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weight
kPPÈOFpOUzWvPFArPikPP oPFjPLinPLrP fPOlPAfPOlP jPLAnPLAHPArP jPLnPLz ePkPPWvPF LpPOA`ÂlPA HPA mLPAiJPFrP wPOAÕPOAitPO E`ÂFkPPkPP kPPrPqnPL,tPOArPLpPOrP ePvhPF iHPAtPOAmLPWvPFA EWvPFLpPOiHPnPLP|
HPzAKPzA:
EtPOnPLHPArP oPFjPLnPL kPPrPA hPFiHP aArP çpPFEtPO
oPFjPLinPLrP fPOlPAfPOlP EtPOnPL rPkPPmLP hPFitPO LpPOAirP -- LpPOA`ÂlPA
sLPmLPAnPL,HPÿA LpPOA`ÂlPA BPOArPQ,wPOAnPL LpPOA`ÂlPA BPOArPQ (HPA HPÿA
LpPOA`ÂlPA hPFAlPkPPA)P| aTPYAð oPFjPLinPLrP fPOlP 3
x 3 x
3 = 27 rPkPPmLP hPFitPO LpPOAirPP| ePrP mLPiDPFz yPEdP EtPOnPLHPArPvhPF
LpPOA`ÂlPA sLPmLPAnPL TPAikPP tPOAhPFilP HUJPFiHPA iyP sLPHP imLPAhPFrPvhPF
sLPmLPAnPL oPFjPLinPLrP P| aAHPArP oPFjPLnPL kPPrPArP sLPmLPbP yPEdP iKPbPAlP
rPAEKP iyP EHPiSPFXP ikPPAinPLA imLPAhPFrP EtPOnPLHPArPvhPF ePkPPvhPF
LpPOA`ÂlPAbP tUOlPECPF nPLA,tPOAhPFilP EtPOnPLHPArPvhPF HPÿA LpPOA`ÂlPA BPOArPQ
HPA hPFAlPkPPA idPKPAiHP,eP sLPÆPFAHPnPLA dLUiWvPFAoPF HPAdP idPoPFbPA yPAbPP|
HPAkPPQ rPvhPFilPA 24WvPFA fPOlPAfPOlPP| tPOArP mLPiDPFz HPAirPAWvPFA LpPOAiHPA
yPEdP KLUÿitPOA imLPAhPFrP iHPSPFQ BPOArPQ hPFbP aArP HPAkPPQ HPAirPAWvPFA
yPEdP oPFWvPFA hPFAlPkPPA hPFbPP| tÖOtPOQEbPkPP nPLÈ÷PrP tÖOtPOQEbPkPP nPLÈ÷PrP
çpPFEtPO oPFjPLinPLrP EtPOnPLEWvPF fPOlPAfPOlPikPP EtPOnPLEWvPF aÌPO EdPibP
iHPAJPFAinPLA yPAkPP,ilPKPArP sFUEHPiDPFrP jPLnPLzP| LpPOA`ÂlPA sLPmLPAnPL =
0,HPÿA LpPOA`ÂlPA BPOArPQ = 1,wPOAnPL LpPOA`ÂlPA BPOArPQ = HPÿA LpPOA`ÂlPA
hPFAlPkPPA = -1P| tPOAhPFilP,çpPFTPmLPHPArP oPFjPLinPL HPÿA LpPOA`ÂlPA
BPOArPQ,EªPtPOQbPEWvPFitPO LpPOA`ÂlPA sLPmLPAnPL,tÖOtPOQbPEWvPFitPO wPOAnPL
LpPOA`ÂlPA BPOArPQ(HPA HPÿA LpPOA`ÂlPA hPFAlPkPPA) -- ePvhPF EtPOnPLEWvPF
oPFjPLinPLrP EtPOnPLEWvPF aÌPO LpPOASPFALpPOAESPF ElPKPilP sLPMKPzAEWvPF hPFiHP
10-1 P| ePmLPnPL kPPirP HPAirPAEWvPF nPLÈ÷PrP LpPOAoPFbPA iyPitPO LpPOAirP aArP
aAmLPAidPrP HPAirPAEWvPF imLPAhPFrP aAiCPF -- atPOePHP çpPFEtPOEWvPF
imLPAhPFirP yPEdP ePkPPEWvPF nPLÈ÷PrP lPAgPFAinPLA yPAbP tPOAhPFilP
oPFjPLinPLrP fPOlPAfPOlPgFUilPA LpPOASPFALpPOAESPF sLPAEjPLibP iyP
nPLÈ÷PrPEWvPF LpPOAoPFbPA yPAiHP isLPvhPF nPLÈ÷PirPrP imLPAhPFrPEWvPFvhPF
KLUÿitPOA HPilP icPFnPLA yPAiHPP|
isLPWvPFA KLUHP sLPhPFijPL kPPrPA yPAbP tÖOtPOQEbPkPP sLPMKPzArP SPFrPNP
EnPLilPP| tÖOtPOQEbPkPP EkPP HPéUF tPOArP kFZOWvPFkPPcPFAilP nPLA EgPFibP
EtPOnPL aiÌPOrP ePkPPWvPFA tÖOtPOQEbPkPP sLPMKPzArP dPSPFEmLPikPP dPÿAwxPFAiHP:
tÖOtPOQEbPkPP sLPMKPzArP HPÿA EdPikPP iTPikPP çpPFTPmLP aÌPO +
3 x (tÖOtPOQEbPkPP sLPMKPzArP HPÿA EdPkPP
iTPikPP EªPtPOQbP aÌPO +
3 x (tÖOtPOQEbPkPP sLPMKPzArP HPÿA EdPkPP
iTPikPP tÖOtPOQbP aÌPO )
aTPYAð aAmLPAidPrP icPFnPLA tÖOtPOQEbPkPP sLPMKPzA 10-1 = -1 + 3
x
(0 + 3 x
1) = -1 + 9 = 8 (dPSPFEmLPkPP)
ePBPOAiHP EhPFisLPHP kPPrPilP aAmLPrPA iLpPOitPO LpPOAErP
imLPAhPFirPrP nPLAmLP
kPP
KP
gPF
GPL
cPF
CPF
jPL
JPF
WvPF
VPF
wPO
WPOL
dPSPFEmLPkPP nPLÈ÷PrP
1
2
3
4
5
6
7
8
9
10
11
12 *
0
0
0
0
1
1
1
1
1
1
1
1 **
0
1
1
1
-1
-1
-1
0
0
0
1
1 ***
1
-1
0
1
-1
0
1
-1
0
1
-1
0
imLPAhPFirPrP nPLAmLP
kPP
KP
gPF
GPL
cPF
CPF
jPL
JPF
WvPF
VPF
wPO
WPOL
dPSPFEmLPkPP nPLÈ÷PrP
1
2
-3
4
5
-6
7
-10
9
-8
11
-12 *
0
0
0
0
1
-1
1 -1
1
-1
1
-1 **
0
1
-1
1
-1
1
-1
0
0
0
1
-1 ***
1
-1
0
1
-1
0
1
-1
0
1
-1
0