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e≤ ( : 8 . 5 : '5 ( e 2p + e 2l ) , 2 '5 " . 5 ! @ . 9. . . C 5 D5 : ) * 8 ! # 9 ! ! ; ! # # α. 8 . # @ α= E # 200 g n # : 8 !# : ; 3 9 7 ' ! # . G 5 GG !"! "# -() #* .#) /0') #11!.) #%,') #2 #) #,-* ' 9 ( . 5: ). : ! 8 ) 5C 8 )5 9 # 8 8! ! 8 ; " + (! ! ; 5 ( ( ! # # ! ; 5 8 ; " 5 ! ) ! ; : ! ( 9 . : 5 % 5 + 8 ; 85: : ) + . : ; ! 8 @ LR = 49 g ,33 LB = 81g ,67 1º LC = 158 g ,02 2º LR = 49 g ,35 LE = 327 g ,91 LF = 376 g ,22 LD = 213 g ,91 ) H # : . I # LR = 49 g ,33 LB = 81g ,67 LC = 158 g ,02 LD = 213 g ,91 LE = 327 g 89 LF = 376 g 20 + ; ( ' ! ! @ F A"%C69B" 6)KB. L% D 4% B9)4 +4M". + D K9M 9 6N")79. ) , JJ&0@ O 9 ( 4! " 8 ! P ' + ' A - B 1*. B ! ! JJ&. &G *F ( , # $ ! & % - . # '/ 0123 # ( 4 " # '/ 53 6! + A 9 5 7 : 5" 5C ( @ : # ! " 5 ; @ , 0 A : # ! C 5 ; @ , 0 A 3 9 " 5C 5 8 " ! , 0 θ BA 5 ' + # . ! " 5 C ' J θ BA . ! 5 LBA 6 θ ". ; V A # N# θ VB C. A : θ " 5C. 9 V B 5 θ V A ! : % ! ( ( : # " 5C , ! 0 9 : A 8 ) Q% B % # 5 # # : 5 ' "A 5 CA # B 5 Q% BQ ! 5 ! 5 # "A 5 : ε" 5 εC : % ; . Q% B B 5 Q% 8 ε" 5 εC # A CA + "A 5 # # 2 ⋅ AV ⋅ ε B : < ' : % 5 ! G ε" 5εC % ! # 8 ; ! " 5C. " # CA 5 . ; 8 BQ 5 % 2 ⋅ BV ⋅ ε A # ! (. ; # !! : ! # . GG A : # ! " ! : 5 . @ e= V 9 L ⋅ ea Vˆ sen 2 # ! A # ! % ! %. G$ . & # ' J1 .3FF1 9 5A 9 ! @ 0 !0 0 !( 5 # # 5 : : # # 5 B ! . 5 ! : # : : ! # : # $G 3 9 . . # : : ' ! + ! + 8 # # ! ! , # # # 0 0 ,G . ! % # # ! : ' C . ! 8 ; L= e ⋅ sen ea Vˆ 2 4 567 9 ( @ ",-". /"0 C,-C. /C0 ! 8! ! @ desde A : LVA , LBA desde B : LVB , LAB " : 85 θ BA . ! 5 B A L θ θ BA . 5 " 5C. 6 ". ; V A ; C. θ VB 9 . ( : ! . % ! ( '7 ; : !"! "#) #1!& %-* 8, "#& ) * 9,:%& ! '0& * -',"! #& #!) #;'"#&1#,! " . ! # ( @ A = θ AB − θ AV B = θ BV − θ BA % "C !( 5 : @ ( X B − X A )2 + (YB − YA ) 2 D AB = 9 ! : 5 "A 5CA % 9 # "CA. # @ v B V Dr A D D = rA = rB senB senV senAˆ V Dr A = senBˆ B Dr A senV $ V Dr B = 9 # # senA B Dr A senV ( 8 9 # GG Aˆ + Bˆ + Dˆ = 200 g Vˆ = 200 − ( Aˆ + Bˆ ) # ! # % -. / 0 . 5 . 8 : + A ! @ "@ " 5A@ ∆ x VA = Dr A ⋅ senθ AV V ∆ y VA = Dr A ⋅ cosθ AV V % A # @ X V = X A + ∆ x VA YV = Y A + ∆ y VA !0 + C@ ∆ x VB = Dr B ⋅ senθ BV V ∆ y VB = Dr B ⋅ cosθ BV V X V = X B + ∆ x VB YV = YB + ∆ y VB % : ! ! B .7 # : " 5 . C 8 85 ! 