Download pdf - פתרונות מועד דצמבר 2011

[1] "

0002-08-008-10002-08-008-1

moc.mudik.wwwmoc.mudik.www

1102

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03928272625242322212 02 91 81 7161514131 21 1101 9 8 7 6 5 4 3 2 1

2 1 4 2 3 1 1 3 2 1 2 1 4 2 1 4 2 1 2 2 2 1 2 3 4 4 4 1 2 1

. , " " *

. 1.

.)1(

., 2. .)2(

. , 3. .)1(

. 4. .)4(

. , 5. . :)1( . :)2( (. ) :)3( .)4(

[2] "

0002-08-008-10002-08-008-1


. , 6. . : )1( . :)2( . : )3( .)4(

. , 7.

. :)1( . :)2( . :)4( .)3(

. , 8.

. : )1( . : )3( . :)4( .)2(

. , 9.

.() :)2( . : )3( . : )4( .)1(

. , 01.

. :)1( . :)3( . :)4( .)2(

[3] "

0002-08-008-10002-08-008-1


... 11. )4(

(. "? )" .)2(

... 21. )2( , .)3(- )2( ...

,( " ? )" ....(, , ) )3( . , ,)2(

- , , )" )4(

"(.? .)2(

... 31. )" )3(

)2( (. " ? (. , " ? )"

.)1(

... 41. )" )4(

....(, , " ? .)2(

[4] "

0002-08-008-10002-08-008-1


. : .

. .

. - | - .

: . )2(- )1( 51. " :)1(

" " | : " , : | :

: " . : ". ,

, . . .

- -" :)2( : " "| : "

" " , | . .

" :)3( : ," " | : ,"

, : | , : " .

: ". . . , .

, .

.)4(

. )4(- )3( ,)2(- )1( 61. :

: " " :)1( : | : " "|

: " . : ".

. . .)1(

[5] "

0002-08-008-10002-08-008-1


: , 71. : ," " :)1(

. : | : ," : "

. . . | : ," " :)2(

. : : ," : "

, . .

.)2(

: . )4(- )2( ,)3(- )1( 81. , " :)1(

" | : ," : ,"

, : " . : | : ," ,

" " , . . .

, " :)3( "| : ,"

: ," , .

. . , " :)2(

"| : ," : ,"

, . . . ,

, .

.)4(

[6] "

0002-08-008-10002-08-008-1


: . )4(- )3( ,)2(- )1( 91." " :)1( , "| :

: | , : ," ,

: " . , . : ,"

. .)1(

" , " . 02. ,

, . ,

. , .)2(

. . 12. :

. . . .

, , . .

. : )1( ,

. . . ,

, : )2( , , . . , : )3( . . ,

, : )4( . . ,

.)1(

[7] "

0002-08-008-10002-08-008-1


. . 22. :

. , . . , .

:( )

: - , " , . : )1(

, . . , " . . , " "

" , . : )2( . , . , " - . , " " ,

. . , .)2(

. . 32.

: , .

: .

-. , ' . , '

, ( ) ', :

[8] "

0002-08-008-10002-08-008-1


. .)3(

, . 42.

. . -, : '

: . 1 : " " . : . 2 . : ' : -,

: : : )1( . : - .

. ' ". " , . " " '

, . ' . ,

. - : . : ' , , .

. . : , -

. : " " . : '

. . .

.)1(

[9] "

0002-08-008-10002-08-008-1


:

, : .

"( )" : ."( )"

. :

. . 52. : "01-7 .

, ... . ...".

.)1(

. . . 62. , -: )1(

, (7-4 ) . .

" , - : )2( . . (8-7 ) , "

, - :)3( . (. 11-01 )

, - :)4( . (. 8-7 " ) "

.)3(

." " , . 72. - ,

, ". "- , " " )4(- )3(, )1( . " "

)2( . , ". " ,

.)2(

[01] "

0002-08-008-10002-08-008-1


, . 82. ". "" " '

- , ' . ,

. - , .)4(

. . 92., " " " " :)1(

":62-52 . , ( ) . . ( )"

" ", - :)2( . . ,

" , - :)3( (. 72-62 " ) ,

. , , -: )4(

. ." " .)1(

. . 03. , : )1(

. . . , : )2(

. , :)3(

. . , . . :)4(

.)2(

[11] "

0002-08-008-10002-08-008-1


-

03928272625242322212 02 91 81 7161514131 21 1101 9 8 7 6 5 4 3 2 1

3 1 1 3 4 4 1 2 3 3 1 3 4 2 4 1 4 1 1 3 1 2 4 4 2 1 3 3 3 4

. , " " *

. 1.

