maht fundation grade 11.pdf
TRANSCRIPT
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lwm pl:n nigEsn BisidbriBaabR&tKNitviTa nig BaNiCkm
CMBUkTI1
sIVtcMnYnBit-sIVtnBVn-sIVtFrNImaRt
CMBUkTI2GnuKmn_Gics,NgEsl nig elakarIt
CMBUkTI3
GnuKmn_RtIekaNmaRtCMBUkTI4
maRTIs nig edETmINg
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eroberogeday
Esn Bisidnig lwm pl:n
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GkRtYtBinitbeckeTs
1-elak lwm qun
2-elak Esn Bisid3-elakRsITuy rINa
4-elak Tit emg
5-elak RBwm suxnit
6-elak pl bunqay
GkRtYtBinitGkraviruT
elak lwm miK:sir
karIkMBTr nig rcnaRkb
kBaa lIKUNaka
GkniBn nig eroberog
elak Esn Bisidnig elak lwm pl:n
rkasiTi
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Garmkfa
esovePA kMEnlMhatfakTI11EdlRbiymitGksikakMBugkanenAkgdenrYmman CMBUkTI1 sItcMnnBit sItnBn nigsItFrNImaRtCMBUkTI2 GnKmnGics NgEsl elakartCMBUkTI3 GnmnRtekaNmaRtCMBUkTI4 maRTsngedETmNg
kgCMBUknImYy@xMJTneRCIserIsyklMhatmkeFIVkMEnyagek,ak,ay enAslCMBUkTI5 lImIt ng edrIevCMBUkTI6RbblIetnig CMBUkTI7si tixMJTnwgeFIVkMEnenAkgPaKeRkay.
CaTIbBab xMJTGkeroberogsUmeKarBCUnBrdlGksikakgRKbmCdan sUmmansuxPaBlRCJaQasv nig TTYln
C&yCMnkgRKbParkic.
tdMbgfTI10 sPa qaM2009
GkniBnnig eroberog
lwm pl:n nigEsn BisidTel : (017) 768 246
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1-sIVtcMnYnBit
2-sIVtnBVn
3-sIVtFrNImaRt
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sVItncMnYnBit CMBUk1 emeronTI1
lMhat
1-sresrbItYbnabnsIVtxageRkam k x....,20,15,10,5 ....,55,30,14,5,1
2-sresrtYnsIVtrabGsxageRkam
kn
)1(a
n
n
= cMeBa 8n1
x cMeBa2nn )2(b = 5n1 3-sresrbYntYnsIVtrabGsxageRkam
k2
n2
nn
)1(a
= xnn
1b
2n
Kc
X2n
n )2n()1( 1nn
n 2)1(d
4-kMnttYTIncMeBaRKb INn nsIVtxageRkam k x...,13,11,9,7,5 ...,5,3,1,1,3
K X...,4,7,10,13,16 ...,9
5,
7
4,
5
3,
3
2
5
-bgHajfasIVt Edl)a(
n 3n
1a
n CasIVtcu .
6-bgHajfasIVt Edl)b( n3n
1n2bn
= CasIVtekIn .
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sVItncMnYnBit CMBUk1 emeronTI1
7-sikaPaBmUNUtUnnsIVtEdlkMntdUcxageRkam
ksIVt EdlINnn )a( n1
an=
xsIVt EdlINnn )a( 5n4na 2n KsIVt Edl*INnn )a( )nln(.4nan XsIVt Edl)a( n 2n1n aa = nig 2a0= 8
-bgHajfasIVt Edl)a(
n n1na 2
n
CasIVtTal.9-etIsIVtxageRkamCasIVtTaleT ?
ksIVt Edl*INnn )a(
nn
1n2na
2
23
n
=
xsVIt Edl*INnn )b( n
bn
=
KsIVt Edl)c( n3n1ncn
= 10-etIbNasIVtxageRkammYyNaCasIVtTalelITaleRkam
nigCasIVtTal? rYcrkeKalnsIVtnImYy@ .
k 1n;nn
1n2na
2
23
n
=
x 2n;4n3n
ea
2
n
n
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sVItncMnYnBit CMBUk1 emeronTI1
11-eKmansIVt Edl CacMnYnKtehIy)a( n n 1a0=
nig .1aaa n2
n1n
kbgHajfasIVt Edl CacMnYnKtCasIVtekIn .)a( n n xbgHajfacMeBaRKb .na,n n
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sVItncMnYnBit CMBUk1 emeronTI1
dMeNaRsay
1-sresrbItYbnabnsIVtxageRkam k ....,20,15,10,5
eyIgBiniteXIjfa
5u51520u
5u51015u
5u5510u
5u
34
23
12
1
=
ehtuenbItYbnabnsIVtenKW
355305uu
305255uu
255205uu
67
56
45
=
=
=
dUcen .35,30,25,20,15,10,5
x ....,55,30,14,5,1 eyIgBiniteXIjfa
22
23
21
22
1
3u3514u
2u215u11u
=
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sVItncMnYnBit CMBUk1 emeronTI1
2
4
2
5
23
24
5u53055u
4u41430u
ehtuenbItYbnabnsIVtenKW
204641408uu
14049917uu
9136556uu
278
267
256
=
=
=
dUcen .204,140,91,55,30,14,5,12-sresrtYnsIVtrabGsxageRkam
kn
)1(a
n
n
= cMeBa 8n1
ebI ena1n= 1a1
ebI ena2n=21a2=
ebI ena3n=3
1a3
ebI ena4n=4
1a4=
ebI ena5n= 51
a5
ebI ena6n=6
1a6=
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sVItncMnYnBit CMBUk1 emeronTI1
ebI ena7n=7
1a7
ebI ena8n= 81a8=
dUcen8
1;
7
1;
6
1;
5
1;
4
1;
3
1;
2
1,1 .
x cMeBa2nn )2(b = 5n1 ebI ena1n= 2a1= ebI ena2n= 1a2=
ebI ena3n=2
1a3=
ebI ena4n=4
1a4=
ebI ena5n=
8
1
a5=
dUcen8
1;
4
1;
2
1;1;2 .
3-sresrbYntYnsIVtrabGsxageRkam
k2
n2
nn
)1(a
=
eKn16
1;
9
1;
4
1;1 .
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sVItncMnYnBit CMBUk1 emeronTI1
xnn
1b
2n
eKn201;
121;
61;
21 .
K 2nn )2n()1(c eKn 4;1;0;1 .X 1nnn 2)1(d
eKn 8,4;2;1 .4-kMnttYTIncMeBaRKb INn nsIVtxageRkam k ...,13,11,9,7,5
eyIgeXIjfa 50.25
54.213
53.211
52.29
51.27
dUcentYTInKW 5n2Un x ...,5,3,1,1,3
eyIgeXIjfa 30.23
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sVItncMnYnBit CMBUk1 emeronTI1
34.25
33.23
32.21
31.21
dUcentYTInKW 3n2Un K ...,4,7,10,13,16 eyIgeXIjfa 160.316
164.34
163.37
162.310
161.313
dUcentYTInKW 16n3Un
X ...,95,74,53,32 eyIgeXIjfa
30.2
20
3
2
=
33.2
23
9
5
32.2
22
7
4
31.2
21
5
3
=
=
=
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sVItncMnYnBit CMBUk1 emeronTI1
dUcentYTInKW3n2
2nUn
=
5-bgHajfasIVt Edl)a( n 3n 1an CasIVtcu .eKman
3n
1an
naM[4n
1a 1n
eyIgn3n
1
4n
1aa n1n
0)4n)(3n(
1aa
)4n)(3n(
)4n()3n(aa
n1n
n1n
=
dUcen CasIVtekIn .)b( n
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sVItncMnYnBit CMBUk1 emeronTI1
7-sikaPaBmUNUtUnnsIVtEdlkMntdUcxageRkam
ksIVt EdlINnn )a(
n
1an=
eyIgmann
1an= naM[
1n
1a 1n
eyIgn 0)1n(n
1
n
1
1n
1aa n1n n1n
eyIgseg;teXIjfacMeBa }1,0{n= ena 0aa n1n < ehIy 0aa:2n n1n > .dUcen minEmnCasIVtmUNUtUn .)a( n
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sVItncMnYnBit CMBUk1 emeronTI1
KsIVt Edl*INnn )a(
)nln(.4nan
eKman )nln(.4nan
naM[ )1nln(41na 1n eKn )nln(4)1nln(41aa n1n
1n
nln41aa n1n
edayRKb eKman1n 11nn
eKTajn INn;aa n1n
dUcen CasIVtmUNUtUn .)a( n8-bgHajfasIVt Edl)a( n n1na 2n CasIVtTal.
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sVItncMnYnBit CMBUk1 emeronTI1
eKmann1n
1n1na
2
2n
=
eyIgeXIjfakalNa nxitCitGnnenan1n
12
xitCitsUn ehIyebI 0n= ena 1a0= .eKTaj cMeBaRKb1a0 n INn .dUcen CasIVtTal.)a( n
9-etIsIVtxageRkamCasIVtTaleT ?
ksIVt Edl*INnn )a(
nn
1n2na
2
23
n
=
ebI ena1n= 2a1= ehIynn
1n2n2
23
xiteTArk
GnnkalNa nxitCitGnn.dUcen CasIVtTaleRkamehIy2CacMnYnTaleRkam.)a( n
xsVIt Edl*INnn )b( n
bn
=
ebI ena1n= 1b ehIyn
xitCitsUnebI n
eKTaj nb0 .dUcen CasIVtTal.)b( n
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sVItncMnYnBit CMBUk1 emeronTI1
KsIVt Edl)c( n3n
1ncn
=
ebI ena0n= 3c0= ehIy 3n 1n xitCit1kalNaxiteTACitGnn.n
eKn naM[ CasIVtTal.3c1 n )c( n10-etIbNasIVtxageRkammYyNaCasIVtTalelITaleRkam
nigCasIVtTal? rYcrkeKalnsIVtnImYy@ .k 1n;
nn
1n2na
2
23
n
=
ebI ena1n= 1a1= ehIynn
1n2n2
23
xiteTArk
GnnkalNan
xitCitGnn.dUcen CasIVtTaleRkamehIy1CacMnYnTaleRkam.)a( n
x 2n;4n3n
ea
2
n
n
ebI ena2n=6
ea
2
2= ehIy4n3n
e2
n
xiteTArk
GnnkalNa nxitCitGnn.
dUcen CasIVtTaleRkamehIy)a( n6
e2
CacMnYnTaleRkam.