9 !"! "#& '1 ',:#, #1 9 ( . : - / ! & + @ tan θ AV = XV − X A YV − Y A (YV − Y A ) ⋅ tan θ AV = X V − X A X V = (YV − Y A ) ⋅ tan θ AV + X A + @ tan θ BV = XV − X B YV − YB (YV − YB ) ⋅ tan θ BV = X V − X B 8 -A @ (YV − YB ) ⋅ tan θ BV = (YV − Y A ) ⋅ tan θ AV + X A − X B YV (tan θ BV − tan θ AV ) = YB ⋅ tan θ BV − Y A ⋅ tan θ AV + X A − X B YV = 6 ! ;: 8 5 : + /. ( -. 5 ! : # YB ⋅ tan θ BV − Y A ⋅ tan θ AV + X A − X B tan θ BV − tan θ AV 8 , # . ; 0 * 9 ' ; ( ( + ! 85 ; 8 9 @ ; ; " 5 C % 2 A ! # ! ; (HV ) A ⋅ HV = 1 1 + (HV ) B ⋅ V V DA DB 1 1 + V V D A DB < 6 6 : ' # N 67 9 : ' . ! + 5 5 . 5 : : 8 ! 67 . # ; . # 8 ; ! 6 : # ! ( . A = O AB − O VA B = OBV − OBA % 5 ! ( ( D AB )UTM = 9 # "CA. (X UTM B − X UTM A )2 + (YUTM B − YUTM A ) 2 @ ( D Av )UTM ( D AB )UTM ( D BV )UTM = = senB senV senAˆ 1 ( D VA )UTM = senA B ( D A )UTM senV ( D BV )UTM = 9 # senBˆ ( D AB )UTM senV ( . GG Aˆ + Bˆ + V = 200 g Vˆ = 200 − ( Aˆ + Bˆ ) 56 % -67 . /67 0 + A ! @ "@ % " 5A # @ (∆ x VA )UTM = ( D VA )UTM ⋅ senO VA ∆ y VA )UTM = ( D VA )UTM ⋅ cos O VA ( X V )UTM = ( X A )UTM + (∆ x VA )UTM (YV )UTM = (Y A )UTM + (∆ y VA )UTM !0 + C@ (∆ x VB )UTM = ( D BV )UTM ⋅ senOBV (∆ y VB )UTM = ( D BV ) TM ⋅ cos O BV ( X V )UTM = ( X B )UTM + (∆ x VB )UTM (YV )UTM = (YB )UTM + (∆ y VB )UTM % : ! "5 C8 = 5 ' % ' 5 ! : ! 67 ' . ( 9 ! : . 5 3 ! ". 5 : C 9 < : # . 5: # # @ # : ∆H BA = t BA + i A − m B + (0.5 − K) (D BA ) R " 5C. # ! 2 ( 67 5 ( ! 5 ! # 9 ! 5 @ DUTM = K 8 58 . DG2 − ∆h 2 h h 1+ 1 1+ 2 R R 5 ! ) . 5R8 7 . : 1$3GS % ( ( DG2 = % 2 DUTM h h 1 + 1 1 + 2 + ∆h 2 2 k R R ! R8 @ + # @ DG2 = ∆h 2 + Dr2 F Dr = DG2 − ∆h 2 " ! " 5C. # # v B # @ V Dr A D D = rA = rB senB senV senAˆ V Dr A = Dr B = senA B Dr A senV ! # V % A (HV ) A ⋅ HV = $ senBˆ B Dr A senV 1 1 + (HV ) B ⋅ V V DA DB 1 1 + V V D A DB ( $ , # $$ ! $& . '/ 0123 ( 6 $- " $4 6! . ) '/ 53 + % ! ! + 8 # : 7 '5 ! ( J % ( % ! . ! ( . 5 5 +". +C. + ! # # @ " ,-". /"0 % C,-C./C0 ,- ./ 0 #@ LAP , LBP , LCP 3 % # ; : ( + 9 ) A 9 5 5 ! ( ( # 9 : 8 : # 8 T 5U 8 5 " ' ! + 9 # ( # T 5U G 9 ! : , 0 5 # 9 . 