.)4(

. 2. . )3(

.( , ) 3. .)3(

. , 4. .)3(

. , 5. . : )2(

. : )3( . : )4( .)1(

. , 6.

. : )1( . :)3( . : )4( .)2(

[21] "

0002-08-008-10002-08-008-1


. , 7. . ( ) : )1( . :)2( . :)3( .)4(

. , 8.

. : )1( . :)2( . : )3( .)4(

. , 9.

. : )1( . : )3( . : )4( .)2(

!"" , "" 01.

. . !" ": )2( .( , ) !" ": )3( . !" ": )4( .)1(

[31] "

0002-08-008-10002-08-008-1


... 11. )1(

)" )4( "(. ") (."?

.)3(

... 21. )1( , .)3(- )1( ...

, "( )" , , .

") )2( - (. " ?

.)1(

... 31. )" )4(

...(. , " ? .)1(

. .. 41. )4( , . )4(- )3( . ..

, " " ) , )3( . , (

...(., , ) , - , ,

)" )2( ."(?

.)4(

[41] "

0002-08-008-10002-08-008-1


. : .

. .

. - | - .

: , )4(- )2(, )1( 51.: ," : ")1(

: | " ". : " .

. , .

.)1(

. )3(- )2( ,)4(- )1( 61. :

: ,"' ' , : ")2( . : |

". : " . . . ,

: ,"' ' , : ")3( . . : |

". : " . . ,

: ,"' ' , : ")1( . : |

". : " . . . ,

. .)4(

[51] "

0002-08-008-10002-08-008-1


: . )4(- )3( ,)2(- )1( 71.: " , : ")1(

: | ". : " .

. , ( ) .

" , : ")2( : | :

: " . , ( ) ".

. . .)2(

. )4(- )2( ,)3(- )1( 81. :

: " : ")2( : | : " "|

. , : .

" " . .

| : " : ")4( : | : " "

. , .

". : " . .

.)4(

[61] "

0002-08-008-10002-08-008-1


: . )4(- )2( ,)1( 91. " | : " : ")1(

: | ..., : "..., " " .

. " ": . . .

"| : " : ")2( | ... , : ..." ,

" " . : : " .

, . " . .

"| : " : ")4( | . .., : ..." ,

" " . : : " .

, . " . .

. .)3(

[71] "

0002-08-008-10002-08-008-1


. . 02. : , : '

. , , : '

. , , , : '

. , , . :

. .)1(

. . 12. . : ,

: . . , :)1(

. , , :)2(

. . , : )3(

. . . , :)4(

. .)3(

[81] "

0002-08-008-10002-08-008-1


. . 22. ,

(. + : *) , ,

. : : : )1(

. . , , , : )2(

. . : )3(

, . : , . ,

. : )4(

. . .)3(

. 32.

: . , , . ) , ,

". : ", , 3 (. , 3 .

:

3

() /

!

2 ()

1 ()

[91] "

0002-08-008-10002-08-008-1


, 3 : 3 (. )

: ,

3

() /

!

2 ()

1 ()

. :

1 . - -" " 1 : )1( . ". " ,

1 . - -" " 1 : )2( . . ,

2 . - -" " 2 : )3( . ". " ,

2 . - - " 3 " 2 : )4( , 3 ,

. . .)2(

, . 42. .

: : ' : ' ( + : *)

[02] "

0002-08-008-10002-08-008-1


" "" " , - . : ',

. : -

. ( + *) . .)1(

:

, : .

:

. . " " :

" " :

.

%97 . 52. %97- : "7 . ." ,

%97 , .. : "3-1 , ,

". ... - .)4(

[12] "

0002-08-008-10002-08-008-1


. . 62. , - .

