İşaret ve sistemler - pamukkale Üniversitesi uygulamalar ve Örnek soru Çözümeri
TRANSCRIPT
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AAAB 8>8 XBPIFFAU \A XX^AMFAUQPOQFIMI 9
Nd. Nr. Iynb C@Z@FCIPIIri. Or. Inam C^A
9. ([AUPDNCFC va [AUPD^ EAFUFAMA)
Iini `iratfar`b par`ydn`c dfup dfminb eaf`rfay`b`z. Aar par`ydn`cf`c mavhut `sa tamaf par`ydnu afna
an`b`z.
9.9.x9(t) =jaj9;t
9.5.x5(t) = a(-9 +j)t
9.8.x8Sb] = aj?b
9.>.x>Sb] = 5hds(b/>) + s`b(b/7) 5hds(b/5 + /t9)
9.
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9.1.
sb9. tamaf par`ydnu fa par`ydn`cfat`r`fmactan`r. [ar`ydn`c irat` `z`b`z va eu `irat`b
drtifimi naar`b`, drtifimi ohb va atc`b naar`b` gasipfiybz.
5.5. Iyrc-zimibfxSb] n`z`s`ba f`c`b rbac naarfar`
xSb] = {9, 5, ;, 8, ?, .xSb + 5], xS5b9], xSb/5 + 9], xS8b/5 + 9] n`z`far`b` afna an`b`z.
zm:
5.9.
5.9.9.
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5.9.5. , x(t)
x(-t)
-x(-t)
x (t)
x (t)^
+
+
t
t
t
t
t
-5
-9 -;,1 ;,1 9 5
-9 -;,1 ;,1 9
-5 -9 -;,1 ;,1 9
-5 -9 -;,1 ;,1 9 5
-5 5
-9 9
9/8
5/8
-5/8
-9/8
9//8 - 5/8 t
i)
v(t) =x(t+5)
t-8 -9,1
9
v(-t) =x(-t+5)
t89,1
9
e)
v(t) =x(t+9)
t-5 -;,1
9
9
8 e`r`m
v(5t) =x(5t+9)
t-;,51-9
9
;,1
9,1 e`r`m
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h)
v(t) =x(t+>)
t-1 -8,1
9
-5
8 e`r`m
v(-8t/5) =x(-8t/5 + >)
t
9
?/8 9;/8>/8
5 e`r`m
n) , x(t)S(t+8/5)+(t-8/5)]
t-8/5 8/5
(9/8)
5.9.1.
t-9 ;,1 5
9
x (t)[
8 >,1 tamaf par`ydnu `fa par`ydn`cfat`r`fm` `irat`
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5.5. 5.5.9. 5.5.5. ,
5.5.8. b`b abarj`s`3
5.5.>.
i)
e)
(Nah`mit`dbXayraftma)
h)
(@btarpdfit`dbIrinaarfama) (yizfmisi ni dfur)
3 3
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n)
(yizfmisi ni dfur)
3
3
Xayraftma
3
3
8. (XX^AMFAU va XX^AM ZAFFCFAU)
8.9.X9, X5va X8`fa tibmf iyrc-zimibf s`stam efdcfir iinic` o`e` e`re`r`ba sar` (cis-cit) eifnrfir.
` =9, 5 va 8 ``bxSb] va ySb] gar e`r s`stam`b o`r` va cfirb ostarmac zara gar e`r s`stam ``b o`r`-c
`f`c`s` iinic` o`e` tibmfibmtr:
tacb
`ltbbxby
,;
],5/S]S
9
9:X
9
]5S>
9]9S
5
9]S]S
5555 bxbxbxby:X
5
]5S]S 88 bxby :X8
Eubi ora, cis-cit s`stam`b o`r`-c `f`c`s`b` (ySb] `faxSb] irisbnic` `f`c`) afna an`b`z. (N`ccit:x9Sb] =xSb]
va ySb] = y8Sb]n`r)
8.5.Efdc n`yiorim iinic`o`e` var`fab oar`-easfamaf` s`stamna b6 ; ``b ySb] = ; dfnuu e`f`bn``ba ora,
8.5.9.xSb] = Sb] o`r`` ``b s`stam c ySb]y` afna an`b`z.(X`stam`b e`r`m rbac havie)
8.5.5.xSb] = uSb] o`r`` ``b s`stam c ySb]y` afna an`b`z.(X`stam`b e`r`m eisimic havie)
8.8.O`r`-c f`c`far` iinic` o`e` var`fab s`stamfar`b zaff`cfar`b` eaf`rfay`b`z.
