Deprecated: Function set magic quotes runtime() is deprecated in /hosting/www/data/community/wiki/wakka php

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'8A;> B0:8E 7=0:>2 2 ?>78F8>==>9 A8AB5<5 AG8A;5=8O =07K205BAO >A=>20=85< A8AB5<K AG8A;5=8O. 865 ?@82545=0 B01;.1, A>45@60I0O =08<5=>20=8O =5:>B>@KE ?>78F8>==KE A8AB5< AG8A;5=8O 8 ?5@5G5=L 7=0:>2 (F8D@), 87 :>B>@KE >1@07CNBAO 2 =8E G8A;0. "01;8F0 1. 5:>B>@K5 A8AB5<K AG8A;5=8O A=>20=85!8AB5<0 AG8A;5=8O=0:822>8G=0O0,13"@>8G=0O0,1.24'5B25@B8G=0O0,1,2,35OB8@8G=0O0,1,2,3,48>AL<8@8G=0O0,1,2,3,4,5,6,7105AOB8G=0O0,1,2,3,4,5,6,7,8,91225=04F0B8@8G=0O0,1,2,3,4,5,1,7,8,9,,16(5AB=04F0B8@8G=0O0,1,2,3,4,5,6,7,8,9,A.B,D,E,F  ?>78F8>==>9 A8AB5<5 AG8A;5=8O G8A;> <>65B 1KBL ?@54AB02;5=> 2 2845 AC<<K ?@>872545=89 :>MDD8F85=B>2 =0 AB5?5=8 >A=>20=8O A8AB5<K AG8A;5=8O: AnAn-1An-2 & A1,A0,A-1,A-2 = nn + An-1Bn-1 + ... + A1B1 + 00 + A-1B-1 + -2-2 + ... (7=0: ﾫB>G:0ﾻ >B45;O5B F5;CN G0ABL G8A;0 >B 4@>1=>9; 7=0: ﾫ72574>G:0ﾻ 745AL 8 =865 8A?>;L7C5BAO 4;O >1>7=0G5=8O >?5@0F88 C<=>65=8O). "0:8< >1@07><, 7=0G5=85 :064>3> 7=0:0 2 G8A;5 7028A8B >B ?>78F88, :>B>@CN 70=8<05B 7=0: 2 70?8A8 G8A;0. <5==> ?>MB><C B0:85 A8AB5<K AG8A;5=8O =07K20NB ?>78F8>==K<8. @8<5@K (45AOB8G=K9 8=45:A 2=87C C:07K205B >A=>20=85 A8AB5<K AG8A;5=8O): 23,43(10) = 2*101 + *10ﾰ + 4*10-1 + *10-2 (2 40==>< ?@8<5@5 7=0: ﾫﾻ 2 >4=>< A;CG05 >7=0G05B G8A;> 548=8F, 0 2 4@C3>< - G8A;> A>BKE 4>;59 548=8FK); 692(10) = 6* 102 + 9*101 + 2. (ﾫ(5ABLA>B 452O=>AB> 420ﾻ A D>@<0;L=>9 B>G:8 7@5=8O ?@54AB02;O5BAO 2 2845 ﾫH5ABL C<=>68BL =0 45AOBL 2 AB5?5=8 420, ?;NA 452OBL C<=>68BL =0 45AOBL 2 AB5?5=8 >48=, ?;NA 420ﾻ). 1101(2)= 1*23 + 1*22+0*21+ 1*2ﾰ; 112(3) = l*32+ 1*31 +2*3ﾰ; 341,5(8) =3*82+ 4*81 +1*8ﾰ +5*8-1; A1F4(16) = A*162 + 1*161 + F*16ﾰ + 4*16-1. @8 @01>B5 A :><?LNB5@0<8 ?@8E>48BAO ?0@0;;5;L=> 8A?>;L7>20BL =5A:>;L:> ?>78F8>==KE A8AB5< AG8A;5=8O (G0I5 2A53> 42>8G=CN, 45AOB8G=CN 8 H5AB=04F0B8@8G=CN), ?>MB><C 1>;LH>5 ?@0:B8G5A:>5 7=0G5=85 8<5NB ?@>F54C@K ?5@52>40 G8A5; 87 >4=>9 A8AB5<K AG8A;5=8O 2 4@C3CN. 0<5B8<, GB> 2> 2A5E ?@82545==KE 2KH5 ?@8<5@0E @57C;LB0B O2;O5BAO 45AOB8G=K< G8A;><, 8, B0:8< >1@07><, A?>A>1 ?5@52>40 G8A5; 87 ;N1>9 ?>78F8>==>9 A8AB5<K AG8A;5=8O 2 45AOB8G=CN C65 ?