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sVItncMnYnBit CMBUk1 emeronTI1
- 14 -
11-eKmansIVt Edl CacMnYnKtehIy)a( n n 1a0=
nig .1aaa n2
n1n
kbgHajfasIVt Edl CacMnYnKtCasIVtekIn .)a( n n xbgHajfacMeBaRKb .na,n n> dMeNaRsay
kbgHajfasIVt CasIVtekIn )a( n
eyIgman 1aaa n2n1n eyIgn INn,01aaa 2nn1n
dUcen CasIVtekIn .)a( n xbgHajfacMeBaRKb na,n n
eyIgman 01a0 >
31831131691aaa
2131391aaa
131aaa
22
23
12
12
02
01
>
>
>
tamlMnaMeneyIgGacsnidanfaRKb .na,n n>
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sVItnBVn CMBUk1 emeronTI2
lMhat
1-sresrrUbmnntYTInsIVtnBVnxageRkam k x....,37,26,15,4 ....,11,7,3,1,5 K ...,23,16,9,2 X ...,27,22,17,12,7
2-sresrRMtYdMbUgnsIVtnBVnEdlkMntedaytY
k 10U;1U 21 = x n37Un 3-eKmansIVtnBVn ...;7;2;3;8 .kKNna nig17U 43U
xetItYTIbun
annsIVtes
Inwg 3224-kMntcMnYntYnsIVtnBVnxageRkam k 102....,,8,13,18 x 171...,.,1,4,9
5
-kgcMeNamsVItxageRkam etIsIVtNamYyCasIVtnBVn?k )1n(613Un
x nn1n0 U4
1UU;3U
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sVItnBVn CMBUk1 emeronTI2
6-eK[ CasIVtnBVnebIeKdwgfa )U( n
k 17U;9U 4535 =
. KNna ?40U x
2
13U;
2
7U 137 = . KNna ?0U
K 18S,12U 122 = . KNna nigd;U1 6U7-eK[sIVtnBVn nig sIVtnBVn...,12,7,2 ...,8,5,2
etIkgcMeNam121
tYnsIVtTaMgBIrenmanbun
antYEdlmantmesIKa ?8-bgHajfasIVt EdlmantYTI kMnteday )U( n n
4
3n2Un
=
CasIVtnBVnekIn .
9
-eK[RMcMnYnCasIVtnBVn. KNnacMnYnTaMgenaebIeKdwgfaplbUkvaesI125 ehIyplbUkBItYdMbUgesI .3810-ebIplbUk 9tYdMbUgnsVItnBVnesInwg 162ehIyplbUk
tYdMbUgnsVItnBVnesI288 .12 KNnaplbUk 30tYdMbUgnsVItnBVnen ?11-rkbIcMnYntKaCasIVtnBVnedaydwgfaplbUkbIcMnYnenesInwg 36ehIyplKuNvaesInwg 1428.
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sVItnBVn CMBUk1 emeronTI2
12-KNnaplbUksIVtnBVnxageRkam
k 146....642
x )20(...859095100 K 1721....185189193
X )3(.....4
33
2
14
4
15
13
-salRbCMumYyragctuekaNBay ehIytamRCugeRTtnsalRbCMuenaeKerobekAGICa 15CYr EdlCYrmuxeKbMputerobn 25ekAGIehIyCYrTIBIrerobn ekAGICYrTIbI27
erobn 29ekAGI.eKerobekAGItamlMnaMxagelIrhUtdlCYeRkay .KNnaekAGIsRmabGg:yTaMgGsEdlmanenAkgsalRbCMu.
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sVItnBVn CMBUk1 emeronTI2
1
-sresrrUbmntYTInnsIVtnBVnxageRkam
dMeNaRsay
k ....,37,26,15,4 tamrUbmn d)1n(UU 1n eKman nig4U1= 11415UUd 12 =
eKn7n1111n114)11()1n(4Un
dUcen 7n11Un .x ....,11,7,3,1,5 tamrUbmn d)1n(UU 1n eKman nig5U1= 451UUd 12 eKn U 9n44n45)4()1n(5n dUcen 9n4Un .K ...,23,16,9,2 tamrUbmn d)1n(UU 1n
eKman nig2U1 729UUd 12 eKn 5n77n72)7()1n(2Un dUcen 5n7Un .
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sVItnBVn CMBUk1 emeronTI2
X ...,27,22,17,12,7
tamrUbmn d)1n(UU 1n
eKman nig7U1= 5712UUd 12 = eKn 2n55n57)5()1n(7Un dUcen 2n5Un .
2
-sresrRMtYdMbUgnsIVtnBVnEdlkMntedaytYk 10U;1U 21 = tamrUbmn d)1n(UU 1n eKman nig1U1= 9110UUd 12 = eKn 8n99n91)9()1n(1Un
ebI ena1n= 189U1 = ebI ena2n= 10818U2 = ebI ena3n= 19827U3 = ebI ena4n= 28836U4 =
ebI ena5n= 37845U5 = dUcenRMtYdMbUgnsVItnBVnKW .37;28;19;10;1
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sVItnBVn CMBUk1 emeronTI2
x n37Un
ebI ena1n=
437U1
ebI ena2n= 167U2 ebI ena3n= 297U3 = ebI ena4n= 5127U4 =
ebI ena5n= 8157U5 =
dUcenRMtYdMbUgnsVItnBVnKW 8;5;2;1;4
.3-eKmansIVtnBVn ...;7;2;3;8 .kKNna nig17U 43U
tamrUbmn d)1n(UU 1n
eKman nig8U1 583UUd 12 = eKn 13n55n58)5()1n(8Un dUcen 72138513)17(5U17 = nig 2021321513)43(5U43 = .
xetItYTIbunannsIVtesInwg 322 eyIgn 32213n5 = naM[ 67n= dUcentYTI67nsIVtEdlesInwg .322
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sVItnBVn CMBUk1 emeronTI2
4-kMntcMnYntYnsIVtnBVnxageRkam
k 102....,,8,13,18
CadMbUgeyIgRtUvkMntrktYTInnsIVtensin .tamrUbmn d)1n(UU 1n eKman nig18U1= 51813UUd 12
eKn23n55n518)5()1n(18Un
edaRsaysmIkar 10223n5
naM[ 25n=
dUcensIVtxagelImancMnYn tY.25 x 171...,.,1,4,9 tamrUbmn d)1n(UU 1n
eKman nig9U1 594UUd 12 = eKn 14n55n59)5()1n(9Un edaRsaysmIkar 17114n5 = naM[ 37n= dUcensIVtxagelImancMnYn tY.37
5-kgcMeNamsVItxageRkam etIsIVtNamYyCasIVtnBVn?k )1n(613Un eyIgn 7n66n613Un
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sVItnBVn CMBUk1 emeronTI2
nig 13n67)1n(6U 1n
eKman 6)7n6()13n6(UU n1n =
efrdUcen )1n(613Un CasIVtnBVn
x nn1n0 U4
1UU;3U
eKman nn1n U4
1UU
eKTaj nn1n U41UU minefrdUcenvaminEmnCasIVtnBVneT .
6-eK[ CasIVtnBVnebIeKdwgfa )U( n k 17U;9U 4535 = . KNna ?40U
tamrUbmn d)1n(UU 1n eKn d34UU 135 )1(9d34U1 = ehIy d44UU 145 )2(17d44U1 = eFIVplsgrvagTMnakTMng nig eKn )1( )2(
naM[8d10 54
d=
tam eKTaj)1(5
91
5
13645
5
4349U1 =
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sVItnBVn CMBUk1 emeronTI2
eyIgn 135
439
5
91d39UU 140 =
dUcen .13U40= x
2
13U;
2
7U 137 = . KNna ?0U
tamrUbmn INn;ndUU 0n
eKn
d13UU
d7UU
013
07
=
=
2
13d13U
2
7d7U
0
0
eFIVplsgeKn 3d6 naM[2
1d=
ehIy 02
7
2
7d7
2
7U0 =
dUcen .0U0= K 18S,12U 122 = . KNna nig ?d;U1 6U
tamrUbmn d)1n(UU 1n nig2
)UU(nS n1n
=
eKn 12dUU 12 naM[ d12U1
ehIy 18)UU(6S 12112 = 3UU 121 = eday d11UU 112 ena 3d11U2 1 = eKTaj 3d11)d12(2
=
naM[ 3d=
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sVItnBVn CMBUk1 emeronTI2
ehIy 15d12U1 .
bnabmk 0)3(515d5UU 16 =
dUcen 0U;3d;15U 61 = .7-eK[sIVtnBVn nig sIVtnBVn...,12,7,2 ...,8,5,2 etIkgcMeNam 121tYnsIVtTaMgBIrenmanbunantYEdlman
tmes
IKa ?tag nig erogKaCatYTI nigtYTIqnsIVt)a( p )b( q p nBVn nig sIVtnBVn...,12,7,2 ...,8,5,2 Edl .*INq;p eyIgn 3p5)1p(52ap
ehIy 1q3)1q(32bq cMeBa nig121p1 121q1 ebI qp aa= ena 1q33p5 )1q(3)1p(5
eKTajn
=
=
k51q
k31p smmUl
1k5q
1k3p
cMeBaRKb .INk eday nig121p1
121q1
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sVItnBVn CMBUk1 emeronTI2
eKTajn
1211k51
1211k31
24k0
40k0
naM[ 24k0 }24;...;2;1;0{k= .dUceneKGacsnidanfakgcMeNam 121tYnsIVtTaMgBIrenman tYEdlmantmesIKa .25
8-bgHajfasIVt EdlmantYTI kMnteday )U( n n
4 3n2Un = CasIVtnBVnekIn .eyIgman
4
5n2
4
3)1n(2U 1n
==
eyIgn 14
1n2
4
5n2UU n1n == efr
eday01UU n1n >
naM[ CasIVtnBVnekIn .)U( n
9-eK[RMcMnYnCasIVtnBVn. KNnacMnYnTaMgenaebIeKdwgfaplbUkvaesI125 ehIyplbUkBItYdMbUgesI .38
tag CaRMcMnYnEdlRtUvrk54321 a;a;a;a;a
tambMrabeKn =
=
125aaaaa
38aa:)S(
54321
21
tag dCaplsgrYmnsVItnBVn 54321 a;a;a;a;a
ena d4aa;d3aa;d2aa;daa 15141312
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sVItnBVn CMBUk1 emeronTI2
RbB&nsmIkar GacsresrCa )S(
smmUl
=
=
125d10a5
38da2
1
1
=
=
25d2a
76d2a4
1
1
eFIVplsgeKn 51a3 1= naM[ 17a1= ehIy 43438a238d 1 =
eKTaj
=
=
=
=
331617a
291217a
25817a
21417a
5
4
3
2
dUcen CaRMcMnYnEdlRtUvrk .33;29;25;21;1710-ebIplbUk 9tYdMbUgnsVItnBVnesInwg 162ehIyplbUk
tYdMbUgnsVItnBVnesI288 .12 KNnaplbUk 30tYdMbUgnsVItnBVnen ?tag CasIVtnBVnenehIy CaplbUkntYdMbUg*INn;n )u( nS
nsVIten .
tamrUbmn 2)uu(n
S n1
n
= eKn 162
2
)uu(9S 919 == naM[ 36uu 91 =
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sVItnBVn CMBUk1 emeronTI2
eday ( dCaplsgrYm )d8uu 19
eKn 36d8u2 1 =
118d4u1 =
dUcKaEdr 288)uu(6S 12112 = naM[ eday48uu 121 = d11uu 112 eKn 248d11u2 1 =
eKnRbB&n ==
48d11u2
18d4u
1
1
smmUl
=
=
48d11u2
36d8u2
1
1
eFIVplsgeKn 12d3 naM[ 4d= ehIy 21618d418u1 = .eKn )uu(15S 30130 eday 118)4(292d29uu 130 = ehtuen 1800)1182(15S30 = .