(X`stam zaff`cfar`3 (`) Ndrusif mnr4 (``) Zimibfi na`mayab m`n`r4 (```) Banabsaf m`n`r4 (`v) E@ED
Cirirf mnr4 (v) Gilzif mnr4)8.8.9.y(t) =x(t)hds;t
8.8.5. )9()( txnt
nty
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zm:
8.9.
X9: X5:
X8: , X9`b c X5b`b o`r`` dfnuubi oraX5b`bc
X8bo`r`` X8bc
ya tac vayi `lt siy ni var`fsa b`b bn`s` ni`mi `lt dfihictr.Eubi ora3
dfihictr.
X
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8.5.
(X`stam`b o`r`-c f`c`s`) e`fo`s`b` cuffibiric38.5.9. ``b
``b
; ;
``b
; 9
``b ``b ``b
Oabaffat`r`f`rsa3
afna an`f`r c` isfbni eu, s`stam`b `mpufs havie yib` s`stam`b zimib efoas`bnac` tibmbi
(ostar`m`ba) cir nar.
8.5.5. ``b
``b ; ;
``b ; 9
``b ``b ``b
(X`stam`b e`r`m eisimic havie)
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8.8.
8.8.9. (`) Ndrusiffc:
dfnuubnib ndrusifnr.
(``) Zimibfi na`mama:
4
dfnuubnib s`stam zimibfi na`abn`r.(```) Banabsaff`c:
X`stam`b d ibnic` c sinaha d ibnic` o`r`fara eif. D yznab s`stam banabsaf. Pib` o`r``b
oafahactac` naarfar`bnab eimsz.
(`v) E@ED Cirirffc:
o`r``b oabf`` `fa sbrf
9
D yznab s`stam E@ED cirirfnr.
(v) Gilziffc:
X`stam sinaha ibfc o`r` naarfar`ba eifnr. D yznab GIL@ZIF@ na`fn`r.
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8.8.5. (`) Ndrusiffc:
dfnuubnib s`stam NDUQXIFnr.
(``) Zimibfi na`mazf`c:
4
dfnuubnib s`stam ZIMIBFI NAMAPABn`r.
(```) Banabsaff`c:
X`stam oam`tac` o`r` naarfar`ba eif. Oafahactac` o`r` naarfar`ba eif na`f. D yznab
BANABXAFn`r.
(`v) E@ED Cirirffc:
o`e` sbrf oabf`cf` e`r o`r`` afa ififm. Pib`
``b
,
``b nr.Eu nurumni c na sdbsuz oabf`cf` dfur c` s`stam
CIUIUX@Znr.
(v) Gilziffc:
Oah`cmanab ndfiy GIL@ZIF@nr.
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8>8 5
. . . .
9. ( )
9.9.
tj^tjatyatx
85)()( ==
85 )()( ==
.
9.9.9. 9() = (5) 9() 4
9.9.5. 5() = 5()
5() 4
9.5.O F@
.
9.5.9. 9);()(
,9);(..),()5(7)(>)( )9(
;5
5
====+=
9.5.5. 9);()(
,;);(..),()(1)(5)(
5)( )9(
;5
5
====++=
9.5.8. ;);()(
9);()(
,5);(..),(5)(
5)()( )5(
;5
5)9(
;5
5
8
8
=====+===
9.8. I = ;
. 6 ; () = ;. E ,
9.8.9.(;) = 4
9.8.5. ; () = ; () = ()
() = 4
9.9. = = = = = =
9.9.9. = hds5 = = = +
= hds8 .
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9.9.5. = hds 5 = hds5 9= = ..
= +
= = hds8 9
9.5.9. + > = 7 s`b5 , ;
+ > = ; C.N.