: "01 . , ": 31 .". ..

: 81-71 ". , ... ..". . "...

.)4(

" . 72. , 42 . "

) . (:

, "" , "" ;

; , , " "

: "... 72-52. , ,

". , . , ,

.)3(

. 82. , " " , ." "

. .

. :)1( : "...23-13 :)2(

". ...". : "...01 :)3( : "...11 :)4(

...". .)1(

[22] "

0002-08-008-10002-08-008-1


- ". " . 92. , " " ,

, . . ,

. - . )1(

. . 03. .

. , :)1(

. . . :)2(

. :)3(

, - . , , (. 92-82 ) ,

. , ... : " :)4(

(. 03-92 " ) .

.)3(

[32] "

0002-08-008-10002-08-008-1


-

5242322212 02 91 81 7161514131 21 1101 9 8 7 6 5 4 3 2 1

4 2 4 1 1 2 2 3 3 3 1 3 4 2 4 3 1 3 4 4 3 3 2 4 3

, " " * .

X . 1. - X .

x: 5

. . 2- 3-

3 x, 51 = X : (1) 5 . 2- 3. =

4 x, 02 = X : (2) 5 . 3- 4. =

6 x, 03 = X : (3) 5 , .3- 2- 6. =

. .)3(

, . 2. .

5 . 2 4 , 3 , :. 7 41 ,

4 4 2 1 2 1 41 3 4 5 1 1 1 1 1 5 2 7 3 .)4( .= = =

. 3. , ,

)DOC DA . OC - DOC . 051-

, . OD- . 51-

.51- , )CDA- , .)2(

A

C

B

D

O051

[42] "

0002-08-008-10002-08-008-1


1 B- A . 4.

. 9-BA

20B

. A - B ,

. 05- 2 5A . 5 B , 0 2 B . =2 A , 52 05 2-

.= = 3 2 5 A B .)3(

, . 5. : , 0 x . . +y x

y x y x 3 1 3 x31 1 x) ( ) ( 3 y x y x

.+ ++ = + = = =

.)3(

. 01 . 6. 6- . 6- , 7

07 ". 11 112 4 07 :6- .

3 6 6 .= =

.)4( . >0 y ,1 x . 7.

y , y

x1x

. =

X , Y .Yy: =2 x . Y

y21

2 . =

Y - , . .

.)4(

. 8. , .

, 801- .63 .)3(

801

[52] "

0002-08-008-10002-08-008-1


, . 9. . 5

. )3- -

. , (.

5 3

.

, 001 : .= 005 5 001:

005 , 3-3

.

: 005

35 0053 003 001

.= = .)1(

. 01. - . 61-

, () .

.)3(

5 3

, + 61

.

[62] "

0002-08-008-10002-08-008-1


. 11. . 8-0 + 61

, () - .

: . , 1791 : (1)

.0062 = 0043 0006 7791 : (2)

.0052 = 0003 0055 3791 : (3)

.0013 = 0043 0056 4791 : (4)

.0012 = 0043 0055

.)4(

1791

3791

47917791

[72] "

0002-08-008-10002-08-008-1


. 21. , 21

- . 31 21 , : . 31 ,

, 2791-1791 : (1) . .

21- 3791-2791 : (2) . . 31 ,

, 4791-3791 : (3) . .

, 5791-4791 : (4) .

.

.)2(

)2(

21-

31-

[82] "

0002-08-008-10002-08-008-1


. . 31. .

: "(1) ( ) , -"

. . . ,

" :(2) , - "

. ( ) . . ,

: "(3) , -"

. . .

: "(4) , 3 - "

- . . ()

. .)4(

. . 41.11

2 2 ,

. . :

11

2 1

2 1

[92] "

0002-08-008-10002-08-008-1


: -

11

2

2 1 113 3 12 2

1 = =

2 2 1 1 2 =

: 2

31 23 3 2 2 .

.)3(

, . 51.

