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8/14/2019 [email protected]

1/19

Mogo|oyao`og~ENvgj'kg

Mos~kfbv


2/19


Mos~kfbv

O Mos~kq !Mos~kfbv-

Ujr~oj + kv o~bfsog`rjo~o~~og`bmbgs hlgrmnb~v bgfjhvbc kgn~ofdbsv'

Bofa grmnb~ kgvkcb sabmos~kq kv fojjbc ogbjbmbgs

O mos~kq kv ~blb~~bc shn{ o fouksoj jbssb~

O=

Bqomujb O fhmuog{ mogrlofsr~bv

vhlov ogc faok~v kgsa~bb mhcbjv O*N*F' Sabfhmuog{ mogrlofsr~bv?5 mhcbj O vhlov* ?>mhcbj N vhlov * 2 mhcbj

F vhlov* ?2 mhcbj Ofaok~v* >5 mhcbj Nfaok~v* 1 mhcbj F faok~vkg Or`rvs'

Ahp sh h~`ogkvb 8

Vhlov ?5mhc-O ?>mhc-N 2mhc F

Faok~v ?2 mhc-O >5 mhc-N1 mhc F

M=

^ h pv

F h jr m gv


3/19


Mos~kfbv - _rky

Paos kv sab h~cb~ hl sablhjjhpkg` mos~kfbv8

?' >n{ >

>' 6 n{ 6

6' ? n{ 6

3' 3 n{ ?

^hp mos~kq Mos~kq ao|kg` hgb

~hp

Fhjrmg mos~kq Mos~kq ao|kg` hgb

Fhjrmg

Broj mos~kfbv?'Mos~kfbv vahrjc ao|b vomb

h~cb~ Ogc

>'Fh~~bvuhgckg` uok~v hlbjbmbgsv vahrjc nb broj


4/19


Occkskhg hl Mos~kfbv

^rjb

Hgj{ mos~kfbv pksavomb h~cb~ fog

nb occbc h~vrns~ofsbc

Bqomujb

O = N= Lkgc sab vrm hl O

,N

O$N =


5/19


Vrns~ofskhg hl Mos~kfbv

^rjb

Hgj{ mos~kfbv pksavomb h~cb~ fog

nb occbc h~vrns~ofsbc

Bqomujb

O = N= Vrns~ofs O l~hm N

O-N =


6/19


Occkskhg , Vrns~ofskhg hlMos~kfbv- _rky

Bqomujb

O = N=

Lkgc sab vrm hl O,N

Bqomujb

O = N=

Vrns~ofs O l~hm N

Hgj{ mos~kfbv pksavomb h~cb~ fognb occbc h~

vrns~ofsbc


7/19


Mrjskujkfoskhg hl Mos~kfbv

Bqomujb

O = N= Lkgc sab u~hcrfs hl

O ,N

Vsbu-? 9\b~kl{ gh' hlfhjrmgv hl O , ~hpv hl N

Fhjrmgv hl O = 6 ^hpv hl N=6

Vsbu-> 9 Mrjskuj{ bjbmbgsvhl lk~vs ~hp hl O ogc sabfh~~bvuhgckg` bjbmbgsv hlsab lk~vs fhjrmg hl N ogcocc

9r jb r m n b ~ h l F h jr m g v h l O va h r jc n b b q r

Vsbu-6 9 Mrjskuj{ bjbmbgsvhl lk~vs ~hp hl O ogc sabfh~~bvuhgckg` bjbmbgsv hlsab vbfhgc fhjrmg hl Nogc occ

Vsbu-3 9 Mrjskuj{ bjbmbgsv hlVbfhgc ~hp hl O ogc sabfh~~bvuhgckg` bjbmbgsv hl sablk~vs fhjrmg hl N ogc occ

ab ~bvrjs mos~k pkjj ao|b ov mog{ ~hpv ov O ogc ov mog{ fhjr

! ) + $ ! ) + $ ! ) + => 1 6 > 2 230

=

! ) + $ ! ) + $ ! )- + => < 6 1 2 >>q> N kv >q3

~cb~ hlON>Q3

rvs Mosfa


10/19


Mos~kq Mrjskujkfoskhg- _rky

Pakfa hl sablhjjhpkg`mos~kfbv fog nbmrjskujkbc

O kv >q> N kv >q> O kv 6q> N kv >q6

O kv 3q2 N kv 2q>

O kv 0q6 N kv >q0 O kv 3q> N kv 6q3

O kv 36>q>6? N kv>6?q3

Paos kv sab h~cb~ hl sab~bvrjsogs mos~kq hlsab lhjjhpkg`mrjskujkfoskhg

O kv 3q> N kv >q3 OqN = 3q3 mos~kq O kv 2q2 N kv >q2 OqN = ghs uhvvknjb

O kv 6q0 N kv 0q3 OqN = 6q3 mos~kq

O kv ;q1 N kv 1q3 OqN = ;q3 mos~kq

O kv 155q ;;; N kv ;;;q3

OqN = 155q3 mos~kq

9rjb rmnb~ hl Fhjrmgv hl O vahrjc nb bqrojab ~bvrjs mos~k pkjj ao|b ov mog{ ~hpv ov O ogc ov mog{ fhjr


11/19


Kg|b~vb hl o Mos~kq?'Cbsb~mkgogs hl o

Mos~kqCbsb~mkgogs hl o mos~kq O kv

p~kssbg ov zOz

Cbsb~mkgogs hl >q>mos~kq

Cbsb~mkgogs hl 6q6

mos~kq

= =O z= ) )O z o ? ? o > > o ? > o > ?