11-rkbIcMnYntKaCasIVtnBVnedaydwgfaplbUkbIcMnYnenesI
nwg 36ehIyplKuNvaesInwg 1428.tag dx;x;dx CabIcMnYnEdlRtUvrktamsmtikmeKGacbeg;ItRbB&n
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sVItnBVn CMBUk1 emeronTI2
=
=
1428)dx(x)dx(
36)dx(x)dx(
naM[
=
=
1428xdx
36x323
=
5d
12x
dYcen CabIcMnYntKaena .17,12,7 7,12,1712-KNnaplbUksIVtnBVnxageRkam
k146....642
eyIgn CasIVtnBVnmanplsgrYm2146;....;6;4;2 nigtYTImYyesI .tYTInnsIVtKW2 n2)1n(22un = ebI ena146un= 146n2= 73n= dUcen 5402
2
)1462(73146....642 =
=
x )20(...859095100 eyIgn )20(,....;85;90;95;100 CasIVtnBVnmanplsgrYm 5nigtYTImYyesI100.tYTInnsIVtKW 105n5)1n(5100un
ebI ena20un 20105n5 25n= dUcen 1000
2
)20100(25)20(...859095100 ==
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sVItnBVn CMBUk1 emeronTI2
K 47251721....185189193
X 227
)3(.....4
3
32
1
44
1
5 =
13-salRbCMumYyragctuekaNBay ehIytamRCugeRTtnsalRbCMuenaeKerobekAGICa 15CYr EdlCYrmuxeKbMputerobn 25ekAGIehIyCYrTIBIrerobn ekAGICYrTIbI27
erobn 29ekAGI.eKerobekAGItamlMnaMxagelIrhUtdlCYeRkay .KNnaekAGIsRmabGg:yTaMgGsEdlmanenAkgsalRbCMu.
25ekAGI
15CYr
cMnYnekAGITaMgGsEdlmanenAkgsalRbCMuKWCaplbUk 15tYdMbUgnsIVtnBVnEdlmantYTImYy 25u1= plsgrYm 2d=
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sVItnBVn CMBUk1 emeronTI2
- 30 -
ehIy 532)115(25u15 = .
ebI CacMnYnekAGIenaN 5852)5325(15
N == ekAGI.
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sVItFrNImaRt CMBUk1 emeronTI3
lMhat
1-kMntpleFobrYmnsIVtFrNImaRtnigsresrbYntYbnabeTotnsIVtnImYy@xageRkam k x....,500,100,20,4 ....,4,22,2,2
2-eKmansIVtFrNImaRt ....,54,18,6,2
kKNnatYTI7 xetIcMnYn CatYTIbunannsIVt ?39366 KKNnaplbUk 15tYdMbUgnsIVtFrNImaRt .3-kMntcMnYntYnsIVtFrNImaRtxageRkam
k 8192....,,8,4,2,1 x
256
5,....,
2
5,5,10,20
4-bgHajfasVItxageRkamCassIVtFrNImaRtEdlmantYTInkMntdUcxageRkam
k x1n
n )3(7u
n
1n )4(8
1
U
5-eK[ CasIVtFrNImaRt ebIeKdwgfa )u( n k 1458U;8U 73 = . KNna qnig ?10U
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sVItFrNImaRt CMBUk1 emeronTI3
x 1280U;20U 63 = . KNna qnig ?1U
K . KNna qnig ?21S;3U 31 =
7S6-KNnaplbUksVItFrNImaRtxageRkam
k8
3...122448
x 6561....313
1
K244
128.....469
X n21n25432 31
2
1....2
1
3
1
2
1
3
1
2
11
7-KNnaplbUksIVtFrNImaRtGnntYEdlman
nig9U2 3
1U5= .
8-KNnapleFobrYmnsIVtFrNImaRtGnntYEdlman
nig5U1= 15S= .9-plbUkBIrtYdMbUgnsIVtFrNImaRtesInwg 9nigplbUksIVtFrNIImaRtGnntYesInwg 25.KNna qnig ebIpleFob1U 0q>
10-sresrCacMnYnsniTanEdlmanTRmgba
nUvcMnYnTsPaKxYbxageRkam k 7.0 x 34.2 K 452.0
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sVItFrNImaRt CMBUk1 emeronTI3
11-tYTI nsIVtnBVnesI14nig tYTI12esI .5 35
KNnaplsgrYmtYTI1nig tYTIn.12-plbUkn tYdMbUgnsIVtmYykMnteday .n nnS 2n
KNnatYTI nsIVt nigbgHajfatYnsIVtenCasIVtnBVn.5
13-tYTI nsIVtFrNImaRtesI nigtYTI6esI3 38
3 .
KNnapleFobrYm tYTI1
nigplbUk8
tYdMbUg .14-KNna aedIm,I[bIcMnYn )1a(,)3a(
nig )2a4(
CabItYtKansIVtFrNImaRtmYy .15-eK[bYncMnYnCasIVtFrNImaRt . KNnatYTIBIr nig tYTIbInsIVtebIeKdwgfa tYTImYyesI6ehIytYTIbYnesInwg 162.
16-eKTijpmYytm dula . GkTijRtUvbgRkCa600030 dMNakkal Edlbeg;ItnCasIVtFrNImaRtmanpleFobrYm
esInwg10
9 . kMntRkEdlRtUvbgtamdMNakkalnImYy@.
17-eKmansIVtnBVn nig kMnteday)U( n )V( n 3U0= nigplsgrYmesI3ehIy 3V0= nigplsgrYmesI .2 kkMnt nig CaGnuKmn_n n.nU nV
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sVItFrNImaRt CMBUk1 emeronTI3
xeKmansIVt kMnteday)W( nn
nn
V
UW=
.
bgHajfa CasIVtekIn ..a )W( n kMntnedIm,I[.b
28
1WW 1nn = .
18-kMntplsgrYm nigtYTImYy nsVItnBVnekIn1U *INnn )U(
ebIeKdwgfa
=
=
4UUU
98UUU
321
23
22
21
KNnatYTI10nigplbUk 10tYdMbUgnsIVt .19-tYdMbUgnsIVtFrNImaRtesI ehIymanpleFobrYmesI3 r Edltmdacxatn rtUcCag 1.
plbUk tYdMbUgesI39
8 nplbUk 6tYdMbUg .
KNnaplbUkGnntYnsIVtFrNImaRt .20-1 edaRsaykg smIkarIR )E(04x8x3: 2
=
2 eKman CasIVtFrNImaRtekInEdlmantYINnn )U( nig nsIVtCacemIynsmIkar .3U 4U )E(
k-TajrkpleFobrYmnsIVten .x-KNnatYTImYy nsIVt .1U
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sVItFrNImaRt CMBUk1 emeronTI3
dMeNaRsay
1-kMntpleFobrYmnsIVtFrNImaRtnigsresrbYntYbnabeTotnsIVtnImYy@xageRkam k ....,500,100,20,4
pleFobrYmnsIVtenKW
5100500
20100
420q
= dUcen .5q=
x ....,4,22,2,2 pleFobrYmnsIVtenKW
222
42
222
2q =
dUcen 2q=
.2-eKmansIVtFrNImaRt ....,54,18,6,2 kKNnatYTI7 xetIcMnYn CatYTIbunannsIVt ?39366 KKNnaplbUk 15tYdMbUgnsIVtFrNImaRt .
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sVItFrNImaRt CMBUk1 emeronTI3
dMeNaRsay
kKNnatYTI7 tamrUbmn 617 quu
eday nig2u1= 32
6
u
uq
1
2=
eKn 145832u 67 =
dUcen .1458u7= xetIcMnYn CatYTIbunannsIVt ?39366 tYTInnsIVtenKW 1n1n1n 3.2quu = ebI ena39366un= 393663.2 1n =
eKTaj91n 3196833 =
naM[ 91n = 10n= dUcencMnYn CatYTI10nsIVt .39366
KKNnaplbUk 15tYdMbUgnsIVtFrNImaRt
tamrUbmn 1q1q
.uu...uuS
15
1152115
=
13
13
132S 15
15
15
.
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sVItFrNImaRt CMBUk1 emeronTI3
3-kMntcMnYntYnsIVtFrNImaRtxageRkam
k 8192....,,8,4,2,1 tamrUbmntYTInnsIVtFrNImaRtKW 1n1n quu
eday 21
2
u
uq;1u
1
21 =
eKn *INn2u 1nn
ebI ena8192un=131n
281922 =
eKTaj naM[131n = 14n= .dUcensIVtxagelImancMnYn 14tY.
x256
5,....,
2
5,5,10,20
tamrUbmntYTInnsIVtFrNImaRtKW1n
1n quu
eday2
1
20
10
u
uq;2u
1
21 =
eKn *INn2
120u
1nn
ebI 2565
un=
ena 2565
2
120
1n
=
122 1n
=
eKTaj naM[121n = 13n= .dUcensIVtxagelImancMnYn 13tY.
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sVItFrNImaRt CMBUk1 emeronTI3
4-bgHajfasVItxageRkamCasIVtFrNImaRtEdlmantYTIn
kMntdUcxageRkam k 1nn )3(7u eday 1nn 37u ena n1n 37u
eKn 337
37
u
uq
1n
n
n
1n=
=
efr
dUcen nu CasIVtFrNImaRtmanpleFobrYm .3q= x n1n )4(
8
1U
eday nn 48
1u
ena 1n1n 48
1u
eKn4
u
uq
n
1n=
efrdUcen nu CasIVtFrNImaRtmanpleFobrYm .4q=
5-eK[ CasIVtFrNImaRt ebIeKdwgfa )u( n k 1458U;18U 73 = . KNna nig ?q 10U
tamrUbmn1n
1n quu
eKn
=
=
1458q.uu
18q.uu
617
213
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sVItFrNImaRt CMBUk1 emeronTI3
eKTaj18
1458
q.u
q.u
u
u2
1
61
3
7= 81q4
=
eKTaj .3q maeTot 373619110 q.uq).qu(quu =
3936631458u 310 dUcen }39366;3;39366;3{u;q 10 x 1280U;20U 63 = . KNna qnig ?1U
tamrUbmn 1n1n quu
eKn
=
=
1280q.uu
20q.uu
516
213
eKTaj20
1280q.uq.u
uu
21
51
3
6= 64q3 =
eKTaj .4q=
maeTot eKTaj213 q.uu=4
5
4
20u
21 =
dUcen 45
u;4q 1= .