@>45<>=AB@8@>20=. 'B>1K ?5@525AB8 F5;CN G0ABL G8A;0 87 45AOB8G=>9 A8AB5<K 2 A8AB5<C A >A=>20=85< , =5>1E>48<> @0745;8BL 55 =0 . AB0B>: 40AB <;04H89 @07@O4 G8A;0. >;CG5==>5 ?@8 MB>< G0AB=>5 =5>1E>48<> 2=>2L @0745;8BL =0  - >AB0B>: 40AB A;54CNI89 @07@O4 G8A;0 8 B.4. ;O ?5@52>40 4@>1=>9 G0AB8 55 =5>1E>48<> C<=>68BL =0 . &5;0O G0ABL ?>;CG5==>3> ?@>872545=8O 1C45B ?5@2K< (?>A;5 70?OB>9, >B45;ONI59 F5;CN G0ABL >B 4@>1=>9) 7=0:><. @>1=CN 65 G0ABL ?@>872545=8O =5>1E>48<> 2=>2L C<=>68BL =0 . &5;0O G0ABL ?>;CG5==>3> G8A;0 1C45B A;54CNI8< 7=0:>< 8 B.4. B<5B8<, GB> :@><5 @0AA<>B@5==KE 2KH5 ?>78F8>==KE A8AB5< AG8A;5=8O ACI5AB2CNB B0:85, 2 :>B>@KE 7=0G5=85 7=0:0 =5 7028A8B >B B>3> <5AB0, :>B>@>5 >= 70=8<05B 2 G8A;5. "0:85 A8AB5<K AG8A;5=8O =07K20NBAO =5?>78F8>==K<8. 081>;55 8725AB=K< ?@8<5@>< =5?>78F8>==>9 A8AB5<K O2;O5BAO @8<A:0O.  MB>9 A8AB5<5 8A?>;L7C5BAO 7 7=0:>2 (I, V, X, L, !, D, ), :>B>@K5 A>>B25BAB2CNB A;54CNI8< 25;8G8=0<: 1(1) V(5) X(10) L(50) ! (100) D(500) M(1000) @8<5@K: III (B@8), LIX (?OBL45AOB 452OBL), DLV (?OBLA>B ?OBL45AOB ?OBL). 54>AB0B:>< =5?>78F8>==KE A8AB5<, 87-70 :>B>@KE >=8 ?@54AB02;ONB ;8HL 8AB>@8G5A:89 8=B5@5A, O2;O5BAO >BACBAB285 D>@<0;L=KE ?@028; 70?8A8 G8A5; 8, A>>B25BAB25==>, 0@8D<5B8G5A:8E 459AB289 =04 =8<8 (E>BO ?> B@048F88 @8<A:8<8 G8A;0<8 G0AB> ?>;L7CNBAO ?@8 =C<5@0F88 3;02 2 :=830E, 25:>2 2 8AB>@88 8 4@.). 2. '/ !!" !'!/ A>10O 7=0G8<>ABL 42>8G=>9 A8AB5<K AG8A;5=8O 2 8=D>@<0B8:5 >?@545;O5BAO B5<, GB> 2=CB@5==55 ?@54AB02;5=85 ;N1>9 8=D>@<0F88 2 :><?LNB5@5 O2;O5BAO 42>8G=K<, B.5. >?8AK205<K< =01>@0<8 B>;L:> 87 42CE 7=0:>2 (0 8 1). >=:@5B878@C5< >?8A0==K9 2KH5 A?>A>1 2 A;CG05 ?5@52>40 G8A5; 87 45AOB8G=>9 A8AB5<K 2 42>8G=CN. &5;0O 8 4@>1=0O G0AB8 ?5@52>4OBAO ?>@>7=L. ;O ?5@52>40 F5;>9 G0AB8 (8;8 ?@>AB> F5;>3>) G8A;0 =5>1E>48<> @0745;8BL 55 =0 >A=>20=85 A8AB5<K AG8A;5=8O 8 ?@>4>;60BL 45;8BL G0AB=K5 >B 45;5=8O 4> B5E ?>@, ?>:0 G0AB=>5 =5 AB0=5B @02=K< 0. =0G5=8O ?>;CG82H8EAO >AB0B:>2, 27OBK5 2 >1@0B=>9 ?>A;54>20B5;L=>AB8, >1@07CNB 8A:><>5 42>8G=>5 G8A;>. 0?@8<5@: AB0B>: 25 : 2 = 12 (1), 12 : 2 = 6 (0), 6 : 2 = 3 (0), 3 : 2 = 1 (1), 1 : 2 = 0 (1). "0:8< >1@07>< 25(10)=11001(2). ;O ?5@52>40 4@>1=>9 G0AB8 (8;8 G8A;0, C :>B>@>3> ﾫ0ﾻ F5;KE) =04> C<=>68BL 55 =0 2. &5;0O G0ABL ?