6.soal beton pbi

22
NIV'I - NIV-I llP{nl€g uep ssno$s'}eld tsepuod qsu?J uB)llplleruad sl?c lsnses -rr"*t--- --*tt-,r-*- ,ut@1-gl : u18ue1 + PuoJeld u?qeg ,uFI 0s : Euelueg dqY ueqeg ,ur6>l 0S : rstued EutPutP uuqog ,tucfl SZZ : .Iqo) 9ZZ ) uoleq nlnhl - t0-1661-Sl-r : INS)S renses rnqn:1S ed,(J roD[eC uuEultuede) roDtBJ qeJosc roDlsc Dntdd ue8uoP IBnsoS der, "r,*r-* rutu?l dnplq uuqeg - llBtu uBqag - nefultlp {epll t86 I ,u6r oo l .ur6r osz Jnllluls tJlpuas lBre8 nuluplp {BPII -'. c0-1661 -91-I INS)S uBp lL6l Elsauopul uolag uErnlErad 'z 9961 Sunpe5 Inlm slseuopul usueqaqued uernlerad 'l ISVCINOd iIdAI NVHVB VIVC HVNVJ ISICINO) NVDNN)DNI-I HNUVDNSd VdI^IgD NVgAg NIDNV NVBAS NYNVSEBhIAd NVUYXYgg) dVCVHUIIJ NVNVHVIS) IVUVAS . IVUVAS NVHVSNUAd NVC NVDN -VgNiIDNiId NYNI)DNNI^IA) IV)VdIC DNVA NVUNJVUA d. NIVU NJ,VUS d NVYNYf,NgUfld ISYIANO.{NI

Transcript of 6.soal beton pbi

NIV'I - NIV-I

llP{nl€g uep ssno$s'}eld tsepuod

qsu?J uB)llplleruad sl?c lsnses

-rr"*t--- --*tt-,r-*-

,ut@1-gl : u18ue1 + PuoJeld u?qeg

,uFI 0s : Euelueg dqY ueqeg

,ur6>l 0S : rstued EutPutP uuqog

,tucfl SZZ : .Iqo) 9ZZ )uoleq nlnhl -

t0-1661-Sl-r :

INS)S renses

rnqn:1S ed,(J roD[eC

uuEultuede) roDtBJ

qeJosc roDlsc

Dntdd ue8uoP IBnsoS

der, "r,*r-* rutu?l dnplq uuqeg -

llBtu uBqag -

nefultlp {epll

t86 I

,u6r oo l

.ur6r osz

Jnllluls tJlpuas lBre8

nuluplp {BPII

-'.c0-1661

-91-I INS)S uBp lL6l Elsauopul uolag uErnlErad 'z

9961 Sunpe5 Inlm slseuopul usueqaqued uernlerad 'l

ISVCINOd iIdAI

NVHVB VIVC

HVNVJ ISICINO)

NVDNN)DNI-I HNUVDNSd

VdI^IgD NVgAg

NIDNV NVBAS

NYNVSEBhIAd

NVUYXYgg)dVCVHUIIJ NVNVHVIS)

IVUVAS . IVUVAS

NVHVSNUAd NVC NVDN-VgNiIDNiId NYNI)DNNI^IA)

IV)VdIC DNVANVUNJVUA d. NIVU NJ,VUS d

NVYNYf,NgUfld ISYIANO.{NI

-

O l.- t. l.

it-rz.,z-g I,g r.-oz,od-.2,e-6 t,e-6 t'gt;Qr,:Q.,r.. rrf ig

t-tr'zt-Lt' Lr,-?"'-'1 e-Ei ;;SlJrtJldr%, qi,tEiliflB

ogie tero relc suoH_c_dolrubt l'-lErtss uar l N3lN 1 33rs

._..__a\

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(,{r:;u;4; NI t't- 11d

! sz q 'E?g

S33UOJ-U3Bt/,1 3t^l lVCl rluc

61,-L! .- _a...-

0 fi38I oqri = ssSuj.s olll l OSli =i '0 10ct

!)z'0 11CI(':al) gNtovol(tSHOrCV.JNn

(rrVls-lNl-l)

'(uriJua.rtsi paacis put,lr u6tsap alEl$ llulll \ rr sitritg oi piau6tsap ierl ssnll s!L{I

NOIJ.V]^!UOJNI ONIM

'\:*. tt"

t""r";

t'$d'A,'J;uI3'ifi6?=#fi

V/N 9v7N 9t96 61"-g t666 6f'BL

pTuuds ueo''l:g6'3 !-009?sv = SOOa)

000f = gNl3VdS

B'9-e'L-

":)'zl.' t'7-ulul

(lfzroPi(1'1)zrog(t^t)uan(rr)uan

1:J3Cl

' '\.-\' '-- " ''.i

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t ".'