5 @ T V U V C W GG 9 : % ! ( + . ( ; ; ; " : .5 "I. CI. ! I CI I "I 6 "I. CI. ! : I ! e = # @ ea ⋅ 2 (lado mayor) 2 + (lado intermedio) 2 2⋅ S 9 ! @ ! o ; "I. CI. o ! : I: 5 o # o % ! ! # , 0 + 5 : # ! ! # # 9 @ : # 9 # ! 0 5 # % 8 : # # ' : # !0 ! + : 5 ! : ' ! ' 9 0 ' , : #@ @ # % 5 : @ 1GX . 5 : ' @ / 5 # B : # % ! ! : 5 , ! : 0 # 4 567 8 ! ( 5 @ " ,-". /"0 / C,-C./C0 @ LAP , LBP , LCP 4C 9)A" YB 9 " +4 ,- ./ 0 5 % +". +C. + ! # 9 ?69 " 9 "% 6%4 + # T W %+C %+" U W %+ %+C " 5 "C 5 C ". C 5 . 9 # T 5U C @ Bˆ = θ BA − θ BC 9 # ! # + ! .5 ' "5 % ! @ $ ( ( + 8 # ;" ) ' ")L " "C" Z ". '+ , JJ 0@ [ + ' A 9)BKB 9M "B7YB. [ 9 ! , JJ 0@ [ B '+ @ + 8 @ BX&* L " [ JJ ( ' A . X&* L " JJ : ! +C D BP sen A = ! # ! @ D BA sen A → D BP = D BA sen α sen α DPB DC sen C = B → D BP = DBC senC senβ senβ +C D BA % sen A sen C = D CB sen β sen α ! : ( : : ," 5 0 ! . 5 @ & sen C D BA ⋅ sen β = C sen A D B ⋅ sen α 9 ! # δ@ : + # D AB ⋅ senβ = tan δ D BC ⋅ senα " ! # # \ ,: # ( 0 . ( + @ senCˆ tan δ = senAˆ 1 A @ a c = b d 9 ! @ b+a d +c = b−a d −c 4 @ senA + senC 1 + tan δ = senA − senC 1 − tan δ 4 ( @ 1 = tan 50 g 1 + tan δ tan 50 g + tan δ = 1 − tan δ 1 − tan 50 g ⋅ tan δ / ! @ tan(a + b) = 9 . tan a + tan b 1 − tan a ⋅ tan b @ * tan 50 g + tan δ = tan(50 g + δ ) g 1 − tan 50 ⋅ tan δ 9 @ 1 + tan δ = tan(50 g + δ ) 1 − tan δ ! : senA + senC = tan(50 + δ ) senA − senC 2 ( a+b sena + senb 2 = a+b sena − senb 2 cos 2 2 ! sen .5 @ @ a−b 2 a−b sen 2 cos @ senA + senC = senA − senC senA + senC 2 = senA − senC 2 % A+C 2 A+C cos 2 1 1 2 sen ( A + C ) cos ( A − C ) 2 2 1 1 2 cos ( A + C ) sen ( A − C ) 2 2 A−C 2 = tan 1 ( A + C ) ⋅ c tan g 1 ( A − C ) A−C 2 2 sen 2 sen cos @ senA + senC 1 + tan δ = senA − senC 1 − tan δ 5 ! senA + senC 1 1 = tan ( A + C ) ⋅ c tan g ( A − C ) senA − senC 2 2 1 + tan δ = tan(50 g + δ ) 1 − tan δ 1 @ 1 1 tan ( A + C ) ⋅ c tan ( A − C ) = tan(50 + δ ) 2 2 / @ 1 1 tan ( A − C ) = tan ( A + C )c tan(50 g + δ ) 2 2 9 @ 9 A+C tan 1 2 tan ( A − C ) = 2 tan(50 g + δ ) 1 (A − C) . 5 : 2 : 9 # +"C &GG @ 8 : δ # A + C + α + β + B = 400 g A + C = 400 g − (α + β + B) 1 1 (A + C) = 200 g − (α + β + B) 2 2 1 (A + C) . 