. . :

, 2 . 1

, 2 . 2 , 4

, 1- . . 1- ( )

.1 : 1 .)1(

. 61. . , " "

C

D

A

B

E

1 + x

1 x

32

1 111

1C

B

A

[03] "

0002-08-008-10002-08-008-1


CD- BA . X ,)EBA- )CDE ,

. )CED- )BEA, . , . CDE- EBA

EA BA: CE CD

: - .=

5 x 3 x3 2 x2 1 x 3 1 x 2 1 x 2) ( ) ( 1 x 3

. += = + = + = .)3(

" " . .71 . ( ) 2-

. . ,

:". " , , = + + + +82 11 7 5 3 2: (1)

. ". " , , = + +01 5 3 2: (2)

. . ". " , , = +5 3 2: (3)

. .)3(

CBA . 81. , CB D .

A- A , . . DA CB

. , CB A

, (. ) (2)- (1) .

. , (BA = BA) .)3(

BC D

A

O

[13] "

0002-08-008-10002-08-008-1


. %08 - . 91., 04 %04 . . %52

. , .

. 061 , 002 : (2) , 04 08 , %04

. 04 (061) %52. 021 - . , . 021 + 04 = 061

.)2(

: , . 02. . =2 - ,

. , , ,

. r 2: '

063 .

(:r-- )'

2 2 2) (

r r4 r2 22 063 063 2 063

.= = .' ' . ,

.)2(

. , 12. . 2 . 6- 6

1 : 2

. ,

, .

, : 1 21

21 . =

rR

[23] "

0002-08-008-10002-08-008-1


. 11 , : 6 , 11 .

6: . 11

.

16 6 : 11 116 . =

111

2' ,

.' .)1(

Y- X . , - 22. - . < + > 05 y x ,03 y x: -

. - . 01 Y . + >y 03 x(: ) . + >04 x 01 03 x(: ) . < + >14 x 11 03 x(: ) . < + >53 x 5 03 x(: ) . <

[33] "

0002-08-008-10002-08-008-1


CBA . 32. DB- . (CA = BA) . )CBA

, .

, . -

: , 05 , 08 =

' . 52 = .)3(- )2(

, 08 , 02 = , ' . 04 =

.)1( .)4(

. . 42.

BC

BC A

E D

. EC BA , .

- . 2 = CA, 1 = BA. . = = + = +5 CB CB 2 1 CB CA BA2 2 2 2 2 2 :

5 1 5 : 2 2 , =

1 2 1 . 1- 2 . . =

.)2(

D

BC

A

2

[43] "

0002-08-008-10002-08-008-1


, 1- x- a - . 52. . xa - ax . a- x -

:

ax xa , ' =8 23 =9 32 = =3 x ,2 a

)3(- )2( , ' =23 25 =52 52 = =5 x ,2 a

)1(

.)4(

[53] "

0002-08-008-10002-08-008-1


-

5242322212 02 91 81 7161514131 21 1101 9 8 7 6 5 4 3 2 1

4 4 1 2 3 1 3 1 1 2 3 2 4 3 3 3 2 3 4 2 2 1 1 2 3

, " " * .

. 1.

. CA DB . CA . DB CA -

DB . , 09 , CA

DB . . , .

.)3( . , 2.

, 7- 024- 1 - 2- . 3- 2- 024- 1

: 7- . 6- 3- 7 . 7 ,... 53,82,12,41,7

06 024: , 024 7

06 = , . 7-

07 024: 6-6

. ' . = .)2(

A

BC

D

O

[63] "

0002-08-008-10002-08-008-1


, q- p . , 3. .1 , - . 1-

, . q, p1 1: .

2 2q p1 1 1: ' = =

4 2 2 . = =

, . ' . , 1-

.)1( 3 . , 4.

. 4 p- .

:m- p , m- p 4 m 3 p4 p m4

3 m 3 .= = =

. ' , .)1(

, 5.

. CBA . . 4

, , .

. , , 1-

3 ., 31 . 21 , 4

.1 31 . '

.)2(

A

C B

44

4

1 1 1 1

[73] "

0002-08-008-10002-08-008-1


. , 6. . 001- , CA- BA , CBA

. 04 a -

BC

A

C BA

001

081 . 081

. 04- a ,. , 081 CBA ,

a , CBA- -, . ( ) .)2( .04-

. .7

- . .