+ > = ; = 5 , = 5
= hds 5 + s`b5 = hds 5 + s`b 5
= hds 5 + s`b 5 + 5s`b5 +5hds5 = > s`b 5 + > hds5 + >hds5 >s`b5
N 3
> s`b5 + >hds 5 + >hds5 >s`b5 + > 5 + 5= 7 s`b 5 > = 7 = 5 = 5 5 > = ; = ; = +
= hds 5 + s`b5 5hds5 = 5 s`b 5 + 5 hds 5 5 hds5 + > s`b 5
E.C. ;= = 9 = 5 5 = 9 = = hds5 + s`b5 5 hds5 , ;
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9.5.5. + 5 + 5 = 1 hds , ;
E :
G :
+ 5
+ 5 = ;
C.N. + 5 + 5 = ; = 9 , = 9 + = hds + s`b :
= hds + s`b+ s`b + hds;= = ; = + = 9 = 9 O : = s`b
,
.
= hds + s`b
= s`b + hds
= hds s`b N 3
hds s`b 5 s`b + 5 hds + 5 hds + 5 s`b = 1hds + 5 hds + 5 s`b = 1hds
1 ;
= 9 , = 5
= hds + 5 s`b O : = + = hds + s`b+ hds + 5 s`b O .
= hds + s`b + s`b + hds s`b + 5 hds E.C. ;= + 9 = ; = 9 = + + 5 = ; = 8 . , 3
= hds + 8 s`b + hds + 5 s`b
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.
= + = s`b hds 8 s`b + hds + 5 s`b = 5 s`b hds + hds + 5 s`b
= 9 hds + 5 s`b , ;
.
9.5.8. 5 = 5 + , ;
5 = ; (G )
C.N. 5 = ; 5 = ; = ; , = 5 , = 9
= + +
= 9 = ; = + +
= + + + = + 5 +
= + 5
= 5
+
+ 5
= = 8 N 3
8 + 5 5 5 + 5 > 5 = 5 + 8 > 5 5 = 5 +
8 = 5 =
> = 9 = = + 5 5 = ; =
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= + = + + + + = 5 + +
= >
+
+
E.C. ;= + + = 5
= 5 + + = 5 + = 9 9 9 9; 5 9; > 9
= 558/9599/<
= > + = > + = ;
= 9/79/?59?/0
= + + + , ;9.8.9. 6 ; 3
= + = +
I 6 ; . E3= = 9 + ,
= = = + , . C , = ; ( ) . 3
;= ;= + , 9.8.5. ; . E 3
+ = .
9 5
H 9+
9 5
H
()
9+
()() H
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= ; + = ; + = ; = /
E.C. ;= = = / (C )
=
= 9 ; 3
+ = 9 + 9 = 9 = / = = = 9 = / + 9 E.C.
;= + 9 = =
= 9 / (C )5. ( )
5.9.I F@
55
99
5
85 +=++++
. 9 = >/8 5 = 9/8 ,
5.9.9. = .
5.9.5. = (;.1) .
5.9.8. () .
5.5.E F@
9 = 9 5 = 9 .
5.5.9. .
5.5.5. ( ) .
5.5.8. .
5.9. + 5 + + 9 + = + 5 5 3
+ 9 +
5= 5
.
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5.9.9. = 3 + 85 9+ 95 5= 5
:
.
= ;3
; + 9 + 5= ; 5
;=
9 ; = 93 9 + ; + 9= 9 9 9=
9 ; 5 3
+85 9 +
95 5= ;
C.N. + + = ; + 9 + = ; = 9 , =
= 9 + .
= 9
+
E.C. ;= + = = 8 , = 9= = = 8 9 + , 5 3
= 9 8 , = 5> 8 , = 9 ?
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. + 9 + 5= 5 = 9 + E.C. y9= C 5C =
C = 8 , C =
y5= C + >C = = 8 9 + , ; . N (F@) 5 , .
+ 85 9 + 95 5= : = + + = 9 = O : = + = 9 + + E :E.C. y9= C 5C + = ; C = 9 , C = y5= C + >C + = ; E
3
= 9 98 95 + 98 5 , F@ 3
= 9 98 95 + 98 5
. E 5 3
= = 9 98 95 + 98 9 >8 95 + 98 5.