@>872545=8O 1C45B ?5@2>9 F8D@>9 G8A;0 2 42>8G=>9 A8AB5<5. 0B5<, >B1@0AK20O C @57C;LB0B0 F5;CN G0ABL, 2=>2L C<=>605< =0 2 8 B.4. 0<5B8<, GB> :>=5G=0O 45AOB8G=0O 4@>1L ?@8 MB>< 2?>;=5 <>65B AB0BL 15A:>=5G=>9 {?5@8>48G5A:>9) 42>8G=>9. 0?@8<5@: 0,73 " 2 = 1,46 (F5;0O G0ABL 1), 0,46 " 2 = 0,92 (F5;0O G0ABL 0 ), 0,92 " 2 = 1,84 (F5;0O G0ABL 1), 0,84 " 2 = 1,68 (F5;0O G0ABL 1) 8 B.4.  8B>35 0,73(10) =0,1011...(2). 3. !, '/  (!"&" '/ !!"+ !'!/ ! B>G:8 7@5=8O 87CG5=8O ?@8=F8?>2 ?@54AB02;5=8O 8 >1@01>B:8 8=D>@<0F88 2 :><?LNB5@5, >1AC6405<K5 2 MB>< ?C=:B5 A8AB5<K ?@54AB02;ONB 1>;LH>9 8=B5@5A. %>BO :><?LNB5@ ﾫ7=05Bﾻ B>;L:> 42>8G=CN A8AB5<C AG8A;5=8O, G0AB> A F5;LN C<5=LH5=8O :>;8G5AB20 70?8AK205<KE =0 1C<035 8;8 22>48<KE A :;0280BC@K :><?LNB5@0 7=0:>2 1K205B C4>1=55 ?>;L7>20BLAO 2>AL<5@8G=K<8 8;8 H5AB=04F0B8@8G=K<8 G8A;0<8, B5< 1>;55 GB>, :0: 1C45B ?>:070=> 40;55, ?@>F54C@0 2708<=>3> ?5@52>40 G8A5; 87 :064>9 87 MB8E A8AB5< 2 42>8G=CN >G5=L ?@>AB0 - 3>@074> ?@>I5 ?5@52>4>2 <564C ;N1>9 87 MB8E B@5E A8AB5< 8 45AOB8G=>9. @>F54C@0 ?5@52>40 45AOB8G=KE G8A5; 2 @-=CN A8AB5<C AG8A;5=8O: ?5@525AB8 >B45;L=> F5;CN G0ABL G8A;0 E, 4;O G53> ?>A;54>20B5;L=> 45;8BL A?5@20 F5;CN G0ABL [E]10 , 0 70B5< 2A5 G0AB=K5 (?>;CG05<K5 ?@8 45;5=88) =0 @ 4> B5E ?>@, ?>:0 =5 ?>;CG8< 2 >G5@54=>< G0AB=>< G8A;> <5=LH55 @; 87>1@065=85 [E]p ?>;CG05BAO ?>A;54>20B5;L=K< ?@8?8AK20=85< : ?>A;54=5<C G0AB=><C >AB0B:>2 >B 45;5=8O  >B ?>A;54=53> 4> ?5@2>3>; ?5@525AB8 >B45;L=> 4@>1=CN G0ABL (<0=B8AAC) G8A;0, B> 5ABL {x}10 , 4;O G53> ?>A;54>20B5;L=> C<=>60BL A?5@20 8AE>4=CN <0=B8AAC, 0 70B5< <0=B8AAK ?>;CG05<KE G8A5; =0 @ 4> B5E ?>@, ?>:0 =5 ?>;CG8< <0=B8AAC, @02=CN =C;N, 8;8 =C6=>5 :>;8G5AB2> F8D@ 2 {E}p ; 87>1@065=85 {E}p ?>;CG05BAO ?@8?8AK20=85< : F5;>9 G0AB8 ?5@2>3> ?@>872545=8O 2B>@>9 B0:>9 65 F8D@K 8 B.4., 4> ?>A;54=59 F8D@K F5;>9 G0AB8; @57C;LB0B 1C45B 8<5BL 284 (E)@ = [E]p, {E}p. @8<5@. 09B8: 12,810 = ?2. 5H5=85: 5@52>48< F5;CN G0ABL: 1210 =11002; ?5@52>48< 4@>1=CN G0ABL (?>;C68@=K< 2K45;5=K F8D@K, 84CI85 2 87>1@065=85 <0=B8AAK 2 42>8G=>9 A8AB5<5): 0,8 x 2 = 1,6; 0,6 x 2 = 1,2; 0,2 x 2 = 0,4; 0,4 x 2 = 0,8; 0,810 = 0,1100110...2 ; @57C;LB0B ?5@52>40: 12,810 = 1100,1100110011...2. @8<5@. 