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t."$/-'B'ru ( )Bl3'C

t"'i-.,. | ,/

t..:" -...4Q/-:)llds'3s

BL

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n

,'."'l'' Ol,,: I.

ONCN

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I3NNV -{3 = edfl

, s.,y99tt ,.,.1s-ggsjl OCigP0 'b,g'?,1pu1qy ptiJfir.r1l 'Er,trp[' I .l.ci .r(-'lEltlJqlJ

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ru E>l 58[ : ZV x

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iz,s:-grJ/\", 0t

zl x oLgx too'o -,0h1 - - f,l r.l

* x 019 x t00'0 = xlhl -: xl IAtr

: u[ra>1aq 8ue,( uetuoru - uatuolnJ

gE: ,(1 x: f,lx9t_ XIX: xlx: 00't I O0'l - x1 7 '(1

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lEl,, : IBluB.I lnld uuEuulnua4

$lfl1-019 : tslol lrBqeg

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FFrygT-=ifT : u>l8trarapuoJuld lurag -

"uUB\, Zt - 17, x Z: lu{orad lereg -

"wl?l (,t = 17, x E i {rIrBJa{ lBJeB -

.tu/E>1882 : yyizxZI'0 : Plds' g-: efte4eq fluef u"qaq - wqeg

ruc 0l : ( S'0 + S'I ) -(,1- t{ -

Iutu8 : IEequeEuuPlQ-rrrru 0l : 1o1od treEtrupl Q -

Luc Zl = ( tq ) p1d Pqel -

cwc6;1oo?l : Bo

"*rtEI 0802 - ne*o e------- nZ n efeq nlnut -

.tuc7E1 SZZ: Iq.o e------- 9ZZ>l uoleq nlnut -

: Llsurlecirered elep - BTBCI

rNrimim:i

I

or x (9r'o - t) 8'oz

,(oorxg/'o)x669

e8'9 x 0[ x 16'0

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i6'O : 9l'0 x tll -2ttt-

szzx 0t x 001

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I

tiilfit,

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t8900'0

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ruru f'0 : co > Lutu 62$0 : tuc 6200'0 :

t8900'0xr0'0+s'l x9'[ )z'l -cD

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'i {Bleu lorluo{

oI < tuc 0Z'l: 00? x Sl'0 x 09Zll :

ruc t0s'0 = ----'9'::-:-y''------ x 80r'0 -0SZ+ 1x ZxjZV

I

t

Ert Olt'lSI - 8'9 ll7, + n6l'6VI -dele A\

EI 8'9 llZ:(r*El OZx cw 8'ZSt) 0t'0 - t{A\

0f'0 : Is{lpou uelsgeo)

zu! 0Z: I{b

(qm) dnplH uuqeg

E4 l6l'6tl : Lu/t\

B]-g'gZt'gL : eu/EI 00tl * ,u 868'r?

Iuolo) l€rag -

{oquIo} }Breg -

ruolcg lBId -r-

IBI€I {lB + 4eq8utl }Brag -

puoguld

e48uur + PuoJuld lereg -

: delV lerog 'l

E1 o8o'sZ :

E1 t'ogt'g:E>1 ==

El oop'z'z :

euF{ OyiZ X cu St'g1

zwp11l x zw 8'ZSt

zwlfl1-6g x zu 8?, :

EunluuEEued -F umle^1eE elEuer lerog -

(de1e ul8uer a Eualueg)

dule dnlnued lgreg -

{pop LLZ'\ :

,,r(oL'L) x 9o'o -trr oL'L _ 0I'f * 09'[ : H,,rH*90'0- {J-*J

: (D r€leg nUB/t\ EunlqEuepg

Er 8'r68'8of :L\S'L9(,+01['lSI:

Z wttlrzl A\. + dele /t\ - ptoJ, /\\

: (tm) ueunEueg IBto.L tereg 'V

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000'8 1 - ,tu1fl[ 097, * ,- (Zt x 0Z) 0['0 - q/$.

