltjt ec skstcmu` ecmsurjrc!
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Mctgec kaekrcltc
msgjrj g mrkmc, ec ljrc msurjaeu` cstc`cbjt prkatr-g rc`jkc dualkgaj`,
vj`gjrcj mjsurjaeu`uksc lj`lu`cjzj lurc`jtkk`c ec `cbjturj ekatrc mjsurjae sk
mjrkmcj mjsurjtj!
Mctgec ec mjsurjrc
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Mctgec ec lgmpjrjtkc6
vj`gjrcj mjrkmkk sc gitkac eka lgmpjrjrcj mjrkmkk ec
mjsurjt lu ctj`gjac,
jpjrjtc`c ec msurj scskzcjz cbj`ktjtcj ekatrc
msurjae k mrkmcj ec lgmpjrjkc prkatr-ua rcbjf,
mjauj` sju jutgmjt,
`jatu` ec mjsurjrc cstc kalnks, kjr prclkzkj mjsurjrkk cstc
lc` mu`t cbj`j lu lcj j ctj`gau`uk utk`kzjt!
Mctgec ec mjsurjrc
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Mctgec ec lgmpjrjtkc skmu`tja6
Msurjaeu` cstc lgmpjrjt lu uau` sju mjk mu`tc ctj`gjacljrc sc utk`kzcjzj `j mjsurjrc cx! mjsurjrc mjsck lu gij`jatj!
Lgmpjrjtkj :6: ekrcltj
Mjrkmk`c dkzklc ljrc suat sk pgzktkvc sk acbjtkvc, sc mjsgjrj
prka mjrkmcj gpus, luagslut, ec scas lgatrjr, ljrc gclnk`kircjzj, cx!6 `uabkmcj, dgrtj, prcskuacj, tcaskuacjc`cltrklj, ctl!
Mctgec ec mjsurjrc
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Mctgej ekdcrcakj` ekrclt
cstc g vjrkjatj j`c mctgeck ec lgmpjrjkc skmu`tja
:6:,
msgjr ekdcrcaj ekatrc msurjaeu` M sk g mrkmc
m ec jlccjk ajtur, luagslut lu prclkzkj
spclkdkljtj,
prclkzkj mjsurjtgrkk cstc lu jtt mjk iuaj, lu lt
prclkzkj mrkmkk m cstc mjk iuak lu lt ekdcrcaj c
cstc mjk mkl!
Mctgec ec mjsurjrc
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Mctgej ec zcrg sju ec lgmpcasjkc
cstc g vjrkjatj j`c mctgeck ec lgmpjrjkc skmu`tja
:6:,
lgast a utk`kzjrcj uauk ctj`ga vjrkjik` m, `j
mjsurjrcj mjrkmkkM8
prclkzkj mctgeck ecpkaec ec prclkzkj ctj`gau`uk sk ecscaskik`ktjtcj jpjrjtu`uk ljrc jau`cjzj ekdcrcatj M -
m!
Mctgec ec mjsurjrc
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Mctgec`c ekdcrcatkj`j sk ec lgmpcasjtkc6
jvjatjf- suatlc`c mjk prclksc mctgec ec
msurjrc, pcatru lj kalcrtktuekacj ecmsurjrc katrgeus ec jpjrjt cstc mkakm,
eczjvjatjf- aclcskt ctj`gjac lu vj`gjrcj
jprgpkjt ec j msurjaeu`uk sju ctj`gjacec vj`gjrc vjrkjik`!
Mctgec ec mjsurjrc
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Mctgej prka lgkalkeca
Yczu`tjtu` mjsurjtgrkk cstc lgkalkecaj ekatrc rcpcrc`c sjuscmaj`c`c jpjrkaae msurjaeu`uk lu lc`c j`c
ctj`gau`uk, ec cx! sui`cru`8
Mctgej prka katcrpg`jrc
sc luagsl mjk mu`tc vj`grk pjrtklu`jrc j`c msurjaeu`uk,
prka lgmpjrjtkc sc stjik`cstc lj vj`gjrcj mjsurjaeu`uksc jd`j a katcrvj`u` ekatrc eguj vj`grk luagslutc,
rczu`tjtu` mjsurjtgrkk sc gikac lu g rc`jkc luagslutec katcrpg`jrc j vjrkjtkck msurjaeu`uk ka jlc` katcrvj`!