2 + @ 1 (A + C) 2 1 N = (A − C) 2 M= "5 @ A=M +N C=M −N / ! ( 8 : 3 9 : . ,"C+ 5 C +0 5 @ ( # : +C D BP = sen A ! D BA sen A → D BP = D BA sen α sen α D BP D BA sen C = → D BP = D CB sen β sen C sen β @ D BA sen A sen C = D CB sen β sen α % ( : ," 5 0 5 @ : D C ⋅ senα senA = BB =M senC D A ⋅ senβ + &GG 8 : # A + C + α + β + B = 400 g B : . ( @ C = (400 − B − β − α ) − A = E − A D BA ⋅ sen A ⋅ sen β = D CB ⋅ sen C ⋅ sen α D BA ⋅ sen A ⋅ sen β = D CB ⋅ sen(E − A) ⋅ sen α [ ] D BA ⋅ sen A ⋅ sen β = D CB ⋅ sen E ⋅ cos A − cos E ⋅ sen A ⋅ sen α [ ] [ ] sen A ⋅ D BA ⋅ sen β + BC ⋅ sen α ⋅ cos E = D CB ⋅ sen α ⋅ sen E ⋅ cos A tg A = D CB ⋅ sen α ⋅ sen E D BA ⋅ sen β + D CB ⋅ sen α ⋅ cos E C=E−A F " # " 8 5: : 9 ! tgAˆ = tg (200 + Aˆ ) # " 5 . 5 ! 6 ; # . " 5 : ! ( A θ AP = θ AB + Aˆ θ CP = θ BC ± 200 − Cˆ % 8 @ B 1 = 200 − A − α B 2 = 200 − C − β B 2 = B − B1 ó D BP D BA sen A = → D BP = D BA sen α sen A sen α D AB D AP senB1 = → D PA = D AB senα senB1 senα D CP DBC senB 2 = → D CP = DBC senβ senB2 senβ 6 A ; ! 5 ". ! ! . X p = X A + D AP ⋅ senθ AP X p = X C + DCP ⋅ senθ CP YP = Y A + D AP ⋅ cosθ AP YP = YC + DCP ⋅ cosθ CP # 4=7 % ! # ( ! ! ( 9 @ J ∆H PC = t PC + i P − mC + C (e + r ) ∆H PA = t PA + i P − m A + C (e + r ) ∆H PB = t PB + i P − m B + C (e + r ) % 8 % ( . 8 9 : # ! @ B t= + ! ! + + Dr A tgV AB ! # # ' ". C 5 8 ( H P ) A = H A + ∆H AP ( H P ) B = H B + ∆H BP ( H P ) C = H C + ∆H CP ! 2+ # . @ (H p ) A ⋅ HP = 1 1 1 + (H P ) B ⋅ P + (H P )C ⋅ P P DA DB DC 1 1 1 + P + P P D A DB DC 6 # 5 : 8 . : ; ! % 5 ( ! @ ( D AB )UTM = (X UTM B − X UTM A )2 + (YUTM B − YUTM A ) 2 ( DBC )UTM = (X UTM B − X UTM C )2 + (YUTM B − YUTM C ) 2 ". C 5 # C . 5 $G ( # ;" + 8 # .5 ! ( "5 56 % -67 . /67 0 A + ! @ "@ " 5A@ (∆ x PA )UTM = ( D AP )UTM ⋅ senO AP ∆ y PA )UTM = ( D AP )UTM ⋅ cos O AP ( X P )UTM = ( X A )UTM + (∆ x AP )UTM (YP )UTM = (Y A )UTM + (∆ y AP )UTM !0 + @ (∆ x CP )UTM = ( DCP )UTM ⋅ senOCP (∆ y CP )UTM = ( DCP )UTM ⋅ cos OCP ( X P )UTM = ( X C )UTM + (∆ x CP )UTM (YP )UTM = (YC )UTM + (∆ y CP )UTM % : ! "5 8 = % ! ( 9 # (D AP ) ∆H = t + i P − m A + (0.5 − K) R A P ) ! A P ( ,8 ! -67 . /67 + 5". ( @ 2 # "5 0 + 67 5 ( " : 8 . ! : # : : 5 # # ! . $ "C " % : ; ". C 5 "C ( ( 2 ( D AB )UTM h 1+ A 2 R k ( D AB ) 2g = % 5 1+ @ hB 2 + ∆h AB R ! + # @ 2 ( D AB ) 2g = ∆h AB + ( D AB ) 2r R8 ( D AB ) r = ( D AB ) 2g − ∆h AB " ! 