0f'0 - Is{npeu uelsgeo)

zwF7-0SZ: tlb

: (qu$ dnplH uuqeg

E>1 L8S'6EZ _ tul6

puoJeld ulEuua

+ puoJBId lereg -

{oqrueJ lBreg -

uoleg ulolo) -

,:alv l {opg -

IBluu'I {opg -

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eu Fl oov(, * e* 6z'z

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zw (ZI x 0Z) z*Ft OZV

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^ylqxl/Y\3 rL HxlA\

7,> 0l'0 : 00'll I 0L'L:

t > LZV'O: 00'8 l l 0L'L =

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snrunr I€{BdlCI

I qurv

x r{9rv

: EunPeg

Jusuc JoseD e,(eg Isnql4slcl

:lc:

siH

V/H

r8Eurl Eurafuedeg a1 edureC tuqHv IBIoI IuluoslroH

udtueg ueuuqule)

fl\ 199'ot =

6880t x 0s'I x s0'0 -.14\xIx

"J: A

: eE8uqag

0S'[ - I

(tgf) t't.L't'l -'lg)S) Eunpog uBp qBulnu Inlun

us?uecuared ugluopod nlnq fZ laqq IrBp 1udup161

: usBtuBlne) JouBc 'cl

a IEm'I: qBUEJ

L LLZ', = J,

: :J rusucl udutag uelsueo) 'J

.ruc731 VY{y: 11

rusoqas "urfutfttp

8ue'( ue8ue8al > 'ruc73>1 Z{0

' '11-:-9-1-:-?l-- *00t6I

: gZZ'0 + t6Z'0

009x(st+og)

08t9 I

(DV------- + : 1o

N lold

fpB

.rsepuod e{ B}eraru u88urq uBqeq uu{rsnqrr}srpuew BSIq ueldereq Ip Jools

nlnFedueru ueSuep risy r{g^A?q rs{ru}suo{ tIBI€pB usBuBcuered Isunsv

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qurrq urfr ueEue8el

urcgI:" rtseduesrdelpqol

ruc gel-: IsePuodrrBrIrBIBPa)tuc 08 : ruqal (mfet) IIBI nleq Isepuod

urc 08 x 08 luduleles leld IsBPuod

ru t-0t0ssnoJls

rrse6 uestdel

ru 3I g6t - x€tu IAI

84 08L'9T : xetu d

II€I nluq rsupuod lseulqtuo4 uu8uep luduelas 1u1d

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rsepuod lu{Btuetu uB{BLrBcueJIO

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zruc 8Z'g :01 Q 8 : rrBEtrBInI IB{BdIO

0802

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1u1d tsuatulp tre{srrecualrg

: lBId uu8ungqred

uol 98S'[ < uo] EL'Lrrpuos IIsBq IrBO

: ut - 0€0 ssnorls sugsuduY

El SgS't nele ,uc./E{ gLtA:ffiE'y-Z{0 - }o

t{€lepe ssno4s rsepuod qelo'trBqu}lp BueA

tts0'0 - b

gZZx 08'0 x E

uc/8l VVE',\ = 107

ruseqos lrexulllP 8uu'( ue8ue8ot

zvx 131 ?rt'6 :

Luo sltuc ott -

uI3 08 x 0B

9.1-:.!:l--.--99l- :S9ZI

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rsePuod ueurelePo)

leduales leld Is€Puod

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rlBI nlgq rsepuod tseulqtuol ue8uep ledueles 1e1d rsepuod rulpluolu IIDIpuucue4O

IdoNY}Ihlo.Iox.(ogx08)€dIsvoNod

zvtc 09'9

zruc l9'l - 08 x 0l

: CI 0 f : tre8trelnl re>1edrq

0802x -------- x tts0'0 - Y

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ncg

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z'n) SZL.9 _ .bt x y xoAx 180'0 - lol V

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szzx 0s'0 x z*neo

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ru 661'0 :90'0 - 0t'0 ' '/, 1- (160'0 :,P - l\z/, a l1o - nee

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ru sr0'0 : 0['0 x sI'0 _ z'ne

( zo'o

0['0 x 00I

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z0'0oo

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Sl SOS'I I : OEL' Lx S'I : IrNE11E; L: IsBPuod ueqeg

: SSNOUIS ISYONOd NYCNYTNNfld

'lf

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4-..).\ - V@o n<. ,/ /L \

rx/oy oo'gez =Z( Afrf )(ell )) - I )xt nM UL = ZnM.

url6y 00'O0Z =xlnMilL=lnM,

Zurl6y 0O'OOZ - dnptH ueqaB leqtlv'q

ur/oy oglgcr =Z( A11txt) ( elL )) - t ) xt n6etL= ZnM,

ru/6.y Og'O/C =q nM ilL = LnM,

Zrrrl6y 9O'OZS = lIeW ueqag leqllv'e: ZLU L lelad eped elerayl ueqag regru ueOuag

ru/6y 6L'V1Z =Z( Affxf ) ( elU )) - I )xt nM ZtL = ZnM.

u/6y 00'002 =xlnMilL=LnM.