Mctgec ec mjsurjrc
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_rclkzkj
_rclkzkjcstc ekdcrcaj ekatrc vj`gjrcj msurjtk vj`gjrcj jecvrjt!
Tj`gjrcj jecvrjt cstc vj`gjrcj gikaut prka
lgmpjrjrcj lu ua stjaejre prkmjr!
_rclkzkj sc ectcrmka prka lj`kirjrc
Lj`kirjrcjcstc prglcsu` ec lgrc`jrc j uaukkastrumcat ec msur lu stjaejreu` ecmsurjrc!
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Ecdkakrcj prclkzkck
_jrjmctrk lj`kirrkk utk`kzjk pcatru ecdkakrcj prclkzkck suat6
Yczg`ukj,
\caskik`ktjtcj,
@kacjrktjtcj,
Nkstcrczksu`,
Ycpctjik`ktjtcj'prclkzkj 'rcprgeultkik`ktjtcj,
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Yczg`utkj jdksjrkk
Yczg`utkj jdksjrkk sju ekslrkmkajrcj cstc6
lcj mjk mkl slnkmijrcj j msurjaeu`uk ljrc pgjtcdk ectcltjt ec kastrumcatu` ec mjsurjrc,
ectcrcmkajt ec mgeu` ec jdkjrc j rczu`tjtu`uk6
ikac ecdkakt ec skstcmc`c ekbktj`c,
mjk s`ji ecdkakt ec skstcmc`c jaj`gbklc!
`kmktjt ec tkpu` ec kastrumcat utk`kzjt!
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: 9 < 5 3
_rclkzkj
Yczg`utkj jdksjrkk jaj`gbklc
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\lncmj dualtkgaj`j j uauk jpjrjt jaj`gbkl pcatru mjsurjrcj uack mjrkmk jltkvc
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\lncmj dualtkgaj`j j uauk jpjrjt jaj`gbkl pcatru mjsurjrcj uack mjrkmk pjskvc!
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\caskik`ktjtc
\caskik`ktjtcjcstc rjpgrtu` slnkmirkk scmaj`u`uk ec kckrcka dualtkc ec scmaj`u` ec katrjrc!
Sa kastrumcat kecj` jrc g scaskik ktjtc lgastjat!
Mgeu` ec vjrkjkc j scaskik`ktkk pc egmcaku` ec msurjrc j`
kastrumcatu`uk cstc6
`kakjr,
ac`kakjr!
-
7/29/2019 Curs 2 : DESPRE MASURARE
44/64
@kakjr - ac`kakjr
Ecvkjkj skstcmjtkl ec `j `kakj kecj` kaeklj crgrk ec ac`kacjrktjtc!
-
7/29/2019 Curs 2 : DESPRE MASURARE
45/64
Nkstcrczks
Msurj vjrkjkck mrkmkk ec kckrc pcatru g vj`gjrc
j msurjaeu`uk lae jlcsjt vj`gjrc sc jtkabc
prka vjrkjkj a jmic`c scasurk j msurjaeu`uk.alrljrc-ecslrljrc+!
Jpjrc ejtgrkt rkbkektkk, vkirjkk`gr, drclrkk`gr,
mjbactksm
-
7/29/2019 Curs 2 : DESPRE MASURARE
46/64
Ekdcrcaj `j lrctcrcj k slecrcj msurjaeu`uk kaekl ua nkstcrczks!
alrljrc
Ecslrljrc
Mrkmc katrjrc
A:
Tj`gjrc msurjtT: T9
Nkstcrczks = T:-T9
Nkstcrczks
-
7/29/2019 Curs 2 : DESPRE MASURARE
47/64
Ycpctjik`ktjtcj
Tjrkjkk`c ec `j `kakj kecj` suat crgrk`c j`cjtgrkk!
Ycpctjik`ktjtcj cstc g msurj j crgrk`gr j`cjtgrkk!