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sVItFrNImaRt CMBUk1 emeronTI3
K . KNna qnig ?21S;3U 31 = 7S
tamrUbmn 21)1q.(31q1q
.uS
2
13 =
= eKTaj .6q
=
mageTot )16(5
3
16
16.3
1q
1q.uS 6
66
17
=
=
dUcen )16(53
S;6q
6
7
.6-KNnaplbUksVItFrNImaRtxageRkam
k8
3...122448
tamrUbmntYTInnsIVtFrNImaRtKW 1n1n quu
eday 21
48
24
u
uq;48u
121
=
eKn1n
n2
148u
ebI8
3un= ena
8
3
2
148
1n
=
eKTaj 71n2
1
2
1
=
naM[ 8n=
dUcenplbUkxagelICaplbUk 8tYdMbUgnsIVtFrNImaRt .
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sVItFrNImaRt CMBUk1 emeronTI3
eyIgn211
2
11
488
3
...122448
8
8
765
256
125696
=
dUcen 876583...122448 = .
x3
295246561....31
3
1=
K243
1261
244
128.....469 =
X n21n25432 31
2
1....
2
1
3
1
2
1
3
1
2
11
n1n 4
11
3
2
9
11
8
9
7-KNnaplbUksIVtFrNImaRtGnntYEdlman
nig9U2 3
1U5= .
tamrUbmnq1
uS 1
Edl CatYTImYy nig qCapleFobrYm .1u
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sVItFrNImaRt CMBUk1 emeronTI3
eKman27
1
9
3
1
qu
q.u
u
u
1
41
2
5
27
1q3 naM[
3
1q
ehIy 273
1
9
q
uu 21 =
=
dUcen 481
3
11
27
S =
= .
8-KNnapleFobrYmnsIVtFrNImaRtGnntYEdlman nig5U1= 15S= .
tamrUbmn q1u
S 1
naM[ 32
15
51
S
U1q 1 =
dUcen
3
2q= .
9-plbUkBIrtYdMbUgnsIVtFrNImaRtesInwg 9nigplbUksIVtFrNIImaRtGnntYesInwg 25.
KNna qnig ebIpleFob1U 0q> tambMrabeKman
>
=
0q,25S
9UU 21
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sVItFrNImaRt CMBUk1 emeronTI3
eKn
=
=
25q1
U
9q.UU
1
11
=
)q1(25U
9)q1(U
1
1
eKTaj 9)q1(25 2 =
naM[25
16
25
91q2 = eday 0q>
eKTaj5
4q= ehIy 5
5
4
1
9
q1
9u1 =
=
dUcen 5u;5
4q 1= .
10-sresrCacMnYnsniTanEdlmanTRmgb
a nUvcMnYnTsPaKxYb
xageRkam
k 7.0 eyIgn ....007.007.07.07.0
9
7
9.0
7.0
1.01
7.0=
dUcen9
77.0 = .
x99
23234.2 = K
495
224452.0 =
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sVItFrNImaRt CMBUk1 emeronTI3
11-tYTI nsIVtnBVnesI14nig tYTI12esI .5 35
KNnaplsgrYm tYTI1nig tYTI .n tag CasIVtnBVnen)u( n
eKman
naM[
=
=
35u
14u
12
5
=
=
35d11u
14d4u
1
1
eFIVplsgeKn 21d7 naM[ 3d=
bnabmk 21214d414u1 = ehIy 1n3)1n(32d)1n(uu 1n dUcen 1n3u;2u;3d n1 .
12-plbUkn tYdMbUgnsIVtmYykMnteday .n nnS 2n
KNnatYTI nsIVt nigbgHajfatYnsIVtenCasIVtnBVn.5 - KNnatY 5U eyIgman n321n U...UUUS
ehIy 1nn1n3211n USU...UUUS
eKTajn1n1n SSU
ehtuen 10)44()55(SSU 22455 = dUcen .10U5=
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sVItFrNImaRt CMBUk1 emeronTI3
- bgHajfatYnsIVtenCasIVtnBVn
eKman n1n1n SSU
eday nnS 2n naM[ 2n3n1n)1n(S 221n eKn 2n2nn2n3nU 221n
eKTajn22)1n(2Un =
eday 2n22n2UU n1n = efrdUcen CasIVtnBVn.)U( n
13-tYTI nsIVtFrNImaRtesI nigtYTI6esI3 38
3 .
KNnapleFobrYm tYTI1nigplbUk 8tYdMbUg .
tamsmtikmeKman
=
=
8
3q.UU
3q.UU
516
213
eKn8
1q
U
U 3
3
6=
naM[2
1q= .
eday eKTaj213 q.UU= 12
2
13
qUU
2231 =
=
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sVItFrNImaRt CMBUk1 emeronTI3
mageTot 256255
24211
2
11
.12q1
q1
uS
8
8
18
=
=
dUcen32
765S;12U;
2
1q 81 = .
14-KNna aedIm,I[bIcMnYn )1a(,)3a( nig )2a4(
CabItYtKansIVtFrNImaRtmYy .KNnatmaedIm,I[bIcMnYn )1a(,)3a(
nig )2a4(
CabItYtKansIVtFrNImaRtmYyluRtaEt )2a4)(3a()1a( 2
0491564'
05a16a3
6a12a2a41a2a
2
22
>
=
eKTajs 53
78a;
3
1
3
78a 21 ===
dUcen 5a;3
1a 21 = .
15-eK[bYncMnYnCasIVtFrNImaRt . KNnatYTIBIr nig tYTIbInsIVtebIeKdwgfa tYTImYyesI6ehIytYTIbYnesInwg 162.
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sVItFrNImaRt CMBUk1 emeronTI3
KNnatY nig2u 3u
tambMrab CasIVtFrNImaRt .4321 u;u;u;u eday ehIy6u1= 162q.uu 314 =
eKTaj 276
162
u
162q
1
3= naM[ 3q=
dUcen 183.6q.uu 12 =
nig .543.6q.uu 22
13 =
16-eKTijpmYytm dula . GkTijRtUvbgRkCa600030 dMNakkal Edlbeg;ItnCasIVtFrNImaRtmanpleFobrYm
esInwg10
9 . kMntRkEdlRtUvbgtamdMNakkalnImYy@.
tag Ca RkEdlRtUvbgtam654321 U;U;U;U;U;U dMNakkalnImYy@ . tamsmtikmeKn
=
=
10
9q
)1(00030U...UU 621
tam eKsresr)1( 00030q1 q1.U6
1 =
eKTaj61 q1
)q1(30000U
= eday 9.010
9q =
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sVItFrNImaRt CMBUk1 emeronTI3
eKn 088.64026$)9.0(1
)9.01(30000U
61 =
=
ehIyedayeRbI q.UU...,;q.UU;q.UU 562312 = eKTaj 479.57623$U2=
765.37806$U;516.42007$U
018.46675$U;131.51861$U
65
43
=
=
17-eKmansIVtnBVn nig kMnteday)U( n )V( n 3U0= nigplsgrYmesI3ehIy 3V0= nigplsgrYmesI .2 kkMnt nig CaGnuKmn_n n.nU nV
xeKmansIVt kMnteday)W( nn
nn
V
UW=
.
bgHajfa CasIVtekIn ..a )W( n
kMntnedIm,I[.b28
1WW 1nn = .
dMeNaRsay
kkMnt nig CaGnuKmn_n nnU nV
tamrUbmnn33ndUU 0n
ehIy n23ndVV 0n dUcen 2n3V;3n3U nn
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sVItFrNImaRt CMBUk1 emeronTI3
xeKmansIVt kMnteday)W( nn
nn
V
UW=
.
bgHajfa CasIVtekIn.a )W( n eyIgman
3n2
3n3
V
UW
n
nn
=
eKn5n2
6n3
3)1n(2
3)1n(3W 1n
=
=
eday 3n23n3
5n2
6n3
WW n1n
=
0)3n2)(5n2(
3
)3n2)(5n2(
15n21n618n21n6 22
>
=
dUcen CasIVtekIn .)W(
n
kMntnedIm,I[.b28
1WW 1nn =
eKman)3n2)(5n2(
3WW n1n
naM[28
1
)1n2)(3n2(
3WW 1nn =
eKTaj 30028416';071n8n4 2 = naM[smIkarKanskg IN.
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sVItFrNImaRt CMBUk1 emeronTI3
18-kMntplsgrYm nigtYTImYy nsVItnBVnekIn1U *INnn )U(
ebIeKdwgfa
=
=
4UUU
98UUU
321
2
3
2
2
2
1
KNnatYTI10nigplbUk 10tYdMbUgnsIVt .dMeNaRsay
- KNnaplsgrYm dnigtYTImYy 1U
eday CasIVtnBVnekInenaplsgrYm321 U;U;U 0d > ehIy 231 U2UU = 2321 UUUU = eKTaj ( eRBa4U2= 4UUU 321 = )
eKman
eday
=
=
4UUU
98UUU
321
23
22
21 4U2=
eKn
=
=
8UU
82UU
31
23
21
eKman 312312321 UU2)UU(UU
eKTaj2
)UU()UU(UU
23
21
231
31
=
9UU
28264UU
31
31
=
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sVItFrNImaRt CMBUk1 emeronTI3
eKnRbB&n
=
9UU
8UU
31
31
naM[ nig CassmIkar1U 3U 09X8X2 = eday enacab 9X;1X 21 = eKTaj 9U;1U 31 = dUcen 9U;4U;1U 321 =
eKn 5)1(4UUd 12 = dUcen nig1U1 5d= .-KNna nig10U 10S
eyIgn 44451d9UU 110 =
ehIy 215)441(52)UU(10
S 10110 ==
dUcen 215S;44U 1010 = .19-tYdMbUgnsIVtFrNImaRtesI ehIymanpleFobrYmesI3 r Edltmdacxatn rtUcCag 1.
plbUk tYdMbUgesI3 98
nplbUk 6tYdMbUg .KNnaplbUkGnntYnsIVtFrNImaRt .
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sVItFrNImaRt CMBUk1 emeronTI3
dMeNaRsay
KNnaplbUkGnntYnsIVtFrNImaRt tamrUbmn
r1
US 1
smtikm 3U1=
ehIy )U...UU(9
8UUU 621321
)r1)(r1(9
8r1
r1r1U
98
r1r1U
333
61
31
=
eKTaj8
11
8
9r3 = naM[
2
1r=
dUcen 62
11
3S =
= .