Zurl6y 00'002 = dnprg ueqag teqllv.g

ru/6y lg'l6t =Z( [t1xt ) ( ell )) - t ) x1 rrpl ZtL = ZnM .

ru/6y SO'O2C =xl nM tlL = LnM ,

Zu.r/6X 00'0/t = rley1 ueqag leqt)tv e'. Zw L leleci eped eleJahl ueqag repu ue6uag

ur/6y Br.Csz =7( 411x1) (ell, )) - I )xt nM Z/L

ui/6y t9'9LZ =xl nM e/L

7ru76y O0'0OZ = dnprpl ueqag

=ZoM,

= Lt'lM ,leqqv q

9L'e

ur9/'t x ru0'l uprnln !eluel lBlad .

sz't

ur9z'c x ru0'I ueJnIn lts]up-I lelad;

ru/6y '6'99y.

=Z( Alx:t ) (ell )) - I ) xt nm UL = ZnM. gz.t,

url6y Cg'OOr =xl nM t.ll = LnM .

Ztul6y O0'0fg = llery ueqag 1eql)tv e: ZLU L 1elad eped elera4 ueqag relru ue6uag

rug't x rugz'c uernln leluel telad;.. do;dr.uy apolag,'1 .. ueleun66uau >toleq eped rpef.ral 6ueA ueQag .

tllO-IOX NVO yOIVB9N\nnlu38 Not3B

untynu.Ls NV9NntlHU3d

f

zgrBeQLQL = axudr

( q.cJ'gB'o )

: eL'9 = Ud =2.i '-

,,pxl+ (,p-,,p- p) sC + ( e Zll-,,p - p )33 =oXU6l .

9t BL6Be =

, gg'0=0 - - -. $lna = ud.

0 t0z06e =

-,.,...i'.".: ,'-i :..' l.r x""i'c : qxlleqexSJxSB'0= 3lequd'

edW 00'OZe =S.l +- \ ' L L 6LZ =3leq e

ffi= SJ.

CgLg =

980 tl cteqCxtl = 3leqe'

6e'ZL =AJ + oo9

Px 009 = 3leq3.

l.uLu 9e =

,p - Llz/l - ,,P .

LuuJ 6e =

P-q = .P.LULU 00 LIL =(tnl+qI+S)-t1 = P.

: tuolol llllala l66ut1

LUIU 9t ='' 'l

".,; i Ll x0L'0 = uluj Lr

'

LUtu 29.692 +_-- Lu 092 0

: nd/UUrrl = a.' r I :ueEuelnllsuaullo'

N 00'ZZ0VZ =oALUN 00 9969 =enhlLUN 00 vgzg =zn!11

urLU 00 00t -qLutu 00'09 L =Ued4 0O'0Zg =Aledyl geg'g t. =3J

'ledeptP 09 3hlVUJ: 000z.des eleo lreo

tuolol lsuau.rroefeg npyl ueleun6lg

uola8 nlnw ueleunolo

'del ( urur 0gl - g 0 )'durn1 (uul 0Zt-gS) <- runurrurul 6rre>16uasueleun6rp

(*og)

9 6trxt Ipxnrqx( .q ),,( 5n+L) =3A,

NY69ZZ =6v gr gggzz . =

(p-rzru)nn x (}-:TATI = u/\ ,

Jasag ue6ue1n1

zruru 0o 009q.Mq.7o! = LUnUIUILU SV.

zruLu lt'0s9 lelol sv .

60'gzE =,S!-S! .

sV 0ZSl I =Al.sV = Ii

.sV gtg 8P601 =ffi=SC.

L/'11966/Z =

uo) 9z'9: snorls I ulll ue6ue6al ledeprp e66utqaguol 9Z'9 =6y 09,6gz9 =

g

dHf 'Y +Z

m-o ( tug = q ) snor15 lsepuod 6un1n6 e,(e6

gg rp soo.rls 6ur1r1ay -

0C0soorlsV-(aHf) qeuel lasa6 eAep eler-eler qelurnf -

( 3 ) snuo3.-: lellN ueetr4rad tedep eleu lrsed llllpas neuel

uesidel gedeptal LuO - ur ! ueuJelepal eped 'qeuel lslpuol uellsurnse lO

uteleg lsBPuod 6un1ng e[eg'(g

Zul/uol 898'C = Q

ledeprp 9'e ueueuJeal e>16ue ue6ua6

' zur/uol to/9'6 =l,N'q'l't'O + b,N'b + ),frl'3f,'! C/Z = O

( ur g'! ueuelepal eped ) rsepuo6 6unxn6 eAe6

ur 0'I = fl-ur 9.0 _ o-

Ztuol6:l Z'l =c-euUuolgt =l-

: lellN ue6ua6

' OZ'L = l.N -

t'LZ = b'N -

9'9 =3,N-: repu ledeplp reaqs lesol rsrpuol eped uelepeday ueneluruad rdetal ueIV lel6uruau