2 " 5C. # # P # @ B Dr A D = rA senB1 senα P Dr A = 5 # + ; senBˆ1 B Dr A senα # C+ 5 + ! # ! # ' ". C 5 + 8 $ ( H P ) A = H A + ∆H AP ( H P ) B = H B + ∆H BP ( H P ) C = H C + ∆H CP ! 2+ # . @ (H p ) A ⋅ HP = & & 1 1 1 + (H P ) B ⋅ P + (H P )C ⋅ P P DA DB DC 1 1 1 + P + P P D A DB DC ( , &$ # ! && . &- " &4 6! '/ 0123 '/ 53 + % ( 7 : ! . : ! 5 5 : $$ C A % @ : # ! " 5 ; @ , 0 @A : ! # A 5 ; @ " C 9 ( #@ ,-". /"0. ,-C. /C0 / 8 !# ! "@ A @ %" C . %" A %A " . %A C 3 ! ! "C 5 # " T W %" A : ! ( A 5 U W %A C % %" C ! ; # U %A " ( A $& + : ! : A : : ;5 85 : ( ! ! 9 9 9 ; ; # ! # : ; ! : 5 4 567 % ( # : # ( : 8 4=7 9 ' ; ( ( + ! 85 % 2 ; A ! 8 . # ; (HV ) A ⋅ HV = 1 1 + (HV ) B ⋅ V V DA DB 1 1 + V V D A DB 6 6 : ' # N ! + 5 67 5 ' . : 8 ; ! ! 67 . 9 : # . 5 : : 8 $* 6 ; . # # ( ! A = O VA − O AB B = OBA − OBV 9 # GG ( . Aˆ + Bˆ + Dˆ = 200 g B = 200 − ( Aˆ + V ) % 5 ! ( ( D AB )UTM = 9 # (X UTM B − X UTM A )2 + (YUTM B − YUTM A ) 2 "CA. @ ( D Av )UTM ( D AB )UTM ( DBV )UTM = = senB senV senAˆ ( D VA )UTM = ( DBV )UTM = senBˆ ( D AB )UTM senV senA B ( D A )UTM senV 56 % -67 . /67 0 + A ! @ "@ " 5A@ (∆ x VA )UTM = ( D VA )UTM ⋅ senO VA ∆ y VA )UTM = ( D VA )UTM ⋅ cos O VA ( X V )UTM = ( X A )UTM + (∆ x VA )UTM (YV )UTM = (Y A )UTM + (∆ y VA )UTM $1 !0 + C@ (∆ x VB )UTM = ( DBV )UTM ⋅ senOBV (∆ y VB )UTM = ( DBV ) TM ⋅ cos OBV ( X V )UTM = ( X B )UTM + (∆ x VB )UTM (YV )UTM = (YB )UTM + (∆ y VB )UTM % : ! "5 C8 = % ' ! : ! % ( " ! : ( DG2 = : . 5 ! ( % 9 @ 2 DUTM h h 1 + 1 1 + 2 + ∆h 2 2 k R R ! + # @ DG2 = ∆h 2 + Dr2 R8 Dr = DG2 − ∆h 2 " ! " 5C. # # v B # @ V Dr A D D = rA = rB senB senV senAˆ V Dr A = V Dr B = senBˆ B Dr A senV senA B Dr A senV $3 % A ! # (HV ) A ⋅ HV = - ( 5 - ( . ) 1 1 + (HV ) B ⋅ V V DA DB 1 1 + V V D A DB = + 5 9 + "5 : ; ! + 5+ 9 ( ! 9 . 5 # 9 # ! . .$ 5& ! # . . $ 5& # * 51 "+ + 5C+ + ! 2 ! GG ! + < # " 5 C. A # .5 5 8 5 # 8 " 5C 8 ( $F 9 # + "C. + + ". C+ + / "C+ → AP1 AB = sen 1 sen B "+ + → AP1 PP = 1 2 sen 3 sen 5 # C+ + → BP2 PP = 1 2 sen 2 sen 6 9 # C+ " → BP2 AB = sen A sen 4 9 @ 9 # "C+ 9 # 9 ! @ AB sen 1 = AP1 sen B AP1 sen 3 = P1 P2 sen 5 P1 P2 sen 6 = BP2 sen 2 P2 B sen A = AB sen 4 . . $. 