20-1 edaRsaykg smIkarIR )E(04x8x3: 2=
2 eKman CasIVtFrNImaRtekInEdlmantYINnn )U(
nig nsIVtCacemIynsmIkar .3U 4U )E(
k-TajrkpleFobrYmnsIVten .x-KNnatYTImYy nsIVt .1U
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sVItFrNImaRt CMBUk1 emeronTI3
- 53 -
dMeNaRsay
1 edaRsaykg IRsmIkar)E(04x8x3 2 =
2
3
24x;
3
2
3
24x
41216'
21 ===
=
dUcen2x;
3
2x
21 =
.2k-TajrkpleFobrYmnsIVten
eKman 2U;3
2U 43 = (eRBa 43 UU< sIVtekIn)
eKman nig213 q.UU= 314 q.UU=
eKn 33
22q
q.Uq.U
UU
21
3
1
3
4=
dUcen .3q= x-KNnatYTImYy nsIVt 1U
eday naM[213 q.UU=27
2
3
3
2
q
UU
223
1 =
dUcen27
2U1= .
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1-GnuKmn_Gics,NgEsl2-GnuKmn_elakarIt
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
1
-KNnatmnkenam
lMhat
k 16 x 225 K 144X 3 3)2y(008.0
g 2)x6(
c 3 27 q 3 64 C3 3x64 2
-sresrkenamxageRkamCaTRmgGics,NgEsl k 4 10x=
x k568=
K 8 h500a=
X x yb
=
3-sRmYlkenam k4 625 x5 1 K 5 32
X532
1
g6 6x c4 4)b7(
q7 7y C5 5)2x(
4-rkEdnkMntnGnuKmn_k x)x(f
=
x 3 x)x(f = K 8x2)x(f
X x34)x(f g 2x3)x(f c 1x)x(f 2
q5x3x2
x)x(f
2
C2xx
3x)x(f
2
=
Q|x|x
1x)x(f
=
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
5-KNnakenamxageRkam
k 3.2 x 33
5.3 K 444
72.9.8 X b10.a3 g ax.ax c
5
y.
x
6
6-sRmYlkenam
k 724
116
2
35.4
3
2 3
x 33 33 y543
xyx16y2x
7-eRbobeFobk 3 25 nig 3 312 x3 2nig 12 45K6 5nig 8 8
8-sRmYlkenam
k 22223 3223
dc.dc
dcd3dc3c
x 1xxx
K 222222 q2pq3q
1
q8pq6p
q3p.
ppq4q3
p
9-sresrkenamxageRkamCaTRmgraDIkal
k 3
1
8 x 4
1
x K 5
1
y X 2
135 )ta( g 4
133 )yx( c 4
153 )yx(
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
10-edaRsaysmIkar
k x322x=
1)1x(
3x4x2=
K 2)32()32( xx=
X 65613 )2( x=
g c
q C981 )4(
x
=
13 )3( x
=
0)6(5 x=
)9(2)4(3 xx
4)32()32( xx=
11
-edaRsayvismIkark x12x > 13x K16
12 x2
X g1xx 816 < x52x5 1632 c256
14 1x3
>
12-edaRsayvismIkar
k x125.016x
>
82x
K 31
3.27 x1x
13-mIgsynykkmYycMnYneTAepJIenAFnaKarmYyedayTTYlnGRtakarRk kgmYyqaM. ryeBl qaMeRkaymk%6 7
KatndkRkBIFnaKarenavijedayTTYlnRksrubcMnYndula . etImIgsymanRkedImcMnYnbunan ?300
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
14-mnusmakmanGayu qaMnykRk eroleTAepJI30 00050
enAFnaKarmYyedayTTYlnGRtakarRk kgmYyqaM.%4 etIKatmanksrubcMnYnbunanebIbcb,nKatmanGayu65qaM?15-mnusmaknTijrfynfImYyeRKOgkgtm dula .00045 rfynenacuf CaerogralqaM.%15
rktmrfynkgryeBl7
qaMeRkay .
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
1
-KNnatmnkenam
dMeNaRsay
k 4)4(16 2 = x 15)15(225 2 = K 12)12(144 2 =
X )2y(2.0)2y()2.0()2y(008.0 3 333 3
g |x|6x6)x6( 2 = c 3)3(27 3 33 = q 4)4(64 3 33
C x4)x4(x64 3 3
3 3
2-sresrkenamxageRkamCaTRmgGics,NgEsl k 4 10x
=
naM[ 10x4=
x k568 = naM[ 8k56 = K 8 h500a= naM[ h500a8 =
X x yb= naM[ ybx =
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
3-sRmYlkenam
k 5)5(625 4 44
=
x 115 K 2)2()2(32 5 55 =
X2
1
2
1
32
15
5
5
g |x|x6 6 = c |b|7)b7(4 4 = q yy7 7 = C 2x)2x(5 5
4-rkEdnkMntnGnuKmn_k x)x(f = GnuKmn_mann&ykalNa 0x
dUcen [;0[D
x 3 x)x(f = GnuKmn_enGackMntnCanicRKb IRx
dUcen IRD = K 8x2)x(f
GnuKmn_mann&ykalNa 08x2 naM[ . dUcen4x [;4[D
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
X x34)x(f
GnuKmn_mann&ykalNa
naM[
0x34
. dUcen ]34
;]D
3
4
x
g 2x3)x(f uKmn_enKann&yCanicelIkElgEtGn 0x= .
dUcen }0{D =
c 1x)x(f =
GnuKmn_enGa2
ckMntnCanicRKb IRx
endUc IRD =
q5x3x2
x)x(f
2
uKmn_mann&ykalNa
=
05x3x2
0x
2Gn
0x
2
5x;1x
dUcen [;2
5][
2
5;0[D
C 2xx3x
)x(f =
2
uKmn_mann&ykalNa
02xx
03x
2Gn
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
2x;1x
3x
dUce 1n [;2][2;1][;3[D Q
|x|x
1x)x(f
=
mn_mann&ykalNaGnuK
0|x|x
01x naM[ 0x >
dUcen [;0]D 5-KNnakenamxageRkam k 6323.2 = x 3333 15535.3 =
K 2623672724 9872.9.8 444 = =
X ab30b10.a3b10.a3 = g 22 ax)ax)(ax(ax.ax
cx5
y6
5
y.
x
6
5
y.
x
6=
Ylkenam k
6
-sRm2
2
3235
3
472
4
116
25.4
3
32 33
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
33 33 y543
xyx16y2x x
0y2xy2x2y2x 333=
beFob7-eRbo k 3 25 nig 3 312 eKman 33 3 3 2.25 2505
=
33 33
24831.231ehIy 2 = dUcen 33 31225 > x 3 2nig 12 45eKman 123 12 4 1622 =
dUcen12 452
6
8-sRmYlkenam
dc
1
dc
dc
dc.dc
3dc3c
22
3 3 dcd2222
322
=
k
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
x )xx
2 xx()1x(x
)1xx(x
1x
x=
222222K-
q2pq3p
1
q8pq6p
q3p.ppq4q3
p
q4p
p
q4p
p
)q2p)(qp()q4p)(q2p(
q3p.
)pq3)(qp(
p
resrkenamxageRkamCaTRmgraDIkal9-s
k 33 88= 1
44
1
xx=x
551
yy=
K
352
135 ta)ta(X
4 334
133 yx)yx( g =
4 5341
53 yx)yx( =
c
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
10-ed
k
aRsaysmIkar
322x=
22=
naM[ 5x5x=
lkxN x( 1)1x 3x4x2 =
1x 1x0
IkarsmmUlsm
=
3x4x
11x
2 eKTajs 3 3x;1x;0x 21 =
K 2)3 x = 2()32( x
32
1 eKman 1)32)(3 = 32( 2
IkarsmmUl 2)32(
1)32(x
x=
sm
1)32(2x
0
1)32(2 xx2
=
eKTaj
0)32( =
1)32( x = dUcen .0x=
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
X 13 )2( x 656
3x
x
8)2(
22
8233
x
=
=
=
eng
aj
dUc 3x=981 )4(
x
=
12x2
22
24
3
2x2
1x
2
=
=
=
=
34 1x
eKT 21
.x
caMgBIrnwg
0)6(5)9(2)4(3 xxx =
EckGg:T x9 eKn
0233
25
2 xx2
=3
tag 03
2t
x
>
=
mans02t5t3 2 =32t;1t 21 =
-cMeBa eKTaj1t1= 13
2 x
=
0x=
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
-cMeBa3
2t2=
3
2
3
x
=
2eKTaj
1x=
dUcen 1x; 2 .
)
0x1= =
qeKTaj ( Kans
0)3( 313x
=
03x=
C 4)2( x=
32()3 x
aneKm32
1= 32
IkarsmmUl 4)32(
1)32(
xsm x =
01)32( 2(4)3 xx2 =
tag 0)32(t 2
x
>
ajs314';01t4t =
eKT 32t;32t 21 -cMeBa ena 32)3232t1 ( x
naM[ .2x
=
-cMeBa 32 ena 32)32( x t2= = .naM[ x 2
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
11-edaRsayvismIkar
naM[M[k x
2>
x>
0
21=
0 x 0x3 na31
= 0x
K 4x2 216
12
=
naM[ 2x
4x2
sX mmUl1xx 816 < 3x3x4 22 <
ajeKT 3x3x4 3 x
Ulsmm 41x3 44 >
ajeKT 41x3 x 1
yvismIkar12-edaRsa k smmUl 2125.016x
>
3x4 2>
eKTaj 3x4 4
3x>
envismIkarenmancemIykgx 82
x
eday 02:IRx x
>
dUc .IR
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
K3
1
eKTaj3
2x <
13-mI kkmYy nGRtakarRk %6 kgm
gsyny cMnYneTAepJIenAFnaKarmYyedayTTYlYyqaM. ryeBl qaMeRkaymk
IFnaKarenavijedayTTYlnRksrubcMnYn7
KatndkRkB 300dula . etImIgsymanRkedImcMnYnbunan ?
tamrUbmn t)i(pA= naM[1 tAp= )i1(
eday 7t;06.0%6i;300$A qaM
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GnuKmn_Gics,NgEsl CMBUk2 emeronTI1
- 69 -
eKn 517.199$p =)06.01(
3007
.
akmanGayu qaMnykRk eroleTAepJIarmYyedayTTYlnGRtakarR kgmYyqaM.
nYnb manGay
14-mnusm 00030 50 enAFnaK k %4 etIKatmanksrubcM unanebIbcb,nKat u65qaM?
tamrUbmn t)i1(pA eday =
=
=
=
35t
04.%4i 50p
0
000
eKn erolnTijrfyn Ogkgtm ula .
uf CaerogralqaM.