Llepns Lleuel uelepeda)t urg L- ueuelepa)t p/s ueelnuJrad qeuel lslpuol e66urqas

( ueunOueq utplaq qepns tselol rell)teslp euatel) I L = 0 qeuel rasa6 npns uellsulnsel6

1e46ueq lsepuod 6un1ng eAeg'(Y

rsvoNod9N\nnru38 Nor3g

w)zv6zurs 9'902

Zucl6>t OO t.

7tuc161 g

unrxnurs NvgNnrlHu3d

E

6v oz'socs r6v 00''ZEroy oz eeg

Ny LZjLZ +- N 9l'8020/Znn < Ny rz'orz {-- N 9z'gozozz

tu6y t6'g?SC =Qlnn = Uhl ,

LuOy eZ'geBZ =7( rd anq7l;) raod MZl - ( cd / ivlq ) lol M = nW ,

: rpefual 6ue{ uauoy1 .

L L aurerl 00OZ,deS rrep lerxv ueqag .raod urpuas leJag .

: gpepal 6ueA ueqag0t I 06 x 06 raod lsuaulo

'puod rasag ue6ue1n1 Ounlqrp ngrad Iepll e66urqas rqnuadtag Llelal uelnluallp 3ua,( geteAg

'leteAs tLlnuaruaru rsepuod leqal '

I'ULU ZeZ(0 Zn.+rD+s)-U

L

LULr' 09 L

LULU 00Cedy{ ozeeQvu gzs'Pr

Ny zr'ort6x og LvovLrloloy nles qeles eped lelxv d-

: resaqas Jaod eped ;pelay ueqag elen: urolol lelxv 6 ledeprp OggZ,deS elep ueg 6x og'rrolr

reod ue6unlrqad lesep reEeqas %gZ llquelp u,toloy lelxv d 000Z,deS eleg peg .

p,oq,f,.|| ,e/1.9'0 = 3A 0 .p.oq,3J^ .g/1.(cq + l) ),9'0 = 3n 0 .

LULUBZ9L (p*MQ),I = oq.

NX Zr'Otl = nn,

@(ce )

( ,r',q ) 0oFxog L Luolox uelnlnueleuecualp tsepuod 1eg6 leqal.

+- ( Al ) Ze-n eleg n1ny1

.- ( ,cl ) $ZZ>t uolag nlnn : ue1eun6r6

=

Yt

t'

:

:

( u30d ) dv3 3-ud lsN3nto'z

(uru Ogt - Ol0 )

(ururgzt-zlQ)

tuur 9l'L9L = S.

ZLUL! $Z'Z\V =SVxg'Q = .SV.

( Zpx,uqxp )

!w

{- uJOy t6 gtgg = u!11 .

ZEZ =(Qztt+0+s)-q = P.

@

urur I t'BzlSV

mErzF r-tirT =

z" rfffi,, ==

99C00'0 =((& l( uUruZ ))-l ) A - I )x( ru/r ) =

tt 6L =(oJ98'o)t$=

280 =

S.

sv,

,l .

LU.

ulNx 9t'9c

L

( urur SZt- e0) 6ue16uis ue4eun6rP

ZIIZ

(ol0z+zl0z)

Zurtu t6'09 | =

Ztutu C6't0C =

SV 9'0 = ,SV .

px/Y\qx(/ = SV'.

22900'0 =((( All( ,U,uZ))-t)A -t)x(tutt) = tr ,

9L 9l =(cJgB'O)/AJ= ru.

te L =( zpxrnq )

fu^l = uU.

LUIJJ llz =(0 Zll+0+s)-t{=P.

uu6y feS'ttg =QluYtt = UW

tuOX SZO'ZO2 = oN: lpepal uaurohl -

nr OO'Z loots Ouelua8 Z/! -

6l Zrcf l : uroloy lelxv -:1edep1p OOoZ.deS qep peo

9Zl9L Jools !suaurlo't

iffiiltii!i

.-..qI