╨╧рб▒с>■  ╚ Ї ■   ∙ pqrstў $%&'()*+· бвгдеж√ ╔                                                                                                                                                                                                                                                                                                                                                     |Cbjbjt+t+лПAAvE      ]tttt└└└╘╘╘╘8 <H$╘u╢xюf4ЪЪ╘╗ ╗ ╗       $+Їd0E└╗ ] ^╗ ╗ ╗ 0■      ╬└FMicrosoft Equation 3.0 DS Equation Equation.3Ї9▓q:└╘ ╘╘tttt╗  . -:╘,b^└ ╘l Ё╙nЗ┴╘╘/╨ -:2820;5=B=K5 ?@5>1@07>20=8O 8 B5>@5<K ;8=59=KE F5?59 3.1 @8=F8? =0;>65=8O ;O >?@545;5=8O B>:0 2 k-9 25B28 A;>6=>9 AE5<K, <>6=> 2>A?>;L7>20BLAO <5B>4>< :>=BC@=KE B>:>2, 2K1@02 :>=BC@K B0:, GB>1K k-O 25B2L 2E>48;0 B>;L:> 2 >48= k-9 :>=BC@. ">340 B>: 2 k-9 25B28 1C45B @025= :>=BC@=><C B>:C Ikk. >6=> 4;O @5H5=8O MB>9 65 7040G8 2>A?>;L7>20BLAO ?@8=F8?>< =0;>65=8O (?@8=F8?>< AC?5@?>78F88), :>B>@K9 D>@<C;8@C5BAO A;54CNI8< >1@07><: B>: 2 k-9 25B28 @025= 0;351@08G5A:>9 AC<<5 B>:>2, 2K7K205<KE :064>9 87 -! 2 >B45;L=>AB8. -B>B ?@8=F8? A?@0254;82 4;O ;N1KE ;8=59=KE M;5:B@8G5A:8E F5?59 8 8A?>;L7C5BAO 2 <5B>45 =0;>65=8O. @8 @0AG5B5 -& ?> <5B>4C =0;>65=8O ?>ABC?0NB A;54CNI8< >1@07><: 0) ?>>G5@54=> @0AAG8BK20NB G0AB8G=K5 B>:8 2 k-9 25B28, 2>7=8:0NI85 >B 459AB28O :064>9 87 -!, <KA;5==> C40;OO >AB0;L=K5 87 AE5<K, => >AB02;OO ?@8 MB>< 2 AE5<5 2=CB@5==85 A>?@>B82;5=8O 8AB>G=8:>2; 1) =0E>4OB B>: 2 k-9 25B28 ?CB5< 0;351@08G5A:>3> A;>65=8O G0AB8G=KE B>:>2. @8<5G0=85 - 5B>4>< =0;>65=8O =5;L7O ?>;L7>20BLAO 4;O >?@545;5=8O 2K45;O5<KE 2 A>?@>B82;5=8OE -& <>I=>AB59 :0: AC<< <>I=>AB59 >B G0AB8G=KE B>:>2. "0: :0:, 5A;8 G5@57 A>?@>B82;5=85 Rkj 1C4CB ?@>B5:0BL A>3;0A=> =0?@02;5==K5 G0AB8G=K5 B>:8 Ikk 8 Ijj, B> 2K45;O5<0O 2 =5< <>I=>ABL  EMBED Equation.3  =5 @02=0 AC<<5 <>I=>AB59 >B G0AB8G=KE B>:>2:  EMBED Equation.3 . 3.2 !2>9AB2> (B5>@5<0) 2708<=>AB8 0AA<>B@8< A:5;5B=CN AE5<C =5:>B>@>9 -&, 87>1@065==CN =0 @8AC=:5 3.10. 0 AE5<5 ?>:070=K B>;L:> 25B28 8 C7;K. @8 MB>< 2 :064>9 25B28 8<55BAO A>?@>B82;5=85. 0 AE5<5 2K45;5=K 425 25B28: m 8 k. @8 MB>< :>=BC@K 2 AE5<5 2K1@0=K B0:, GB>1K k-O 25B2L 2E>48;0 B>;L:> 2 k-9 :>=BC@, 0 m-O  2 m-9 :>=BC@. ><5AB8< 2 25B2L m -! Em (?