5.197304)04.01(50000A 35 =
15-mnusmak fImYyeRK 0d0045
rfynenac rktmrf%15
ynkgryeBl 7qaMeRkay .cemIyRMBIrqaMeRkaymkrfynmantm 14426$
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GnuKmn_elakarIt CMBUk2 emeronTI2
lMhat
1-rksmIkarnGnuKmn_RcasrbsGnuKmn_xageRkam k x K3x4y 1x3y 2 3y3x 22 =
X g c6xy 1xy2 = 14
y
9
x 22=
q x5
y=
C 2xy
2-eK[GnuKmn_ 2x)x(f . cUrkMntrkGnuKmn_Rcas )x(f 1 rYcsgRkabrbsva .
3-sgRkabnGnuKmn_xageRkam k xxlogy 5 xlogy 7 K
X gxlogy 10
xlogy 15 xlogy 5.0 c xlogy 3.04-bMElgCaTRmgelakarIt
k x10000104 = 2831
= K 21641
=
X 251
5 2 =
g 641
4 3 =
c 210 3010.0 =
q Cyx a = ckA=
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GnuKmn_elakarIt CMBUk2 emeronTI2
5-sRmYl
k x K2log3
3
10log5
5
10
a alog X g caq qlog 64log4 1.0log10 Q 16log 2 j 1log106-edaRsaysmIkarelakarIt
k
x3xlog3 = 216logx =
K 1)9xlog(xlog =
X 1xlog2 g2
1xlog9 =
c3
1xlog8 = q xlogxlog 3 =
C 2)3x(log)3x(log 44 =
Q 11xlog 2
5 =
j 33 43 2 2logxlogxlog =
7-edaRsayvismIkarelakarIt k )3x(logx2log 42 x )7x(log)5x3(log 33
K 11x
xxlog
2
2
4 3
x
15
1
15
g 3x
04.05
1
1x
0x
eKTaj naM[2x16=
416x =
K 1)9xlog(xlog = lkxN
>
>
09x
0x0x >
eKn 10log)9x(xlog = eKTaj 010x9x2 = eday 0cba =
X eKTaj1xlog2 2
12x 1 =
g2
1xlog9 = eKTaj 39x 2
1
=
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GnuKmn_elakarIt CMBUk2 emeronTI2
c3
1xlog8 = eKTaj 28x 3
1
=
q xlogxlog 3 = lkxN naM[
>
0xlog
0x1x
eKn xlogxlog3
1=
0xlog9xlog2 =
0)9xlog(xlog = eKTajs .910x;1x
=
C 2)3x(log)3x(log 44 =
lkxN naM[
>
>
03x
03x3x >
smIkarGacsresr
525x
25x
4)3x)(3x(
2)3x)(3x(log
2
2
4
=
=
=
eday (lkxNxagelI)3x > dUcen .5x=
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GnuKmn_elakarIt CMBUk2 emeronTI2
Q 11xlog 25 =
smmUl 51x2
=
62x
24x
251x
2
2
=
=
j 33 43 2 2logxlogxlog = lkxN 0x
eKn 33 43 2 2logx.xlog =
4
2x
8
1x
2x
2
33 6
=
=
7-edaRsayvismIkarelakarIt k )3x(logx2log 42 lkxN 0x >
eKn )3x(log2
1x2log 22
1x4
303xx4
)3x(log)x2(log
)3x(logx2log2
2
22
2
22
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GnuKmn_elakarIt CMBUk2 emeronTI2
eday enaeKTaj0x > 1x0
dUcen CasMnMucemIysmIkar .]1;0]x x )7x(log)5x3(log 33 lkxN
3
5x>
eKn 12
57x7x5x3
dUcen [;3
5]x
K 11x
xxlog
2
2
eKTaj108
6977logx
108
69773 3
x ==
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GnuKmn_elakarIt CMBUk2 emeronTI2
X 3xx3x2 2122
0)12)(12(
012)12(2
x3x
3x3xx
=
=
eday eKn012x>
3x012 3x
11-ebI . bgHajfazyx )ab(ba = )yx(zxy tag 0t)ab(ba zxx
>
eKTaj
=
=
=
tlogz
tlogx
tlogx
ab
b
a
eKmanblogalog
1
)ab(log
1tlogz
tttab
yx
xy
y
1
x
1
1
tlog
1
tlog
1
1z
ba
=
=
dUcen )yx(zxy .12-ebI cba 1232 = . bgHajfa )b2a(cab
tag0t1232 cba >
eKTaj
=
=
=
tlogc
tlogb
tloga
12
3
2
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GnuKmn_elakarIt CMBUk2 emeronTI2
eKman2log23log
1
)2.3(log
1tlogc
tt2
t12
b2aab
a
2
b
11
tlog
2
tlog
11c
23
=
=
dUcen .)b2a(cab 13-ebI 23a nig 23b .
bgHajfa 1b1 1a1 1 =eKman 1)23)(23(ab =
a
1b=
eKna1
a
a
11
1
b1
1
=
ehtuen 1a1
aa1
1b1
1a1
1=
dUcen 1b1
1
a1
1=
.
14-ebI .ab11ba 22 =
bgHajfa)
3
balog(2blogalog
=
?eKman ab11ba 22 =
ab9bab2a 22=
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GnuKmn_elakarIt CMBUk2 emeronTI2
ab9)ba( 2 = ab3
ba 2
=
eKn blogalog)ablog(3
balog
2
ebI eKTajba > )3
balog(2blogalog
= .
15-ebI nigaMlogx = bMlogy = .
bgHajfa baab
Mlogxy
eKmanylogxlog
1
)xy(log
1Mlog
MMMxy
ba
ab
b
1
a
1
1Mlog
Mlog
1
Mlog
1
1Mlog
xy
yx
xy
=
=
dUcenba
abMlogxy
.
16-edaRsaysmIkarelakarIt k 25logxlog)3x2(log2 1021010
lkxN2
3x03x2
>
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GnuKmn_elakarIt CMBUk2 emeronTI2
eKn 25logxlog)3x2(log100log 102101010
624x;224x
41216';012x8x
x25)3x2(100)x25log()3x2(100log
21
2
2
2
10
=
=
=
=
x 13)xlog8(log6 8x = lkxN 1x;0x
tag naM[xlogt 8 8logt1 x
smIkarsmmUl 13)tt
1(6 =
25144169;06t13t6 2=
eKTajs 34
6
513t;3
6
513t 21 ===
-cMeBa eKTaj3t= 5128x3xlog 38 =
-cMeBa3
4t= eKTaj 168x
3
4log 3
4
8 =
dUcen 512x;16x 21 =
K 25xlog9log 9x = mans 81x;3x 21 = X 19logxlog 2x9 = smIkarKans .
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GnuKmn_elakarIt CMBUk2 emeronTI2
17-edaRsayvismIkarGics,NgEsl
k2x3x
12525
7
6x6x9x2
55 )2x3(3x2
x 273x >
3x33 3x
> K tag082.64 xx > 02t x >
0)4t)(2t(
08t6t2
>
>
naM[ 4t2t0 >
eKTaj 1x220 x < 2x42x > dUcen [;2][1;]x
X 4 3
x
15
115
4
3x515 4
3x
g3
2x04.0
5
1 3x
>
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GnuKmn_elakarIt CMBUk2 emeronTI2
c 2x9
1003.0 x
18-edaRsayvismIkarelakarIt k 1xlog 2x3
smmUl
2x3x
12x30
2x3x
12x3
smmUl
1x
1x
3
2
x1
1x
dUcen [1;3
2[x .
x tag015xlogxlog 224 < 0x;xlogt 4 > eKn 015t2t2 <
5t30)3t)(5t(
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GnuKmn_elakarIt CMBUk2 emeronTI2
eKn [ ]4
32)13(log)13(log x4
x4 <
tag )13(logt x4
2
3t
2
1t0)1t2)(3t2(
03t8t4
04
3t2t
4
3)2t(t
2
2
>
>
==
=
eKn oooo 48.28436052.75x52.75x4
1xcos
=
X 0ysin
ycosycos3 =cos3 0ycoty =
0)1ysin3(ycos =
3
1ysineKTaj 0ycos
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
dUcen y ooo 47.199y;52.340y;90 = .
g 2sin2 01x =
o
oo
o
210sinx2s
s
in
)30180sin(x2in
30sinx2sin
2
1x2sin
=
eKTaj Zk;108.k15x180.k105x oooo eday o0 o360x dUcen o ;285 oo 195xx;105x = c xsin6 xcos5xsin8 22 =
03
2)1x(sin
03
5xsin2xsin
05xsin6xsin3)xsin1(5xsin8xsin6
2
2
2
22
=
=
=
smIkarKans .q t5x2cot2 oo 80.201x80.21x4.0x2an =
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
C 08ytanysin3 =
3
1ycos3ycos0)1ycos3)(3y(cos
03ycos8ycos3
03ycos8ycos3
0ycos8)ycos1(3
0ycos8ysin3
08ycos
ysin
.y
2
2
2
2
=
=
=
=
=
eKTajQ
sin3
oo52.250y;47.109y =
5ysin7ycos3 2
3
1ysin2ysin0)1ysin3)(2y(sin
02ysin7ysin3
5ysin7ysin33
=
5ysin7)ysin
2
2
2
=
j
j
1(3
eKTa oo 47.199y;58.340y =
0)2
zsin21(2
zcos02
zcos22
zcot
=
eKTaj2
1
2
zsin0
2
zcos =
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
dUcen z = ooo 300z;30z;180 = .
aj
.
d xtan( 050tan)30 oo
=
eKT ooo 180.k30x0)30xtan( eday 0 o360x
dUcen oo 210x;30x =5
-eK[
cos2sin3x
ign y
sin2cos3
mnmMuRsYckrkt cMeBa x y=
eKn s2co3cos2sin3
co5sin
ins
Zk;180.k7.785tan
s
oo
CacMnYnefrcMeBaRKbtmn
efr .
kaN
xbgHajfa2 yx 2
eKn 22 sincos3()cos2sinx 22 )23(y
13)cos(sin13 22 = dUcen yx 1322 =
6
-eK[RtIe manABC Atan
AcosBsin
sin BcosA=
.Ca Ekg .bgHajfa AB RtIekaNC
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
dMeNaRsay
CaRtIekaNEkgbgHajfa ABCeKman Atan
Assin
Bssin=
coB
coA
00 90C90BA0)BAcos(
0BsinAsinBcosAcos
AcosAsinBsinAsinBcosAcosAcosAsin
Acos
Asin
AcosBsin
BcosAsin
=
=
=
dUcen CaRtIekaNEkgRtg .ABC C
7-eK[RtIekaN ABCman Aos2Bsin
Csin=
c .rkRbePT ABC.
dMeNaRsay
eKman AcosBsin2CsinAcos2Bsin
Csin=
eday )BAsin()BA(sinCnsi eKn AcosBsin2)BAsin( =
2
BA0)BAsin(0AcosBsinBcosAsin
AcosBsinAcosBsinBcosAsin
=
=
=
dUcen CaRtIekaNsmtkMBUl .ABC C
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
9-Gg;tFAB ckrgVgmYyEdlmankaMesInwg cm2E CaBIrGg;t.