= =O z

=O z o?? - o?>$' bsb~mkgogs hl sabMos~k' kgh~ hl sab Mos~k' hlofsh~ hl sabMos~k' ~ogvuhvb hl sab

gj{ vqro~b mos~kfbv fog ao|

o?6


12/19


q -Bqb~fkvb

Lkgc sab Cbsb~mkgogs

hl mos~kq O 9

Ckllb~bgfb Nbspbbg

Mos~kq ,Cbsb~mkgogs9

?'Mos~kq kv ghs ojpo{vvro~b'

Cbsb~mkgogs kvojpo{v vro~b'

>'Cbsb~mkgogs kvbgfjhvbcnbspbbg sphuo~ojjbj jkgbv

6'Cbsb~mkgogs fog nb

~bcrfbc sh o


13/19


Kg|b~vb hl o Mos~kq

>'Mkgh~ hl o

Mos~kq O mkgh~ hl og bjbmbgs oki

kv cbghsbc n{ Mki kv ovrn-

cbsb~mkgogs hlojj bjbmbgsv Ohnsokgbc n{ bjbmkgoskg`

ksa ~hp ogc isa fhjrmg'

6'Fhlofsh~ hl o

Mos~kq Fhlofsh~ kv o mkgh~ pksa

vk`g

Ks kv p~kssbg ov Fki = !-?+k$i Mki

F?? = !-?+?$? M??

= !-?+>M??

=

F?> = !-?+?$> M?>

= !-?+6

M?>

??=

==

?>=

' bsb~mkgogs hl sab Mos~k' kgh~ hl sab Mos~k' hlofsh~ hl sab Mos~k'S~ogvbuhvb' cihkgs hl sab Mos~k

k`gMos~k


14/19


3' S~ogvuhvb hl sab

Mos~kqS~ogvuhvb hl o mos~kq O kvcbghsbc n{ OS

OS =

=


15/19


2'Ocihkgs hl o

Mos~kq O mos~kq hnsokgbc n{

~bujofkg` ksv bjbmbgsvpksa sabk~ fh~~bvuhgckg`fhlofsh~v ogc saog

sodkg` s~ogvuhvb kvfojjbc Ocihkgs mos~kq'Ghsbc ov Oci'!OS+

Vsbu->9 VrnvsksrsbFhlofsh~v kg O ogcs~ogvuhvb ks'

Oci'!O+ =Oci'!OS+ =

g|b~vb h oMos~kq

' bsb~mkgogs hl sab Mos~k' kgh~ hl sab Mos~k' hlofsh~ hl sab Mos~k' ~ogvuhvb hl o mos~k' cihkgs hl sab Mos~k

= - 9sbu ? Lkgc sabhlofsh~v hl O

=Fhlofsh~ hl > !- +? $? > ) Mkgh~ hl >

=Fhlofsh~ hl 1 !- +? $? ? )=Fhlofsh~ hl 1 3

=Fhlofsh~ hl > - ) Mkgh~ hl 3

3


16/19


Kg|b~vb hl o mos~kq

O kv O-?

= OciOS

O-? = ?(>5

g|b~vb h oMos~kq

zO z=

Bomujb

=Oz - =6> ?> >5- 9sbu ? Lkgc sabbsb~mkgogs hl O- 9sbu > Lkgc sabhlofsh~v hl O - 9sbu 2 Ouuj{ lh~mrjoh~ Kg|b~vb

- 9sbu 3 Lkgc sab!cihkgs OS+

=Fhlofsh~ hl > !- +? $? > ) Mkgh~ hl >

=Fhlofsh~ hl 1 !- +? $? ? )=Fhlofsh~ hl 1 3

=Fhlofsh~ hl >

- ) Mkgh~ hl 3

3


17/19


Mos~kq-Ouujkfoskhgv

OQ= N O-?!OQ+ = O-?N

!O-?O+Q = O-?N

KQ= O-?

N

Q= O-?N

OO-? = K

Kgurs-Hrsurs Mos~kq

U~hcrfskhg Mos~kq

Cbmogc Mos~kq


18/19


Mos~kq-Ouujkfoskhgv

?' Vruuhvb o vkmujklkbc bfhghm{ kg|hj|bv irvs 6fhmmhckskbv9 o`~kfrjsr~b * mogrlofsr~kg` *s~ogvuh~soskhg' U~hcrfskhg hl ?(> rgks hl o`~kfrjsr~b~brk~bv > rgksv hl mogrlofsr~kg`* ?(3 rgks hls~ogvuh~soskhg' U~hcrfskhg hl ? rgks hl

mogrlofsr~kg` ~brk~bv rgksv hl o`~kfrjsr~b ogc rgksv hl s~ogvuh~soskhg' U~hcrfskhg hl ? rgks hls~ogvuh~soskhg ~brk~bv ?(6 rgksv hl o`~kfrjsr~b ogc rgksv hl mogrlofsr~kg`' P~ksb sab kgurs-hrsursmos~kq hl sakv bfhghm{'


19/19


Kcbgsks{ Mos~kq

K =

K =

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