0945< 29,2510 = ?8. 5H5=85 8<55B 284 1) 2910 = 358 ; 2) 0,2510 = 0,28 ; 3) 29,2510 = 35,28. @8<5@. 0945< 79,2610 = ?16. 5H5=85: 1) 7910 = 4F16 ; 2) 0,2610 = 0,4016 ; 3) 79,2610 = 4F,416. @8 ?5@52>45 4@>1=>9 G0AB8 <K >3@0=8G8;8AL =0E>645=85< 42CE 7=0G0I8E F8D@ ?>A;5 70?OB>9, 81> ?5@52>4 B>G=> A45;0BL =52>7<>6=>. ! ?@0:B8G5A:>9 B>G:8 7@5=8O ?@54AB02;O5B 8=B5@5A ?@>F54C@0 2708<=>3> ?@5>1@07>20=8O 42>8G=KE, 2>AL<5@8G=KE 8 H5AB=04F0B8@8G=KE G8A5;. ;O MB>3> 2>A?>;L7C5<AO B01;.2 G8A5; >B 0 4> 15 (2 45AOB8G=>9 A8AB5<5 AG8A;5=8O), ?@54AB02;5==KE 2 4@C38E A8AB5<0E AG8A;5=8O. "01;8F0 2. !>>B25BAB285 G8A5; 2 @07;8G=KE A8AB5<0E AG8A;5=8O 5AOB8G=0O(5AB=04F0B8@8G=0O>AL<5@8G=0O2>8G=0O0000111122210333114441005551016661107771118810100099111001101210101113L01112!14110013D15110114E16111015F171111 ;O ?5@52>40 F5;>3> 42>8G=>3> G8A;0 2 2>AL<5@8G=>5 =5>1E>48<> @0718BL 53> A?@020 =0;52> =0 3@C??K ?> 3 F8D@K (A0<0O ;520O 3@C??0 <>65B A>45@60BL <5=55 B@5E 42>8G=KE F8D@), 0 70B5< :064>9 3@C??5 ?>AB028BL 2 A>>B25BAB285 55 2>AL<5@8G=K9 M:2820;5=B. 0?@8<5@: 11011001= 11011001, B.5. 11011001(2) =331(8). 0<5B8<, GB> 3@C??C 87 B@5E 42>8G=KE F8D@ G0AB> =07K20NB ﾫ42>8G=>9 B@804>9ﾻ. 5@52>4 F5;>3> 42>8G=>3> G8A;0 2 H5AB=04F0B8@8G=>5 ?@>872>48BAO ?CB5< @07185=8O 40==>3> G8A;0 =0 3@C??K ?> 4 F8D@K - ﾫ42>8G=K5 B5B@04Kﾻ: 1100011011001 = 1 1000 1101 1001, B.5. 1100011011001(2)= 18D9(16). ;O ?5@52>40 4@>1=KE G0AB59 42>8G=KE G8A5; 2 2>AL<5@8G=CN 8;8 H5AB=04F0B8@8G=CN A8AB5<K 0=0;>38G=>5 @07185=85 =0 B@804K 8;8 B5B@04K ?@>872>48BAO >B B>G:8 2?@02> (A 4>?>;=5=85< =54>AB0NI8E ?>A;54=8E F8D@ =C;O<8): 0,1100011101(2) =0,110 001 110 100 = 0,6164(8), 0,1100011101(2) = 0,1100 0111 0100 = 0,C74(16). 5@52>4 2>AL<5@8G=KE (H5AB=04F0B8@8G=KE) G8A5; 2 42>8G=K5 ?@>872>48BAO >1@0B=K< ?CB5< - A>?>AB02;5=85< :064><C 7=0:C G8A;0 A>>B25BAB2CNI59 B@>9:8 (G5B25@:8) 42>8G=KE F8D@. @8<5@. 0AA<>B@8< ?5@52>4K 2 A<5H0==KE A8AB5<0E. 7 2-=>9 A8AB5<K 2 8-=CN (42>8G=>-2>AL<5@8G=>5 87>1@065=85):
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87 2-=>9 A8AB5<K 2 16-=CN (42>8G=>-H5AB=04F0B5@8G=>5 87>1@065=85):
87 16-=>9 A8AB5<K 2 2-=CN (H5AB=04F0B5@8G=>-42>8G=>5 87>1@065=85):
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