.= + + +7.0 2.0 0.0 5.0 0.0 : (1) .= + + +4.2 0.0 4.2 0.0 0.0 : (2) .= +1.1 1.1 0.0 : (3)

.= + + + + +9.4 8.1 6.2 0.0 0.0 5.1 0.0 : (4)

.)4(

[83] "

0002-08-008-10002-08-008-1


. .8 - .

001- . : ,. ,

. 722 : (1) . 001 : (2) . 232 : (3)

. 36 : (4)

.)3(

. .9 - . 001 - , 82

, . 001 - 81

. , , 32 = 5 82 : : (1) .61 = 2 81 001 - 001 - , 7 = 82 53 : : (2)

.207 = 81 027 , 53 = 82 36 : : (3) .7 = 81 52 001 -

[93] "

0002-08-008-10002-08-008-1


001 - , 43 = 82 26 : : (4) .03 = 81 84

, . 001-

.)2(

. .01 - .

.052 .

.)3(

[04] "

0002-08-008-10002-08-008-1


C- B, A 3 . 11. . )CBA ,

. , Y-

.081- )CBA .)3(

b- a. , 21. , b a2 . >b a ,

, - +b a , . . .-

:= =1 b,2 a . . . = + 6 2 2 12) (: (1) . . = +2 1 1 2) (: (2) . , - , = 2 1 22: (3) . .- = 1 1 2) (: (4) .)3(

, 01 - x2- %02 . 31. , , . 01- x-

:x 52 x 001 x4 01 01 01 x2x4 x04 02

01 001 001 . = = = = =

: a .

04 a 01 01 01 52a a52 a4 001 001

.= = = = .)4(

: . 41.4 2 4 2 4 42 2 2

18 9 9 3 9 9 = = =

.

.)2(

y

)0,0(x

)3,1(A

)0,1(B

)2,1(C

[14] "

0002-08-008-10002-08-008-1


21 . 51. . " 1- ,

, . ." 1

, (. )

3 ( 3 ) ( 2 ) .

. ( 1 )

. 5 . .)3(

. " 06 . 61.2

7 , '

. . ' . ' ',

2 7

. '

'

'

2 7

'

- '

- '

01 53 2 52 53 17 53 52 =

21 24 2 81 24 27 03 03 =

. , )2( .)2(

= +

2

1

3

[24] "

0002-08-008-10002-08-008-1


. . 71., 4 2 . 05 , 05

. . 021 , . .021- .

: , 08 , 02 : (2)

, = +041 06 08 . 06 , 03 , . . 021 "

, . , (1) .

, 04 , 01 : (1) . .= +021 08 04 . 08 , 04

.)1(

. , 81. E . a

DE EAa2

, a- , . = =

a - 2

, ) =09 AOF . . FA

R FOa.

2 AO , = =

, AEO .

2 2 2 2 2

AO AO AO AE EOa a a a a a2 2 2 22 2 4 4 2 2

. = = + = = + = +

:FOA FA 2 2 2 22

FA FA FA OF OAa3 a3 a a a a2 2 2 222 4 2 4 2

= = + = = + = +

.)1(

O

A

C B

D

F

aE2

a2

a2

[34] "

0002-08-008-10002-08-008-1


DCBA . 91. . " 5 FE ." 22

. DFEA . AD+ DF+FE +EA - . FD+EA = EB+ BA = EA , FD = EB AD- BA . " 11- .AD+DF + FE +61 = 5 + 11 = EA : .)3(

, $ . 02. : $ n . )5($

. =3 n $) ( ,=1 n + =1 1 n $ n $) ( ) (, >1 n . + = + =1 4 $ 1 1 5 $ 5 $) ( ) ( ) (: , =5 n

. , . =1 n -

+ = + + = +2 3 $ 1 1 1 4 $ 1 4 $) ( ) ( ) ( :=4 n 3 + )2($= 2 + 1 + )1-3($ = 2 + )3($ :=3 n + = + + = +4 1 $ 3 1 1 2 $ 3 2 $) ( ) ( ) ( :=2 n .= + = +7 4 3 4 1 $) ( , =3 n $) ( :=1 n

.)1(

4 . 12. . , . 01-

, . 01 = 04 = :. 01 - ,

. 1. : 1 ,

.= = + + +73 x 04 x 1 1 1 .)3(

4

A

C B

D

5 "

E

F

[44] "

0002-08-008-10002-08-008-1


, r . 22. .