-
7/29/2019 Curs 2 : DESPRE MASURARE
48/64
_rclkzkc iuaYcpctjik`ktjtc iua
Ycpctjik`ktjtcj slzut _rclkzkc slzutYcpctjik`ktjtc iua
-
7/29/2019 Curs 2 : DESPRE MASURARE
49/64
Crgrk ejtgrjtc mceku`uk
Mgekdklrk`c mceku`uk jmikjat ljrc kad`ucatcjzjjpjrjtu` ec mjsurj suat6
Smkektjtcj, Jlc`crjkcj,
Tkirjkk`c,
Ucmpcrjturj,
_rcskuacj,
Cdcltc`c skstcmu`uk ec dkxjrc!
-
7/29/2019 Curs 2 : DESPRE MASURARE
50/64
Crgrk
Ec lc suat kmpgrtjatc crgrk`c7
Ukpurk ec crgrkatmp`tgjrc sk skstcmjtklc.prclkzkc k jlurjtcc+
Cstkmjrcj crgrk`gr
Agtjrcj rczu`tjtu`uk k crgrkk
Urjtjrcj crgrk`gr ka dgrmu`c ec lj`lu`
Lgmikajrcj crgrk gr atmp`tgjrc skskstcmjtklc
Ljrjltcru` stjtkstkl j` crgrkk
-
7/29/2019 Curs 2 : DESPRE MASURARE
51/64
Ec lc suat kmpgrtjatc crgrk`c7
Eguj mjsurjtgrk j`c tcmpcrjturkk lgrpu`uk ajkatc sk eup
jemkakstrjrcj uauk mcekljmcat suat6
!9L k !5L
Cstc scmakdkljtkvj lrctcrcj tcmpcrjturkk7
Yjspuasu` ecpkaec ec crgjrcj jsglkjt msurtgrkk
.!9?!?:+L k .!5 ?!?:+Lscmakdkljtkvj
.!9?!3+L jae .!5 ?!3+Lacscmakdkljtkv
C k e
-
7/29/2019 Curs 2 : DESPRE MASURARE
52/64
"yyCj
yyyCr
Eka pualtu` ec vcecrc mjtcmjtkl sc l`jskdklj ka6
Crgjrc jisg`ut rcprczkat ekdcrcaj ekatrc vj`gjrcj rcj` y k
jprgxkmjtkv j uack mrkmkgikaut prka msurjrc y"6
Crgjrcj rc`jtkv6
Crgjrcj jisg`utj cstc g mjrkmc cxtcaskvj, kjr crgjrcj rc`jtkv
cstc g mjrkmc katcaskvj
Crgrk ec mjsurjrc
-
7/29/2019 Curs 2 : DESPRE MASURARE
53/64
Crgrk`c brgsg`jacsuat6-al`lrk j`c prkalkpkk`gr ec msurjrc,
- rczu`tju` acjtcakck cxpcrkmcatjtgru`uk,
- suat brcc`k ec lj`lu`!
Crgjrcj ec pjrj`jx - lktkrcj uack mrkmk sc djlc dr lj rjzj vkzuj`s
dkc pcrpcaeklu`jr pc sljrj brjejt a ercptu` lktkrkk!
Crgrk ec mjsurjrc
Tj`grk`c jdcltjtc ec crgrk brgsg`jac6
ekdcr cscakj` ec lc`c`j`tc vj`grk
sc c`kmkaj `j rcpctjrcj mjsurjtgrkk!
Crgrk ec mjsurjrc
-
7/29/2019 Curs 2 : DESPRE MASURARE
54/64
Crgrk`c skstcmjtklc6 suat bcacrjtc ec g kad`uca ljrc jdcltczj tgjtcmjsurjtgrk`c! \c ejtgrcjzj6
- lj`kirjrkk sju ctj`garkk kalgrcltc j jpjrjtc`gr ec mjsurj,
- jp`kljrkk brcsktc j prglceurkk ec mjsurjrc sju ec lj`lu`,
- mjsurjrcj ka lgaekkk ekdcrktc ec lc`c ka ljrc j dgst ctj`gajt
jpjrjtu`!
Crgrk ec mjsurjrc
Crgrk`c skstcmjtklc6
suat brjvc ecgjrclc au sc c`kmka `j rcpctjrcj msurjtgrkk, sc ecpkstcjzj prka msurjrcj lu mctgec ekdcrktc sju prka
msurjrcj lu jlc`jk jpjrjt j mrkmk`gr lu vj`gjrc
luagslutj,
sc c`kmkaj djrj j rcpctj mjsurjtgrk`c!