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= + = 89 + + 9 + 9 + 5
= 59 +
+ 9
+ 5
. E , .
;= 5 + + = 9= 5 + = 5= 5 + + 9 + =
5.9.5.
=
+ 9+ 5= > 5
+ 9 + 5= ; E 5.9.5 . 3
= 8 9 + 1
< 9
5
.
= , = .E ; 3 + 9+ 5= + 9 + 5 = 8 +8 +5 > = = 9 = 9 = O 3 = 9 + , ; E.C. y9= C 5C 5 = ;
C = > , C = 8
y5= C + >C + 7 = ;
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E = 3= > 9 8 95
95
= 5 , F@ 3= 5= > 9 8 95 5 95 5
= >9 > > 5. , 3
= = > 9 8 95 95
>9 > 95
> 95
5
= + = 9 + 98 9 + 9 95 5
5.9.8. A , F@
CIBDBC OAACFAMA .
]Sbx ]Sby
5
8
5
9 9
]S]}S{s cbybyc
=
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5.5.
]Sbx ]Sby
5
9
>
9
]Sbl
5.5.9. = = =
= 9
= s= 3
+ 9> 5= 95 9.
5.5.5. = . E = . + 9> 5= 95 9 .
= ; 3 ; + 5= ; 9 ;= 9 ; 9 ;
= 9 3
9 + 9= 9
; 9=
; ; 9 5 . 3 + 9> 5= ; , 5
C.N. + = ; = = / , = = /G :
=
hds
+
s`b
: .
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O : = hds + s`b E.C. ;= = 9
9= = = 9
= 95
hds 5 s`b 5 5.5.8. .
+ 5= 9
G : +
5= ; C.N. + = ; = = / , = = /= hds + s`b E .
9= = 9 =
5=
= 9
=
= hds + s`b , F@ , = 9 .
= 3 = N 3
+ = 9 = = hds + s`b + = . 39= + = ; = 5= + = ; = = hds + s`b +
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= 9 F@ 3= 9= hds 9 + s`b 9+ 9
= s`b hds + 9
= s`b hds + 9 3
= = hds + s`b + s`b hds + 9
. E 3
= + = hds + s`b + s`b hds + 9
.
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8>8 8
. . . .
9. ()
.
9.9.= 5 , = 58 = =4 9.5.
t-9 9
9
;
a-ta
t
g(t)
t9;
x(t)
8
-9
5
= =4 9.8.
b-9 9;
xSb]
b1 ?
55
9
-9
5 >8
9
;
-5
9
5
9
= =4 9.>. = 9 , = = =4 :9.9.
= = = 9>
+
= 9 + .
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8 + ; 8 + = 9 , 8 . = 5 , 5 1 .
= 5 97
, 1 .
6 1,
= >
9
8 + = 9.
= 5
9
8 + = 9 . = 5 6 1 8 + = 9 .
= 5 97
, 6 1 .
= 5 97
, 1
5 97 , 6 1 ,
1 = 5 = . . 6 1 = 5 = 5. .,
= 5
. 91 . 7? , 1
.
9.5.
9 .= ; .
= 5 = 5 = 5 9 ;
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-9
9
;
a-a
x() g(t-)
t
t-8 t-9
9
-9
5
-9
9
;
a-a
x() g(t-)
t
t-8 t-9
9
-9
5
5
-9
9
;
a-a
x() g(t-)
t
t-8 t-9
9
-9
5
5 8
-9
9
;
a-a
x() g(t-)
t
t-8 t-9
9
-9
5
5 8 >
-9
9
;
a-a
x() g(t-)
t
t-8 t-9
9
-9
5
5 8 > 1
= 9. + 5. + 5. = + = + + +
= + + >
; 9
= 9. + 9.
+ .
= +
= 9 +
+
9
+
= +
9
= 9. + 9.
= +
= 9 +
+
9
= + +
= 9. =
=
>
> .= ; .
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=; 9 9 ; + + > ; 9 + 9 + +
>; >
.