, . , r2- . . 2 :1:1 - .

r2 r2 2 , .=

: -

3 33 3) (

2 2 2

2 r 2 ar2 .)2( .= = =r2 r r2 r h r

, - 001 . 32. - . .

. :

. 001 34 = 75 , 34 . 92 = 12 001 , 17 .75 + 92 = 68 , = + .)1(

, . 42.. .

, . )

. + =1 2 3 , + =6 5 11, + =6 6 21, + =1 1 2 : (. .

.)4(

2 . 52. +2 1

, . , . ""

2 1 . , , " " : -

) (

) () (2 2 2 2 2 2 2 1 2 22 1 2

2 1 2 1 2 1 2 1 2 11 2 1

+ + + = = = = =

.)4(

r2r2

[54] "

0002-08-008-10002-08-008-1


-

726252423222120291817161514131211101 9 8 7 6 5 4 3 2 1

3 3 4 1 4 2 2 4 1 4 2 3 1 3 2 2 4 1 3 1 1 2 3 3 1 4 2

, " " *

.

, , "lacisyhp"- latnem" 1.

. , , . - thguoht: )1( - htlaeh: )2( - nosaer: )3( - ydob: )4( "

". .)2(

. hguohtla 2. . syawla-, elbailer

. - ylralimis: )1( - yllautneve: )2( - ylgnisirprus: )3( - ylirassecen: )4( ." , " .)4(

- "noitcif", "segairram yppah ",( )" scinyc " 3. . ,

? - nommoc: )1( - luferac: )2( - erawa: )3( - evila: )4( ." " .)1(

[64] "

0002-08-008-10002-08-008-1


".dog"- "eguh", "eznorb" 4. . , ,

, - nigram: )1( - ecafrus: )2( - eutats: )3( - lairetam: )4( ." " .)3(

". sdnuos"" sthgis" 5. . .

, - egnahcxe: )1( - dnapxe: )2( - ecneirepxe: )3( - esucxe: )4( ." " .)3(

' ". tsegral"" aera" 6. . -

- yna dnoyeB: )1( - fo smret nI : )2( - fo daetsnI: )3( - fo desoppo sA: )4( ." ' ' " .)2(

. , noituloveR lairtsudnI" " 7., enihcam - "yrenihcam"- "esaercni"-

. ?

- deziretcarahc: )1( - desaeler: )2( - deretsam: )3( - detagitsevni: )4( ." " .)1(

[74] "

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, , ". deniater"-" daer", "enoyreve" 8. .

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." , .)1(

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." .)3(

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". ycneiciffe s'rekrow"- "seinapmoc" 11. ., -

- etaidar: )1( - nethgilne: )2( - esnaelc: )3( - tsoob: )4( - "

." .)4(

[84] "

0002-08-008-10002-08-008-1


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. )3(

[94] "

0002-08-008-10002-08-008-1


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[05] "

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. )2(

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.)2(

[15] "

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. )4(

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: , (. 7-6 ) "gniugirtni yllautcelletni ssel mees osla yam yehT"

". doirep laicurc a erew seirutnec ruof esoht teY: " .

. )1(

. 52. ,

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, 62.: . .

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.)3(

yreppils 72. . 32

".dne dna gniggeb tcaxe eht tuoba gnieergasid sralohcs htiw ,yreppils osla tub": ". "

.)3(

[25] "

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." .)3(

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- latnemiger: )1( , - citsimissep: )2( , - laivirt: )3( - cigetarts: )4( 7191 "

." .)4(

[35] "

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[45] "

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. "slamina"- "seitilauq ","tnempoleved" 8. .

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." , .)1(

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- gnicnuop: )1( - gnikaorc: )2( - gninruom: )3( - gnigdub: )4( ." " .)1(

[55] "

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[65] "

0002-08-008-10002-08-008-1


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[75] "

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".ylidaets sesaercni nemow fo htaed eht ,pord ot nigeb slevel negortse s'nemow taht emit .

.)3(

[85] "

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