@8 MB>< 4@C38E -! 2 AE5<5 =5B), 0 2 25B2L m  0<?5@<5B@   A<>B@8 @8AC=>: 3.11. ">340 -! Em 2K7>25B A;54CNI85 B>:8 2 25B2OE k 8 m:  8AC=>: 3.1  EMBED Equation.3  (3.1) >MDD8F85=BK g 8<5NB @07<5@=>ABL ?@>2>48<>AB59. >MDD8F85=B gmm  2E>4=0O ?@>2>48<>ABL 25B28 m, :>MDD8F85=B gkm  2708<=0O ?@>2>48<>ABL 25B259 m 8 k. 7 2K@065=89 (3.1) A;54CNB >?@545;5=8O 2E>4=>9 8 2708<=>9 ?@>2>48<>AB59 25B259 -&. E>4=0O ?@>2>48<>ABL m 9 25B28  MB> :>MDD8F85=B ?@>?>@F8>=0;L=>AB8 <564C B>:>< MB>9 25B28 8 55 -! ?@8 >BACBAB288 -! 2 4@C38E 25B2OE -&. 708<=0O ?@>2>48<>ABL 25B259 k 8 m  :>MDD8F85=B ?@>?>@F8>=0;L=>AB8 <564C B>:>< k-9 25B28 8 -! m-9 25B28 ?@8 >BACBAB288 -! 2 4@C38E 25B2OE AE5<K. "5>@5<0 2708<=>AB8 D>@<C;8@C5BAO A;54CNI8< >1@07><: 2 ;N1>9 ;8=59=>9 F5?8 B>: 2 k-9 25B28, 2K720==K9 -! Em, =0E>4OI59AO 2 m-9 25B28,  EMBED Equation.3  1C45B @025= B>:C Im m-9 25B28, 2K720==><C -! Ek (G8A;5==> @02=>9 -! Em), =0E>4OI59AO 2 k-9 25B28,  EMBED Equation.3  EMBED Equation.3 . @8 ?@0:B8G5A:>< 8A?>;L7>20=88 B5>@5<K 2708<=>AB8 206=> 8<5BL 2 284C 2708<=>5 A>>B25BAB285 2 =0?@02;5=8OE B>:>2 8 -! 2 AE5<0E =0 @8AC=:0E 3.11 8 3.12. &5?8, 4;O :>B>@KE =5 2K?>;=O5BAO ?@8=F8? 2708<=>AB8, =07K20NB =5>1@0B8<K<8 F5?O<8.  =5>1@0B8<K< -& >B=>AOBAO =5;8=59=K5 F5?8. 3.3 "5>@5<0 > :><?5=A0F88  ;N1>9 -& 157 87<5=5=8O B>:>@0A?@545;5=8O 2 =59 A>?@>B82;5=85 <>65B 1KBL 70<5=5=> -!, G8A;5==> @02=>9 ?045=8O =0?@O65=8O 2 70<5=O5<>< A>?@>B82;5=88 8 =0?@02;5==>9 2AB@5G=> B>:C 2 MB>< A>?@>B82;5=88. ;O 4>:070B5;LAB20 B5>@5<K 2K45;8< 2 AE5< -& >4=C 25B2L A A>?@>B82;5=85< R, ?> :>B>@>9 B5G5B B>: I, 0 2AN >AB0;L=CN G0ABL AE5<K >1>7=0G8< ?@O<>C3>;L=8:><  @8AC=>: 3.20. A;8 2 2K45;5==CN 25B2L 2:;NG8BL 425 >48=0:>2KE 8 ?@>B82>?>;>6=> =0?@02;5==KE -! , G8A;5==> @02=KE ?045=8N =0?@O65=8O 2 A>?@>B82;5=88 R B>:0 I (E = IR; @8AC=>: 3.21), B> B>: I 2 F5?8 >B MB>3> =5 87<5=8BAO. #1548<AO, 2 B><, GB> @07=>ABL ?>B5=F80;>2 <564C B>G:0<8 0 8 A 2 AE5<5 =0 @8AC=:5 21 ?@8 MB>< 1C45B @02=0 =C;N. 59AB28B5;L=>  EMBED Equation.3 . >, 5A;8  EMBED Equation.3 , B> B>G:8 0 8 A <>6=> >1J548=8BL 2 >4=C B>G:C. ;8, 4@C38<8 A;>20<8, 70:>@>B8BL CG0AB>: 0A 8 ?>;CG8BL AE5<C =0 @8AC=:5 22.  =59 2<5AB> A>?@>B82;5=8O R 2:;NG5=0 -! .  8AC=>: 3.2 @8<5G0=85  0 @8AC=:5 3.2 ?@O<>C3>;L=8:>< A 1C:2>9  >1>7=0G5= 0:B82=K9 42CE?>;NA=8:, B> 5ABL 42CE?>;NA=8:, 2 A>AB025 :>B>@>3> 8<5NBAO 8AB>G=8:8 -! 8;8 B>:0. 3.4 "5>@5<0 >1 M:2820;5=B=>< 35=5@0B>@5 > >B=>H5=8N : 2K45;5==>9 25B28 42CE?>;NA=8: ?@8 @0AG5B5 <>6=> 70<5=8BL M:2820;5=B=K< 35=5@0B>@><, -! :>B>@>3> @02=0 =0?@O65=8N E>;>AB>3> E>40 =0 7068<0E 2K45;5==>9 25B28, 0 2=CB@5==55 A>?@>B82;5=85 @02=> 2E>4=><C A>?@>B82;5=8N 42CE?>;NA=8:0  A<>B@8 @8AC=>: 3.3. 5B>4 @0AG5B0 B>:0 2 2K45;5==>9 25B28, >A=>20==K9 =0 70<5=5 0:B82=>3> 42CE?>;NA=8:0 M:2820;5=B=K< 35=5@0B>@><, ?@8=OB> =07K20BL <5B>4>< M:2820;5=B=>3> 35=5@0B>@0, <5B>4>< 0:B82=>3> 42CE?>;NA=8:0 8;8 <5B>4>< E>;>AB>3> E>40 8 :>@>B:>3> 70<K:0=8O.  8AC=>: 3.3 >A;54>20B5;L=>ABL @0AG5B0 B>:0 MB8< <5B>4>< A;54CNI0O: 0) =09B8 =0?@O65=85 Uab x.x =0 7068<0E @07><:=CB>9 25B28 ab; 1) >?@545;8BL 2E>4=>5 A>?@>B82;5=85 R2E 2A59 AE5<K ?> >B=>H5=8N : 7068<0< ab ?@8 70:>@>G5==KE 8AB>G=8:0E -! 8 @07><:=CBKE 25B2OE A 8AB>G=8:0<8 B>:>2; 2) ?>4AG8B0BL B>: ?> D>@<C;5  EMBED Equation.3 , (3.2) 345 R  A>?@>B82;5=85 2K45;5==>9 25B28. A;8 A>?@>B82;5=85 25B28 ab A45;0BL @02=K< =C;N (R = 0), B> 4;O =55 1C45B 8<5BL <5AB> @568< :>@>B:>3> 70<K:0=8O, 0 ?@>B5:0NI89 ?> =59 B>: 1C45B B>:>< :>@>B:>3> 70<K:0=8O (I:.7). 7 (2.2) ?@8 R = 0 ?>;CG8<  EMBED Equation.3  8;8  EMBED Equation.3 . (3.3) 7 (3.3) A;54C5B <5B>4 M:A?5@8<5=B0;L=>3> >?@545;5=8O 2E>4=>3> A>?@>B82;5=8O. ;O MB>3> A;54C5B 87<5@8BL =0?@O65=85 E>;>AB>3> E>40 =0 7068<0E @07><:=CB>9 25B28 (Uab x.x) 8 B>: :>@>B:>3> 70<K:0=8O (I:.7) ?@8 :>@>B:>< 70<K:0=88 25B28 8 =09B8 R2E :0: G0AB=>5 >B 45;5=8O Uab x.x =0 I:.7. 0720=85 <5B>40 >1JOA=O5BAO B5<, GB> 4;O =0E>645=8O Uab x.x 8A?>;L7C5BAO E>;>AB>9 E>4 25B28, 0 4;O >?@545;5=8O 2E>4=>3> A>?@>B82;5=8O 42CE?>;NA=8:0  >?KB :>@>B:>3> 70<K:0=8O 25B28 ab. 3.5 0;0=A <>I=>AB8 @8 ?@>B5:0=88 B>:>2 G5@57 A>?@>B82;5=8O 2 =8E 2K45;O5BAO B5?;>. 0 >A=>20=88 70:>=0 A>E@0=5=8O M=5@388 :>;8G5AB2> B5?;0, 2K45;ONI55AO 2 548=8FC 2@5<5=8 2 A>?@>B82;5=8OE AE5<K, 4>;6=> @02=OBLAO M=5@388, 4>AB02;O5<>9 70 MB> 65 2@5<O 8AB>G=8:0<8 ?8B0=8O. "> 5ABL 4>;6=> 2K?>;=OBLAO C@02=5=85 M=5@35B8G5A:>3> 10;0=A0, :>B>@>5 ?