Gg;t
.Uc .
eKdwgfa ACs;atFEdlmanmMupites
I .KNna o
60
kRkTLapceRmokfas AOB.
O
B
A xRkTLapRtIekaN AO B KRkTLapGg;tfast
dMeNaRsay
kRkTLapceRmokfas AOB
eyIgn 21 R2
1S eday
360;cm2R o
=
dUcen 21 cm2
S3
4.3
.2
1 ==
.
pRtIekaNxRkTLa AOB
eyIgn 202 s.OA2
1S= cm360sin.2.2.
2
1AinOB. =
;tfastUcKRkTLapGg
)cm(33
2 eyIgn SSS 213
=
2 .
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
10-KNna
k 960sin o
=
)60180sin(240sin)3602240sin(
ooooo
2
360sin
o
x 1215cos oooo 135cos)3603135cos(1215cos =
2
245sin)4590cos(
ooo
K2360sin)360860sin(2940sin o ooo =
2
3
6cos)
62cos(
6
13cos ==X
g 1ta 4
tan)54
tan(4
19n
=
2
3
3sin)63sin(3
17
sin ===
cNna 11-K
)2
3sin()sin()
2 k sinsin (
0cossincossin = .
x 21)1)(1()1)(21(c )3cos(25sin47tan320os 0)cos()2sin()2
2cos()
2sin( =K
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
12-eKman tantantantantantan
Edl 2,,2
-
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
tag A
010cos10cos
10cos60cos210cos
)70cos50(cos10cos
70cos50s10cos
oo
ooo
ooo
000co
=
dUcen .0A=
tagB
2
4
3]
2
1110cos2[
2
110cos
]120cos20cos[2
110cos
70cos50cos10cos
o2o2
ooo2
ooo2
=
tag222
C
2
3)20cos20(cos
2
1
2
3
)20cos120cos220(cos21
23
)140cos100cos20(cos2
1
2
3
2
140cos1
2
100cos1
2
20cos1
70cos50cos10cos
o0
000
000
000
o2o2o2
=
=
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
14-bgHajfa
k
n .
)Acos1)(Asin1(2)AcosAsin1( 2
tag A=
2)AcosAsin1(
)Acos1)(Asin1(2
Acos)Asin1(2)Asin
Acos)Asin1(2Asin22
AcosAcos)Asin1(2AsinAsin21
AcosAcos)Asin1(2)Asin1(
Acos)Asin1(
22
22
2
1(2
dUce A)cos1)(Asin1(2)AcosAsin1( 2
AcosAsin
1AtanAcot
=
x
eKman AcosAsinAsin AcosAtanAcot
AcosAsin
1
AcosAsin
AsinAcos 22
=
=
AcosAsin
1AtanAcot
=
dUcen .K = 22 sintan)sin)(tansin(tan
tag A )sin)(tansin(tan
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
=
2222
2
2
2
tansin1tan1sin
1cos
1sin
1cos
11cos
sin
sincos
sinsin
sinA
.X
1
cos
dUcen
22 sintan)sin)(tansin(tan
cotcossin1sin
11
tag )sin1)(sin
11(A
=
=
=
cotcossin
cos
sin
sin1
sin
sin1)(sin1(
22
cotcossin1sin
11 .
IkarxageRkam
dUcen
15-edaRsaysm
c4 01xcos4x2cosxos3
=
cos40)1xcos2)(1xcos2(
02xcos4xcos2x
01xcos4)1xcos2(xcos4
2
23
23
=
=
=
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
0xcos2( = )1xcos2)(1xcos2)(1
eKTaj Zk;k23x3cos2xcos 1
=
Zk;k24
3x
4
3cos
2
2xcos
Zk;k24
x4
cos2
2xcos
=
==
16-keK[
ncMnYnefr nig .eKman
eKTaj
n qAsinp)AsiAcos2()AsinA(cosAcosAsin2 222
cUrrktm p q
AcosAsin21)AsinA(cos 2
( AcosAsin4Asin34)AsinAcos2 22
3Asin3qAsinp 22
dUcen p 3q;3 .xeK[ xsinba)xcot2xtan5(xcosxsin 2cUrrktmncMnYnefr nig b.a
tag A )xcot2xtan5(xcosxsin si xn32xcos2xsin5 222
dUcen a .3b;2 =
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
17-edaRsayvismIkarxageRkam
2
1
3
2
cos
2
1
3 edayxcos
k
3
2cos)xcos(
3
eKTaj Zk;k23
2
3xk2
3
2
x Zk;k23
k2
x 1)6
xtan(
)4
(tan)6
xtan(
aj k4
3xk
4
6 eKT
Zk;k12
11xk12 dUcen .
smIkarxageRkam
18-edaRsay
0cos2sin2 =2
2
2
4
232t;2
4
232
t1 =
1t2 2
8162;02t2
)1t1(cost;0cos2cos2
0cos2)cos1(2
2
2
2
2
=
=
=
=
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
4 eKn cos
2
2cos
=
dUcen Zk;k24 .19-eK[ manmMu CamMuRsYc .
gHajfaABC 3
kb Ctan.Btan.AtanCtanBtanAtan = xtag . bgHajfa 33TCtanBtanAtanT ?
aydMeNaRskbgHajfa Ctan.Btan.AtanCtanBtanAtan =
eKman ena CBA CBA eKn )Cn()B taAtan(
CtanBtanAtanCtanBtan
)(CtanBtanAan
CtanBtanAtan1
BtanAtan
BtanAtan1t Atan =
dUcen Atan Ctan.Btan.AtanCtanBtan = .faxbgHaj 33T
eKman CtanBtanAtanT eday CamMuRsYcenaC;B;A 0Ctan;0Btan;0Atan >
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smIkarnigvismIkarRtIekaNmaRt CMBUk3 emeronTI3
- 166 -
tamvismPaB eKman GMAM
33
27T =
27T
T27
T
T3
T
CtanBtanAtan3
CtanBtan
2
3
3
3
dUcen
Atan
33CtanBtanAtanCtanBtanAtanT
-
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1-maRTIs2-edETmINg
-
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maRTIs nig edETrmINg CMBUk4 emeronTI1
lMhat
1-Tinn&ykgePsCdanmYybgHajfa enAfsuRkeKlkkaehVnEkv EtRkUcqa 125Ekv nig sura Ekv .160 210
enAfesAreKlkkaehVn 145Ekv EtRkUcqa 130Ekvnigsura Ekv ehIyenAfGaTitlkkaehVn 120Ekv275
EtRkUcqa 155Ekv nig sura Ekv .325 cUrbgHajBtmanenCamaRTIs nig RblMdabnmaRTIsen .2-KNnamaRTIsxageRkam
k x
52
73
01
64
15
26
105
98
03
42113
981
K
28
42
57
31
14
23
X
125
3613
523
132
3-eK[maRTIs
=
513
15D;
103
94C;
97
149
129
B;
83
416
213
A
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maRTIs nig edETrmINg CMBUk4 emeronTI1
KNna
k xBA3
CAB
K D4C5C2
X g)AB(3A D7)C3(2 c )CD(2A 4-KNna
k
56
47
12
132
2412
x 156
5
29
423
5-eK[
c36
20
10
21
0a
7b
02
10
rktm nig c.b,a6-eKdwgfatmsMbuRtcUlTsnaBiBNmYysnwksRmabkUnekg
erol mnuscas erol nigCnbreTs 10000 erol2000 5000 cMnYnsMbuRtEdlnlkenAcugsh_kngeTAenmansegbkg
taragxageRkam
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maRTIs nig edETrmINg CMBUk4 emeronTI1
kUnek
g mnuscas CnbreTsfesAr
205 160 70fGaTit
310 200 65
ktagtmsMbuRtCamaRTIsCYrQrC
xtagBtmankgtaragxagelICamaRTIs N KKNnaplKuN . etIFaturbsmaRTIs tag[GIV?CN CN7-eKmanmaRTIs
=
= m9
412C;
3
10
k
4
1
B;30
24A
kKNna nig2A 1A EdlCamaRTIsRcasn A xrktmk edIm,I[ CamaRTIsktaBA KrktmmedIm,I[edETmINg esInwgedETmINgn .A C
8-eK[maRTIs
=
11
13B;
45
12A . KNna
k nig xBA 1BA 1111 AB,B,A
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maRTIs nig edETrmINg CMBUk4 emeronTI1
KetIGkseg;teXIjyagNacMeBa 1BA nig 11AB
9
-rkmaRTIs Edl X k
=
9
11X
23
25 x
11
132X
11
11
10-rktm nig Edlepgpata;q;p b
k
1
4
q
p
13
310 x
=
b
15
1
a
12
34
K
=
03
51
21
12
1b
a1
11-kgsmIkar
=
32
10
21
32
01M cUrRblMdabnmaRTIsM
nigrkmaRTIs .M
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maRTIs nig edETrmINg CMBUk4 emeronTI1
dMeNaRsay
1-Tinn&ykgePsCdanmYybgHajfa enAfsuRkeKlkkaehVnEkv EtRkUcqa 125Ekv nig sura Ekv .160 210
enAfesAreKlkkaehVn 145Ekv EtRkUcqa 130Ekvnigsura Ekv ehIyenAfGaTitlkkaehVn 120Ekv275
EtRkUcqa 155Ekv nig sura Ekv .325 cUrbgHajBtmanenCamaRTIs nig RblMdabnmaRTIsen .dMeNaRsay
bgHajBtmanenCamaRTIs nig RblMdabnmaRTIsen
tag ACamaRTIsbgHajGMBIBtmanen .eKn CamaRTIskaerlMdab
=
325155120
275130145
210125160
A 33 .