9.8.= 5, 9,9, ;, ;, 5 , = ;,5,9, ;, ;, 5, 9 , = =4 > 9 ; 9 9 9 ; ; ; 9 > 1 ; 9 ; ; 9 > 9 ; 9 > 1
; > ; ; > ; 9 ; ; 9
; 9 ; ; 9; ; ; ; ; ; ;
; ; ; ; ; ; ;; > ; ; > ; > ; 9 > ; 9 9 ; > = > ; 9 > ; 9 9 ; >
9.>.
= = = 9
= 9
= 9= 9 9= 9 9 9
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5. ( )
,
. .
= + 9> 5: = = + 9> 5
/: 5 . : 6 ; = ; 5= ; . 6 ; = ;
.
: .
6 + 9> 5
= 9 + 9> . 9 = 1>6 .
: = .
+9> 5 =
+ 9> 5 = + 9> 5= = . = ;. = ;. , .
= ;.
6 ;
= ;
.
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= ;
= ; ; + 5= ; ;= 9 = 9 9= ; = 5 5= = 8 8= ; = > >= = 1 1= ; =
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8>8 >
. . . .
9. ( () )
9.9.() () L .
() = >. L
. C () .
9 () = 5(+ 9) 5( 9) ,
=
=+=
5
5)9(5)9(5
>
9 559
9
5
==
5)()(
,...5,9,5
5
5
9=
=
=
() . E ! ,;= ;.
() L :
=
=
==
555
)(
() = 8 ; = 5/8. O , () L
,
=
=
==
85
8
>
8
5
5
5
55
8
9 85
8
5
9
9
8
5
() L :
=
=
==
8
5
8
5
8
5
8
>)(
9.5.() () 56 6 5 .
() = > ;= /5 ,
>>55 ; 6666
5
5;
==
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;;;; ;,;; ===
;99
;999 ;,/53;,/5/5 =====
;55
;555 ;,;3;,;; =====
;88
;888 97;,8/5397;,8/58/5 =====
() = 8 ;= 5/8 ,
8855 ; 6666
;;;; ;,8/>8/> ===
;99
;999 ;,/?8.93;,/?8.9/?8.9 =====
;55
;555 97;,/7
58
55
59
5;
5=+++++== =
,9>
9)(
>
9 8
9
8
9
5
===
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,()
89.08%9
0889.;==
. , .
() ,
,8
7>
8
9)(
8
9 9
9
5
9
5
===
;88
;888 ;,;3;,;; =====
;>>
;>>> ;,/>88.;3;,/>88.;/>88.; =====
;11
;111 97;,/8>.;397;,/8>.;/8>.; =====
() ,
,1071.55 1
1
51
5>
58
55
59
5;
5=+++++== =
, ()
>1.0?%8/7
1071.5==
. , ()
.
9.>.() () () ()
.
() ,
-
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,...5,9,8
5
59(55)( 8
9==
+9 1 > ;)( =
5. ( () )
5.9. L .
= >.
9>
9
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95
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58
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9 L )9(5
93;)39(
5
93; 859; +====
= 5.
5959
59 9
;
=
== 3 = ;, 9
9 L 5
83
5
99; ==
9 ()
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5.5. .
L .
;8
;9 >1
885>1
99;5
53;3
5
53; ======
5
83
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9 9
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L
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58
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;
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;
5 ,1.5,9
5.>. =* L .
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;
=== =
;885599;;;8
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;
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;98;5995;558
;
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;;895598;88
8
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, = ; . I ,
==
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. I ; = 5/>
. E
. . I .
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5(5
83;3
5
98;59; ======
. E(= ;, 9, 5, 8)
;>3;>3;>3;> 888555999;;; ========
.
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==
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>5>585>55>895>5>
59>8559>5559>9559>5
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,
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.
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.
==
. N
5.> /5 . , = >
)39(1.;3;)39(1.;3; 859; +==== ;31.93;31.; 859; ====
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:
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+=+++== = 1.;5885;99;8
; 99
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=+++== = 1.;;895598;8
; 88
L
+=++=+++==
= ;555
8
855
9;
8
;
5 >8>0.
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. E , 9 = ;, 9, 5, 8
.
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( ) 5>8>0.88818
9>8>0.5>815
5>8>0.91819
9>8>0.
.
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5>85>55>95>
++
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= ;, 9, 5, 8 . E
: