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Getmgtioes
O}e|tha
|edh
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O}
e|t
ha|e
dh
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Getmgtioes. O}e|th a|edhn}m dmse||hjjedh vh| je Di|mooi` Am`m|ej dm Getm|iejms Md}oeti~hs "dagm)* dm je _}lsmo|mte|e dmMd}oeoi` Lsioe* _mo|mte|e dm Md}oeoi` Vljioe.
_mo|mte|e dm Md}oeoi` VljioeEjh`sh J}keglih I|e{lej
_}lsmo|mte|e dm Md}oeoi` LsioeKhs Nm|`e`dh Ah`{jm{ _`obm{
Di|mooi` Am`m|ej dm Getm|iejms Md}oeti~hsGe|e Mditb Lm|`jdm{ \myms
Ohh|di`eoi` to`ioh'vmdeaaioeGe|e O|isti`e Ge|t`m{ Gm|oedhE`e Jijie \hgm|h {u}m{Ejmris Ah`{jm{ D}j{eidms
E}th|msVije| Dh`ek Oestijjh Ej~e|edh* oth| Ge`}mj Ae|oe Gh`tms*Mj~ie Vm||}su}e Grigh* Gia}mj `amj Jm` Bm|``dm{*Die`e Ce|i`e Bm|``dm{ Oest|h* Kmss Ge`}mj Bm|``dm{ _hth*Ejge \hse Oe`t` Jhkm|h* Ob|istie` E||mdh`dh De{
\m~isi` to`ioh'vmdeaaioe
`amj De`imj ~ije G}kioe* De`imje Esm|mt H|ti{ Ge|ti`m{*Ge|ae|ite _hth Gmdi`e
Esmsh|msJh}|dms Ege|h Gh|m`hJmtioie Ge|e dm jhs `amjms Ah`{jm{ E||mdh`dhsoe| Vejeoihs Omlejjhs
Ohh|di`eoi` mdith|iejDi|mooi` Mdith|iej* dagm(smvEjmke`d|h Vh|tijje dm L}m`
O}idedh mdith|iejMdqi` \hkes AeglheOitjeji Yeoeve`tji _m|~i` Ge|ti`m{
V|hd}ooi` mdith|iejGe|t` Ea}ije| Aejjmahs
Nh|geoi`Kssioe Lm|m`iom A`i{ \eg|m{* El|ebeg Gm`ms @m{*Ge|e dmj _ea|e|ih ~ije Ge|oiej* Geaeji Aejjmahs {u}m{
Vh|tedeDismh dm ohjmooi`; Oe|jhs Vejjmi|hIj}st|eoi` dm vh|tede; \hoh Vedijje
_ma}`de mdioi`*
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Je _mo|mte|e dm Md}oeoi` Vljioe* m` mj ge|oh dm je \mnh|ge I`tma|ej dm je Md}oeoi`Lsioe* vje`tme }` `}m~h m`nhu}m dm jil|hs dm tmrth* u}m beom `nesis m` mj t|elekh yjes eoti~idedms dm jhs ej}g`hs ve|e mj dmse||hjjh dm jes ohgvmtm`oies lsioes ve|e je
~ide y mj t|elekh. Mstm m`nhu}m i`oh|vh|e ohgh evhyh Tmo`hjhaes dm je I`nh|geoi`
y Ohg}`ioeoi` "TIO)* getm|iejms y mu}ivegim`ths e}dih~is}ejms m i`nh|gtiohs*
u}m k}`th oh` jes liljihtmoes dm e}je y msohje|ms* m`|iu}mom` mj oh`hoigim`th m` jes
mso}mjes gmrioe`es.
Mstm jil|h dm tmrth i`tma|e mst|etmaies i``h~edh|es ve|e mj t|elekh m` mj e}je*
dmge`de`dh ohgvmtm`oies dhom`tms u}m ev|h~mobm` disti`tes n}m`tms dm
i`nh|geoi`* }sh i`tm`si~h dm je tmo`hjhae* y ohgv|m`si` dm jes bm||egim`tes y jhs
jm`a}ekms u}m `ihs y k~m`ms }tiji{e` m` je shoimded dmj oh`hoigim`th. Ej gisgh
timgvh sm l}soe u}m jhs mst}die`tms edu}im|e` belijidedms ve|e ev|m`dm| vh| s}
o}m`te y u}m jhs ved|ms dm negijie ~ejh|m` y eohgvem` mj oeglih beoie je mso}mje
gmrioe`e dmj n}t}|h.
_} mjelh|eoi` ms mj |ms}jtedh dm }`e sm|im dm eooih`ms dm ohjelh|eoi` oh` gjtivjms
eoth|ms* ohgh je Ejie`{e vh| je Oejided dm je Md}oeoi`* eshoieoih`ms dm ved|ms dm
negijie* i`~mstiaedh|ms dmj oegvh dm je md}oeoi`* h|ae`isghs m~ej}edh|ms* gemst|hs
y ohjelh|edh|ms dm di~m|ses disoivji`es* es ohgh mrvm|ths m` dismh y mdioi`. Thdhs
mjjhs be` m`|iu}moidh mj oh`tm`idh dm mstm jil|h dmsdm disti`tes vjetenh|ges y e
t|e~s dm s} mrvm|im`oie. Je _mo|mte|e dm Md}oeoi` Vljioe jms mrtim`dm }` sm`tidh
ea|edmoigim`th vh| mj ohgv|hgish dmghst|edh oh` oede `ih |msidm`tm m` mj
tm||ith|ih gmrioe`h y oh` eu}mjjhs u}m sm m`o}m`t|e`
n}m|e dm j.
_mo|mte|e dm Md}oeoi` Vljioe
aV|msm`teoi`
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aOh`hom t} jil|h
5=5
aI`tma|h jh ev|m`didhEbh|e evjioe|s jhs oh`hoigim`ths oh`st|}idhs m` mj ljhu}m.\ms}mj~ m jhs sia}im`tms
v|hljmges.
Hlsm|~e mj sia}im`tm teljm|h y oh`tmste jes v|ma}`tes.
5. U} n|eooi` dmj teljm|h |mv|msm`te`
jhs o}ed|hs |hkhs8
d)56 666 # 9 666 # 466 # =6 # >
dm $ 5.O}`th di`m|h
tim`m m` thtej8
e) $ 4 52>
l)$ 4
o) $ 4
d)$ 4 5
?. Oe|jhs tim`m ? le||es dm ege|e`th.
U}im|m |mve|ti|jes m`t|m j y s}s t|ms egiahs. U} n|eooi` dm jes
le||es dm ege|e`th jm oh||msvh`dm e oede }`h8
e) 5 . .
Mj ev|m`di{ekm u}m edu}im|es ej t|eleke| oh` t} jil|h dm Getmgtioes tm l|i`de|bm||egim`tes ve|e de| shj}oi` e v|hljmges dm t} ~ide die|ie |mjeoih`edhs oh` jes
getmgtioes.
T} jil|h dm Getmgtioes oh`ste dm oi`oh ljhu}ms u}m* gmdie`tm jes eoti~idedms v|hv}mstes* tml|i`de` mst|etmaies ve|e dmse||hjje| t} vm`segim`th getmgtioh.
Oede ljhu}m oh`tim`m;
I`tma|h jh ev|m`didh
Dh`dm |mshj~m|s v|hljmgesevjioe`dh jh ev|m`didh m` mjljhu}m.
E}thm~ej}eoi`
Ve|e u}m ~ejh|msjhs ev|m`di{ekms yeotit}dms u}m besjha|edh d}|e`tm mj
ljhu}m.
Jmooih`ms
Oh` ~e|ies eoti~idedmsu}m jjm~e|s e oelh m`mu}ivh h dm ge`m|ei`di~id}ej.
M~ej}eoi`
M` je u}m tm de|s o}m`te dmj e~e`omdm t} ev|m`di{ekm d}|e`tm mj ljhu}mmjiaim`dh }`e |msv}mste oh||mote dm
o}et|h hvoih`ms.
99
@gm|hs `et}|ejms
\ms}mj~mv|hljmgesm`dh`dmsm}tijiommj~ejh| vhsioih ejdmjhs
daithsm` mjsistmgedmoigej.a5^ejh| vhsioih`ej
_ia`inioedh y }sh dm jhs gm|hs
Jh u}m oh`h{oh.
\ms}mj~m jhs v|hljmgessia}im`tms;
Mj th dm _mlesti` u}im|m ohgv|e| }`h dm msths jil|m|hs. O}j dm jhs t|ms jil|m|hs tim`m geyh| dmso}m`th8
Dm eo}m|dh oh` je i`nh|geoi` u}m bey m` jhs oe|tmjms*mj ohsth sm
v}mdm o}l|i| m` veahs smge`ejms.O}`ths veahs smge`ejms tm`d|e
u}m beom| mj th dm _mlesti` ve|e ohgv|e| mj jil|m|h E8
Dm o}`th sm|e mj jtigh veah8
Oh` o}j dm jhs t|ms jil|m|hs tm`d|e u}m beom| gs veahs smge`ejms8
Mj th dm _mlesti` ~ih u}m vhde disgi`}i| mj `gm|h dm veahs
smge`ejms si oede smge`e veaele jh mu}i~ejm`tm e dhs* t|ms h beste
o}et|h veahs k}`ths.Mso|ilm mj ghdmjh dm jil|m|h u}m oh||msvh`dm e
oede }`e dm jes o}m`tes u}m bi{h mj th dm _mlesti`.
4veahs dm$466?veahs dm$665ve ahdm$4=65ve ahdm$5=6
Jil|m|h
=veahs dm$466?veahs dm$
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(55 55;=? . .
Oede jmooi` i`oj}ym;
Oh`ti`e di~i|ti`dhtm ej timgvh u}m ev|m`dms m i`oh|vh|es `}m~es belijidedms u}m tm
vm|giti|` |mshj~m| v|hljmges e` gs i`tm|mse`tms%
Eja}`es ~moms m`oh`t|e|s jes smooih`ms sia}im`tms;
Deth i`tm|mse`tm
Tm v|msm`te i`nh|geoi`sh|v|m`dm`tm y e ~momsvhoh oh`hoide.
\mth
Oh` v|hljmgesi`tm|mse`tms u}mtim`m` }` geyh|a|edh dm dino}jted.
Oh`s}jte m`
Oh` i`nh|geoi` dh`dmvhd|s egvjie| y mkm|oite|t}s oh`hoigim`ths. Mjioh`h u}m jhs disti`a}mtm |mo}m|de mnmot}e| jelsu}mde m` i`tm|`mteohgveedh dm }` ed}jth.
Jh u}m oh`h{oh
Oh` eoti~idedmsve|e u}m |mo}m|dmsoh`hoigim`thsedu}i|idhs m` jmooih`ms*ljhu}ms h a|edhse`tm|ih|ms.
Mkm|oioihs y v|hljmgesoh` jhs o}ejmsdmse||hjje|s mst|etmaies yv|homdigim`ths ve|e de|shj}oi` e v|hljmges u}msm tm v|msm`te` te`th m` jemso}mje ohgh m` je ~idedie|ie.
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a`diomLjhu}m I
V | m s m ` t e o i ` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?Oh`hom t jil|h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Ev|m`di{ekms msvm|edhs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5 ^ejh| vhsioih`ej . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 < Ohgve|h gmdides dm tevmtms y jisth`ms. . . . . . . . . . . . . . . . . . . . . . . . 54 ? O e ` t i d e d m s m u } i ~ e j m ` t m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Ae`e| h vm|dm| oh` je edioi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Oejo}je n|eooih`ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5< Jhs v|moihs oh` om`te~hs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =6 5? _ } o m s i h ` m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =? 54 G}jtivjioh vh| 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . => 5= _}ge h |mste dm n|eooih`ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . =2 5> \ms}mj~h v|hljmges y }tiji{h je di~isi` . . . . . . . . . . . . . . . . . . . . . . . . >5 51 Nia}|es y o}m|vhs amhgt|iohs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >? 52 Idm`tinioh o}m|vhs amhgt|iohs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >= 59 `a}jhs m` }` o|o}jh8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . >9
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?9 Dm }` gmt|h vh| }` gmt|h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5?2 46 Jedh vh| jedh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 45 Jh gs v|hleljm ms u}m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 4< Jhs {eveths dm ghde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
I`tma|h jh ev|m`didh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5=5M~ej}eoi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5= 4? Mj |mve|th . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5=1 44 Mj ohoim`tm ms8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>6 4= O}`th u}mde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>? 4> N|eooih`ms dm gmt|hs ohgvjmths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>= 41 O}`ths v}mdh ohgv|e|8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5>2 42 O}`th nejte ve|e 568 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
49 Jhs t|i`a}jhs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51? =6 J e s | m o t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 =5 Jes ohgli`eoih`ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
I`tma|h jh ev|m`didh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525M~ej}eoi` . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5266) # " ) # " ) 7
" ) # " ) # " ) # " ) 7
5. Nh|gm` mu}ivhs.
Jme` jes sit}eoih`ms v|hv}mstes m` oede }`h dm jhs i`oishs. Dmsv}s* e`ejiom` jes mrv|msih`ms u}m sm m`o}m`t|e` m` mj sia}im`tm
|mo}ed|h. \mjeoih`m` je mrv|msi` u}m si|~m ve|e |mshj~m| oede }`e dm jes sit}eoih`ms
v|hv}mstes. Mso|ile` dmlekh dm oede mrv|msi` mj i`oish u}m jm oh||msvh`dm. Oejo}jm` mj |ms}jtedh dm oede mrv|msi`. E`htm` mj |ms}jtedh oh||moth ej ni`ej dm oede i`oish.
5
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5555
l) Nm|`e`dh t|e`svh|te ohstejms dm `e|e`kes m` s}oegi`. Jjm~e }` ohstej oh` 5 smooih`ms dm 266esim`ths oede }`e3 4 oh` 466 esim`ths oede }`e y }`e
oh` lhjhs |hkhs* 5 lhjh e`e|e`kedh y > dm ohjh|
~m|dm* o}`ths v}`ths sm ae`e`8
n) M` }`e vevmjm|e sm m`t|mae|h` jhs sia}im`tmse|to}jhs; 4 oekes oh` 266 ahges oede }`e3 = veu}mtms
oh` lhjses oh`
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5
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5?5?
?. \meji{e jes dmsohgvhsioih`ms dm jhs sia}im`tms gm|hs.e) 1 2
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5454
@gm|hs n|eooih`e|ihs\ms}mj~m v|hljmges m` jhs u}m sm |mu}im|e mrv|mse| y ohgve|e|gmdides dm jh`ait}d* oeveoided* }tiji{e`dh n|eooih`ms* m` nh|ge
`}g|ioe y a|nioe.
_ia`inioedh y }sh dm jhs `gm|hs
a>5>
Jmm jes v|ma}`tes y s}l|eye je |msv}mste oh||mote. Mgvjme jes ti|es dmj
\moh|teljm 5 ve|e ey}de|tm e |mshj~m| h ~m|inioe| t} |msv}mste.
Dm jes sia}im`tms ti|es o}j ms je smooi` gs oh|te8
_mooi` oh` 5< _mooi` oh`
Dm thdes jes sia}im`tms ti|es o}j ms je smooi` gs je|ae8
_mooi` oh`
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5151
Jh u}m oh`h{oh. \ms}mj~m mjv|hljmge sia}im`tm.
Mrv|mse dm t|ms ge`m|es disti`tes
ogh veae|es je oe`tided smejede
m` oede e`}`oih si t}~im|es gh`mdes
dm 56*
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52252
5. M` }`e tim`de dm d}joms tviohs gmrioe`hs* dh` J}is* mj d}mh* s}mjm vmdi| e s}sojim`tms u}m jm vea}m` mj igvh|tm mreoth dm s} ohgv|e* v}ms `}`oe tim`m oeglih.
\m`mtm oh` }` ohgvem|h y oh`tmstm` jes v|ma}`tes sia}im`tms.
O}`th sm bel| dm veae| vh| }`e ohoede y }` oeghtm8 Oh` u} gh`mdes h lijjmtms veae|e` si u}im|m` }se| mj g`igh `gm|h dm
gh`mdes8 _i Ge`}mj u}im|m ohgv|e| dhs geoe||h`ms y }`e `e|e`ke* o}`th bel| dm
veae|8
Ogh beom ve|e veae| oh` mj g`igh `gm|h dm gh`mdes8
_i sjh o}m`te oh` dhs gh`mdes dm 56 vmshs* o}`th jm nejte ve|e ohgvjmte|8 Oh` o}`tes gh`mdes dm 56 vmshs y dm 56 om`te~hs v}mdm Ge`}mj |meji{e| s}
veah8 Keigm ohgv|e smis oeje~m|es dm e{oe| y smis veje`u}mtes* vm|h ve|e veae| sjh
tim`m }` lijjmtm dm =6 vmshs. O}`th di`m|h jm shl|e h jm nejte8
@e|e`kes$2.=6 o(}
Ohoedes
$?.=6 o(}
Geoe||h`ms
$1.66 o(}
Oeghtms
$=.=6 o(}
Veje`u}mtes
$4.=6 o(}
Oeje~m|es
$
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5959
Oe|gm` tim`m $9=.=6 y oh` mjjhs u}im|m ohgv|e| d}joms. O}`ths y dm o}jms d}joms dm
je vai`e e`tm|ih| v}mdm ohgv|e| ve|e aeste| mreotegm`tm mse oe`tided dm di`m|h8
U} tivh dm d}joms v}mdm ohgv|e| Nm|`e`de si u}im|m aeste| mreotegm`tm $5
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6 cijgmt|hs*
o}`th di`m|h aeste| m` ohgl}stiljm8
Ebh|e ohgvjmte je sia}im`tm telje y ~m|inioe si t} |ms}jtedh ms oh||moth.
Jit|hs Ohsth Cijgmt|hs
5 $9.9> 5
5= 526
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>
Jh u}m oh`h{oh. ]tiji{e mj \moh|teljm < ve|e nh|ge| jhso}m|vhs amhgt|iohs. Dmsv}s* mso|ilm s} `hgl|m m` mjjhs.
O}m|vhsMrvjh|e o}m|vhs amhgt|iohs
ve|e e`eji{e| dinm|m`tms v|hvimdedms.
Oh`st|}ooi` dm o}m|vhs
amhgt|iohs
a>Nia}|es
Ebh|e* m` je sia}im`tm telje* mso|ilm jhs deths u}m nejte`.
O}m|vh amhgt|ioh@gm|hdm oe|es
@gm|hdm ~|tioms
@gm|hdm e|istes
V|isget|ie`a}je|
V|isge|mote`a}je|
O}lh
V|isgevm`teah`ej
V|isgebmreah`ej
Vi|gidmo}ed|e`a}je|
Hotemd|h
Oh`sm|~e y a}e|de t}s o}m|vhs amhgt|iohs3 jhs }tiji{e|s m` je sia}im`tm jmooi`.
Vai`es 595'599
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?66?6
M`t|m mj o}lh y mj v|isge o}ed|e`a}je|* o}j tim`m geyh| `gm|h dm oe|es8
O}`tes oe|es |mote`a}je|ms tim`m mj v|isge vm`teah`ej8 O}`tes oe|es m` nh|ge dm vm`tah`h tim`m mstm v|isge8
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?5?5
U} tim`m` m` ohg` jes oe|es dm msths o}m|vhs amhgt|iohs8
O}`ths oe|es |mote`a}je|ms tim`m` jhs sia}im`tms o}m|vhsamhgt|iohs8 V|isge t|ie`a}je| V|isge |mote`a}je|
V|isge vm`teah`ej V|isge bmreah`ej M` jhs o}m|vhs e`tm|ih|ms* o} tes oe|es h sh` |mote`a}je|ms8
\mthO}`tes oe|es |mote`a}je|ms tim`m }` v|isge hoteah`ej8
O}e`dh dhs nia}|es tim`m` jes gisges
jh`ait}dms* jhs gisghs `a}jhs y je
gisge nh|ge sh` oh`a|}m`tms.