-
7/29/2019 Curs 2 : DESPRE MASURARE
55/64
-
7/29/2019 Curs 2 : DESPRE MASURARE
56/64
Crgjrcj ec mjsurjrc
C k e
-
7/29/2019 Curs 2 : DESPRE MASURARE
57/64
Ka dualtkc ec sursc`c ec crgrk sc ecdkacsl6
Crgjrcj ec mgec` - crgjrcj ejtgrjt kmpcrdclkuak`gr mgec`c`grdkzkl k
mjtcmjtkl jsglkjtc mjsurjtgrkk!
Crgjrcj ec katcrjlkuac - crgjrcj ectcrmkajt ec kad`ucac`c pc ljrc
mkf`gjlc`c ec msurjt sju gpcrjtgru` `c cxcrlkt jsuprj mrkmkk msurjtc!
Crgjrcj kastrumcatj`- jasjmi`u` crgrk`gr ljuzjtc ec mkf`gjlc`c ec
msur!
Crgjrcj ec mctge - crgjrcj ejtgrjt kmpcrdclkuak`gr mctgec`gr utk`kzjtc!
Crgjrcj ejtgrjt cxpcrkmcatjtgru`ukecpkaec ec lj`ktk`c k lgaekkj
pskng-dkzkl j gpcrjtgru`uk!
Crgrk ec mjsurjrc
-
7/29/2019 Curs 2 : DESPRE MASURARE
58/64
_rkalkpj`c`c sursc ec crgrk a prglcsu` ec mjsurjrc
-
7/29/2019 Curs 2 : DESPRE MASURARE
59/64
Ecsprc prclkzkj lj`lu`u`uk
Yczu`tjtu` uauk lj`lu` sju j` uack msurtgrk sc cxprkmprkatr-ua aumr!
\lrkcrcj uauk aumr cxprkm brjeu` ec prclkzkc j`
jltkvktkk pc ljrc g rcprczkat!
@j slrkcrcj uack vj`grk mjsurjtc sc utk`kzcjz agkuak`c ec6
lkdr cxjlt
lkdr scmakdkljtkv!
Lkdr cxjltcstc lkdrj j lrck vj`gjrc cstc lcrt!
-
7/29/2019 Curs 2 : DESPRE MASURARE
60/64
Ecsprc prclkzkj lj`lu`u`uk
Cxcmp`u6
\c msgjr `uabkmcj @ = :9,5
-
7/29/2019 Curs 2 : DESPRE MASURARE
61/64
Lkdr scmakdkljtkvj uauk aumr cstc tgtj`ktjtcj lkdrc`gr ljrcdgrmcjz aumru` rcspcltkv, lu cxlcpkj `uk zcrg, ejl sc jd` `jstabj aumru`uk!
Aumcrc`c jprgxkmjtkvcsc slrkuaumjk lu lkdrc scmakdkljtkvc!
Cxcmp`c6
Lgcdklkcatu` ec ek`jtjkc j` j`umkaku`uk cstc6 = ?,???95 H-:!
Aumjru` lgatkac egu lkdrc scmakdkljtkvc6 = 9,5 :?-3 H-:!
Jllc`jrjtkj brjvktjtkgaj`j6b = ;,>? m's9
J eguj lkdrj eupj zclkmj`j cstc lkdrj cxjltj sk scmakdkljtkvj!
Ecsprc prclkzkj lj`lu`u`uk
-
7/29/2019 Curs 2 : DESPRE MASURARE
62/64
Agtjrcj crgrk`gr sk j rczu`tjtu`uk
Tj`gjrc 55, crgjrc 3 553
Tj`gjrc :9>, crgjrc
-
7/29/2019 Curs 2 : DESPRE MASURARE
63/64
Cstkmjrcj crgrkk ec lktkrc
Gslk`gslgprc`jtkv `j `rbkmcj urmck ekvkzkuak, pcatru
:T'ekvkzkuac = T8 `jrbkmcj urmck ~?!: ekvkskga = ?!:T .?!:+T
-
7/29/2019 Curs 2 : DESPRE MASURARE
64/64
Cstkmjrcj crgrkk ec lktkrc
Tg`tmctru ekbktj` crgjrc lgaskecrjtj 3 ka urmtgjrc lkdrj
scmakdkljtkvj .