5 ' : 1 . $. &. # * @ AB ⋅ AP1 ⋅ P1 P2 ⋅ P2 B sen 1 ⋅ sen 3 ⋅ sen 6 ⋅ sen A = AP1 ⋅ P1 P2 ⋅ P2 B ⋅ AB sen B ⋅ sen 5 ⋅ sen 2 ⋅ sen 4 sen B sen 1 ⋅ sen 3 ⋅ sen 6 = =E sen A sen 5 ⋅ sen 2 ⋅ sen 4 7 A+ B = 2+3 senB =E senA % 2 5$@ 2+3 = H / @ A + B = H = 2+3 → B = H-A $J senB = E → sen(H - A) = E ⋅ senA senA senH ⋅ cosA - cosH ⋅ senA = E ⋅ senA senH ⋅ cosA = (senA) ⋅ (E + cosH) tg A = sen H E + cos H B=H−A 9 ! ( 8 : ) # : . : : 5 . # 8 ' P1 A = AB ⋅ sen B sen 1 P1 B = AB ⋅ sen(A + 5) sen 1 P2 A = AB ⋅ sen(B + 6) sen 4 P2 B = AB ⋅ sen A sen 4 θ AP1 = θ BA + A + 5 &G θ AP2 = θ BA + A θ BP1 = θ BA − B θ BP1 = θ BA − B − 6 5 + 5+ ! = + ( > : + . + . +$ + 8 . ; 9 ! ! # : : 8 + .C,-. /0. " ( ,-. /0 5 ! : # 4 α # ! "5 # 2 . "C+ . + C+ .. ",-. /0 . α . α$ . β . β . β$ . : ': ! ! @ & 9 # "C+ @ BP1 AB = sen α 1 sen A 9 # C+ + @ BP1 BP2 = sen α 2 senβ 1 9 # C+ +$@ BP3 BP2 = sen α 3 senβ 2 9 # C+$ @ BP3 BC = sen C senβ 3 ! @ AB ⋅ BP1 ⋅ BP2 ⋅ BP3 BP1 ⋅ BP2 ⋅ BP3 BC = senα 1 ⋅ senα 2 ⋅ senα 3 senC senA ⋅ senβ1 ⋅ senβ 2 ⋅ senβ 3 AB BC = senα 1 ⋅ senα 2 ⋅ senα 3 senC senA ⋅ senβ 1 ⋅ senβ 2 ⋅ senβ 3 senA BC ⋅ senα 1 ⋅ senα 2 ⋅ senα 3 = =M senC AB ⋅ senβ1 ⋅ senβ 2 ⋅ senβ 3 + # ' @ A + C = (n − 2) ⋅ 200 − (α 1 + α 2 + α 3 + β 1 + β 2 + β 3 + B) A+C = N sen A =M sen C A+C = N (sen(N − A)) ⋅ M = sen A (sen N ⋅ cos A − cos N ⋅ sen A) ⋅ M = sen A tgA = senN 1 M + cos N & C=N−A : + 5 ; ! : # ! 5 5 8 @ D PA1 = D BA sen(200 − A − α 1 ) sen α 1 D BP1 = D AB sen A senα 1 θ Ap1 = θ BA + A θ BP1 = θ BA − (200 − A − α 1 ) D BP3 = D CB D CP3 = D CB sen C sen β 3 sen(200 − C − β 3 ) sen β 3 θ BP3 = θ CB + (200 − C − β 3 ) θ CP3 = θ CB − C D BP2 = D BP1 sen β 1 sen α 2 D BP2 = D BP3 sen α 3 sen β 2 θ BP 2 = θ BC + (200 − C − β 3 ) + (200 − α 3 − β 2 ) ( 5 ! &$ C9M4") . N D 4B7 . C) BQ9). ) 269 " +"M4 . D 5 9%A B . " , JFG0 BB Q. ) 5, JF30 , JF$0@ 7 4 Z BN69M N") Z " 79L 9)4. , J3F0 ")L " ! "C" Z ". '+ , JJ 0@ [ + ' A 9)BKB 9M "B7YB. [ , JJ 0@ [ B '+ + 8 @ BX&* L " [ JJ ( ' A . X&* L " JJ 4L 9 ". L% , JF&0 6)9B. LD+) 9. ] , JJ 0 A"%C69B" 6)"B. L% D 4% B9)4. + . K9M 9 6N")79. ) [ 9 ( ! 8 ! [ ' + A4% - BX1*. B ! ! JJ&. &G *F , JJ&0@ ' &&