@8 ?8B0=88 AE5<K B>;L:> >B 8AB>G=8:>2 -! 8<55B 284  EMBED Equation.3 . (3.4) A;8 G5@57 8AB>G=8: -! B5G5B B>: I B0:, GB> =0?@02;5=85 B>:0 A>2?0405B A =0?@02;5=85< -!, B> 8AB>G=8: -! 4>AB02;O5B 2 F5?L 2 548=8FC 2@5<5=8 M=5@38N (8;8 <>I=>ABL), @02=CN EI (?@>872545=85 EI 2E>48B 2 C@02=5=85 (3.4) A ?>;>68B5;L=K< 7=0:><). A;8 =0?@02;5=85 B>:0 2AB@5G=> =0?@02;5=8N -! , B> 8AB>G=8: -! =5 ?>AB02;O5B M=5@38N, 0 ?>B@51;O5B 55 8 ?@>872545=85 EI 2E>48B 2 C@02=5=85 (3.4) A >B@8F0B5;L=K< 7=0:><.  >1I5< A;CG05, :>340 2 -& 459AB2CNB ?5@5<5==K5 =0?@O65=8O 8 B>:8, CA;>285 10;0=A0 <>I=>AB8 <>65B 1KBL 70?8A0=> 2 A;54CNI5< 2845:  EMBED Equation.3 , (3.5) 345 un  =0?@O65=85 8;8 @07=>ABL ?>B5=F80;>2 <564C C7;0<8 B>9 87  25B259, B>: 2 :>B>@>9 in. K@065=85 (3.5) B0: 65 =07K205BAO B5>@5<>9 "5;;5465=0. @>872545=85 unin=pn  <3=>25==0O <>I=>ABL n-9 25B28. "> 5ABL, D>@<C;0 (3.5) 2K@0605B 70:>= A>E@0=5=8O M=5@388 4;O -&: AC<<0@=0O <3=>25==0O <>I=>ABL 2A5E 25B259 @02=0 =C;N. @8<5G0=85  5@5<5==K5 =0?@O65=8O 8 B>:8 (2 >B;8G85 >B ?>AB>O==KE) >1KG=> >1>7=0G0NB AB@>G=K<8 A8<2>;0<8 u 8 i. 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                                                                                                                       ┐┐┐┐┐┐            ┐┐┐┐┐┐                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ┐┐┐                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ┐┐┐      ┐┐┐ЯЯЯ                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ┐┐┐                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ┐┐┐                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ЯЯЯ            ЯЯЯ                                                                                                                                                                                                                                                                           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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ┐┐┐┐┐┐                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    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