2-KNnamaRTIsxageRkam
k
=
=
16
62
27
5624
7135
0216
52
73
01
64
15
26
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maRTIs nig edETrmINg CMBUk4 emeronTI1
x
105
98
03
42113
981 (KanRbmaNviFIbUk)
K
28
42
57
31
14
23
=
=
43
32
251874
432213
X
125
3613
523
132
=
=
2412
10155
3562153
9118332
3-eK[maRTIs
=
513
15D;
103
94C;
97
149
129
B;
83
416
213
A
KNna
k
=
92479
1412948
126399
97
149
129
83
416
213
3BA3
=
332
2397518
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maRTIs nig edETrmINg CMBUk4 emeronTI1
x (KanRbmaNviFIbUk )CAB
K D4C7D4C)52(D4C5C2
=
=
=
=
5073
678
20705221
4632028
2052
420
7021
6328
513
154
103
947
X A4B3A3B3A)AB(3A
=
=
533
68754813
32271221
16524827
84361427
83
416
213
4
97
149
129
3
g D7C6D7)C3(2
=
=
=
25109
6111
3591
735
6018
5424
513
157
103
946
c ( minGaceFVIRbmaNviFIn ) .)CD(2A
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maRTIs nig edETrmINg CMBUk4 emeronTI1
4-KNna
k
56
47
12
1322412
=
=
=
911
640
51226214
101612122824
)5)(1()4)(3()1)(2()6)(1()7)(3()2)(2(
)5)(2()4)(4()1)(12()6)(2()7)(4()2)(12(
x 156
5
29
423
68155315241087
15)6)(4()5)(2()29)(3(
=
5-eK[
c36
20
10
21
0a
7b
02
10
rktm nig cb,a
c36
20
10
21
0a
7b
02
10
5c,3b,1a
141c3
6b2
1a
1c36
01
14b2
0a=
=
=
=
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maRTIs nig edETrmINg CMBUk4 emeronTI1
6-eKdwgfatmsMbuRtcUlTsnaBiBNmYysnwksRmabkUnekg
erol mnuscas erol nigCnbreTs 10000 erol2000 5000 cMnYnsMbuRtEdlnlkenAcugsh_kngeTAenmansegbkgtaragxageRkam
kUnekg mnuscas CnbreTs
fesAr 205 160 70fGaTit310 200 65
ktagtmsMbuRtCamaRTIsCYrQr C
eyIgn
=
10000
5000
2000
C
xtagBtmankgtaragxagelICamaRTIs N
eyIgn
=
65200310
70160205N
KKNnaplKuN CN
=
10000
5000
2000
65200310
70160205CN
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maRTIs nig edETrmINg CMBUk4 emeronTI1
=
=
=
1712000
1910000CN
650000100000062000
700000800000410000CN
)10000)(65()5000)(200()2000)(310(
)10000)(70()5000)(160()2000)(205(CN
FaturbsmaRTIs tag[RkcMnUlsrubBIkarlksMbuRtCN
sRmabfesArnig fGaTit .7-eKmanmaRTIs
=
=
m9
412C;
3
10
k4
1
B;30
24A
kKNna nig2
A 1
A
EdlCamaRTIsRcasn A eKn
=
=
90
1416
30
24
30
24AAA
2
tamrUbmn
ac
bd
bcad
1A 1
Edl 3d;0c;2b;4a =
ena
=
=
3
10
6
1
4
1
40
23
12
1A 1
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maRTIs nig edETrmINg CMBUk4 emeronTI1
xrktmk edIm,I[ CamaRTIsktaBA
eyIgman
=
=
1032k41
3
10
k4
1
30
24BA
edIm,I[ CamaRTIsktaluRtaEtBA6
1k0
3
2k4 .
KrktmmedIm,I[edETmINg esInwgedETmINgnA C
eKman 1230
24)Adet( =
36m12m9
412)Cdet(
eday 1236m12)Cdet()Adet( =
eKTaj .2m 8-eK[maRTIs
=
11
13B;
45
12A . KNna
k nigBA 1BA
=
111
15
11
13
45
12BA
=
6
5
6
116
1
6
1
511
11
6
1BA
1
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maRTIs nig edETrmINg CMBUk4 emeronTI1
x 1111 AB,B,A
=
=
=
=
=
65
611
6
1
6
1
3
2
3
53
1
3
4
2
3
2
12
1
2
1
AB
2
3
2
12
1
2
1
31
11
2
1B
3
2
3
53
1
3
4
25
14
3
1A
11
1
1
KetIGkseg;teXIjyagNacMeBa 1BA nig 11AB
eyIgeXIjfa 111 ABAB = .9-rkmaRTIs Edl X
k
=
911X
2325
tag
=
2
1
x
xX
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maRTIs nig edETrmINg CMBUk4 emeronTI1
eKn
=
9
11
x
x
23
25
2
1
=
9
11
x2x3
x2x5
21
21
eKTajn
=
9x2x3
11x2x5
21
21 naM[ 3x,1x 21
dUcen .
=
3
1X
x
11
132X
11
11
tag
=
dc
baX
eKn
11
132
dc
ba
11
11
22
26
dbca
dbca (minGac)
dUcenKanmaRTIs NabMeBjlkxNeneT .X10-rktm nig Edlepgpata;q;p b
k
1
4
q
p
13
310
1
4
qp3
q3p10
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maRTIs nig edETrmINg CMBUk4 emeronTI1
eKTaj 2q,1p1qp3
4q3p10
= .
x
=
b15
1a
1234
=
b
15
1a2
3a4
eKTaj 7b;3ab1a2
153a4=
=
=
K
=
03
51
21
12
1b
a1
=
03
51
2b1b2
a21a2
eKTaj
=
=
=
=
02b
31b2
5a21
1a2
( RbB&nK
ancemIy ) .
11-kgsmIkar
=
32
10
21
32
01M cUrRblMdabnmaRTIsM
nigrkmaRTIs .M
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maRTIs nig edETrmINg CMBUk4 emeronTI1
- 181 -
dMeNaRsay
lMdabmaRTIs MkgsmIkar
=
32
10
21
32
01M bBaakfamaRTIs Mman
lMdab .32
tag
=
fe
dc
ba
M
eKman
=
f3f2e
d3d2c
b3b2a
32
01
fe
dc
ba
eKTaj 32
b2b3 nig 3
1
a1b2a =
3
1d1d3 nig
3
2c0d2c
1f3f3 = nig 0e2f2e =
dUcen
=
1031
32
3
2
3
1
M .
-
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maRTIs nig edETrmINg CMBUk4 emeronTI1
lMhat
1-KNnaedETrmINg
k734
123
432
x322
112
131
K 144153
321
2-KNnaedETrmINgedayeRbIkarBnattammIn&r
k263
014
211
x250
134
111
K325
140113
3-brimaRtctuekaNEkgmYymanRbEvg . eKdwgfaRbEvgTTwgcm86 dg elIsRbEvgbeNay . rkvimaRtnctuekaNeday2 cm2
eRbIkaredaRsaytamviFIRkam&r .4-eKlkEpBuRTa kg50 kg kg1 mantm3500erol . buEnedayBuRTaenmanEpFMnigEptUcenaEptUceKlkEt erolkg3000 kg1
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maRTIs nig edETrmINg CMBUk4 emeronTI1
nigEpFMlkf5000erolkg .kg1
etIEpBuRTaFMmanbun
anKITLRkam nig tUcbun
anKITLRkam ?5-eKdwgfaplbUknbIcMnYnesInwg 20cMnYnTI1esInwgplbUkncMnYnTI nig TI esInwg dgcMnYnTI1. rkcMnYnnImYy@ ?2 3 3
6-brimaRtRtIekaNmYymanRbEvg . eKdwgfaRCugEdlEvgCagm18
eKes
Inwg2
dgRCugEdlxICageK . RCugmYyeTotCamFmnBVnnRCugEdlEvgCageK nig RCugxICageK .rkRbEvgRCugnImYy@nRtIekaN ?
7-edaRsayRbB&nsmIkar
k
=
=
6y3
1x
2
1
0yx
4
3
x
=
2yx2
6yx
K X
=
y615x3
5y2x
=
=
=
8z2yx
15zy2x4
14z2y3x2
g c
=
=
5z2y7x3
10zyx4
10z3y2x
=
=
1z6y2x4
4z3y7x
2z3yx2
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maRTIs nig edETrmINg CMBUk4 emeronTI1
dMeNaRsay
1-KNnaedETrmINg
k34
234
74
133
73
122
734
123
432
=
3747534
)89(4)421(3)314(2
x22
12
32
123
32
11
322
112
131
=
312245 =
K 4453
314
132
14
15
144
153
321
=
11196141 =
2-KNnaedETrmINgedayeRbIkarBnattammIn&r
k 6314
223
04
26
01
263
014
211
524282 =
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maRTIs nig edETrmINg CMBUk4 emeronTI1
x50
34
20
14
25
13
250
134
111
10381 =
K25
40
35
10
32
143
325
140
113
5520530 =
3-brimaRtctuekaNEkgmYymanRbEvg . eKdwgfaRbEvgTTwgcm86 dg elIsRbEvgbeNay . rkvimaRtnctuekaNeday2 cm2 eRbIkaredaRsaytamviFIRkam&r .
tagx
CabeNay nig CaTTwg ( KitCa )y cm
tambMrabeKnRbB&n
=
2xy2
86y2x2
bnabBIedaRsayeKn cm15y,cm28x = .4-eKlkEpBuRTa kg50 kg kg1 mantm3500erol . buEneday
BuRTaenmanEpFMnigEptUcenaEptUceKlkEt erolkg3000 kg1 nigEpFMlkf5000erolkg kg1 .etIEpBuRTaFMmanbunanKITLRkam nig tUcbunanKITLRkam ?
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maRTIs nig edETrmINg CMBUk4 emeronTI1
tag xnig erogKaCaTmnEpBuRTatUc nig BuRTaFM(KitCa )y kg
tamsmtikmeKnRbB&n
=
350050y5000x3000
50yx
bnabBIedaRsayeKn kg5.12y;kg5.37x =
5-eKdwgfaplbUknbIcMnYnesInwg 20cMnYnTI1esInwgplbUkncMnYnTI nig TI ehIycMnYnTI esInwg dgcMnYnTI1.2 3 3 3
rkcMnYnnImYy@ ?tag erogKaCacMnYn TI1TI2TIz;y;x 3
tambMrabeKnRbB&n
=
=
x3z
zyx
20zyx
bnabBIedaRsayeKTTYn 30z,20y;10x = .6-brimaRtRtIekaNmYymanRbEvg . eKdwgfaRCugEdlEvgCagm18 eKesInwg 2dgRCugEdlxICageK . RCugmYyeTotCamFmnBVnnRCugEdlEvgCageK nig RCugxICageK .
rkRbEvgRCugnImYy@nRtIekaN ?tag aCaRCugxIbMput bCaRCugEvgbMput nig CaRCugTIbI.c tambMrab )1(18cba =
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maRTIs nig edETrmINg CMBUk4 emeronTI1
nig)2(a2b= )3(2
bac
=
eKnRbB&n
=
=
=
0c2ba
0ba218cba
bnabBIedaRsayeKTTYln m6c,m8b,m4a = .7-edaRsayRbB&nsmIkar
0yx3