]` vhjah`h |ma}je| ms }`e nia}|e vje`eo}yhs jedhs tim`m` je gisge jh`ait}d y s}s
`a}jhs i`tm|`hs tim`m` je gisge gmdide.
Oh` evhyh dm s} v|hnmsh| dmsoe|a}m` mj v|ha|ege Vhjy u}msm m`o}m`t|e m` je sia}im`tm di|mooi`;bttv;((qqq.vmde.ohg(dhq`jhed(Oh` mstm v|ha|ege* mrvjh|m` jhs sjidhs vjet`iohs u}msm i`oj}ym`* es ohgh s}s dmse||hjjhs vje`hs. M` mu}ivhs*smjmooih`m` }`h dm jhs dmse||hjjhs vje`hs ve|e oh`st|}i| mjo}m|vh amhgt|ioh m` vevmj.
Oh`s}jte m`...
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?
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????
5. \m`mtm oh` }` ohgvem|h. Jmm m` ~h{ ejte jes i`st|}ooih`msu}m s}am|istm ve|e jjmae| e }`h dm jhs j}ae|ms smjmooih`edhs* si`
gm`oih`e| dm u} j}ae| sm t|ete. T} ohgvem|h di| e u} j}ae| tm
|mnm|istm. N}m oh||moth mj j}ae| u}m gm`oih` t} ohgvem|h8 Ebh|e ms mj t}|`h dm t} ohgvem|h. Ejt|`m sm m` je jmot}|e*
dm ge`m|e u}m jhs dhs v}mde` jmm| jes t|eymoth|ies e t|ms jhs
j}ae|ms smjmooih`edhs.
_}vh`aeghs u}m ~i~ms m` je oese `gm|h 562. Mso|ilm e
oh`ti`}eoi` ogh jjmae|es e oede }`h dm t}s j}ae|ms v|mnm|idhs.
Je |hse dm jhs
~im`ths `hs vm|gitm
jhoeji{e| m` }`
geve jhs v}`ths
oe|di`ejms; @h|tm*
_}|* Mstm y Hmstm.
O}e`dh sm de` i`st|}ooih`ms ve|e jjmae| e }` j}ae| dmlm
beom|sm oh` oje|ided y v|moisi`. Ms `momse|ih i`dioe|mj `hgl|m dm jes oejjms* `gm|h dm o}ed|es u}m tim`m`
u}m |moh||m|sm beoie mj @h|tm h _}|* Mstm } Hmstm. E ~moms
|ms}jte tij gm`oih`e| j}ae|ms oh`hoidhs ohgh |mnm|m`oie*
vh| mkmgvjh* je iajmsie h mj gm|oedh.
Deth i tm|mse`tmJe |hse dm jhs ~im`ths tegli` msoh`hoide ohgh je |hse `}tioe3 ejMstm sm jm oh`hom tegli` ohghH|im`tm h Jm~e`tm y ej Hmstm*ohgh Hooidm`tm h Vh`im`tm.
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?4?4
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?=?=
_i mst` m` je mso}mje* ogh be|e` ve|e jjmae| ej Oestijjh dm
Obev}jtmvmo8
_hl|m mj vje`h dm je vai`e e`tm|ih|* smejm` oh` }`e j`me dmohjh| |hkh o}j sm|e mj |moh||idh u}m |meji{e|e` ve|e t|esjede|sm
dmsdm je mso}mje beste mj Oestijjh dm Obev}jtmvmo. Ohgve|m` s} |moh||idh oh` mj u}m bioim|h` ht|es ve|mkes. O}j n}m je hvoi` gs oh|te ve|e jjmae|8
]` a|}vh dm smis ej}g`hs dmoidi ~isite| mj G}smh @eoih`ej dm
E`t|hvhjhae. Es u}m hlsm|~e|h` mj vje`h y t|e{e|h` }`e |}te.
Ogh bioim|h` ve|e jjmae| si ve|tim|h` dm je mso}mje8
G}mst|m` s} |msv}mste e thdh mj a|}vh y dmsv}s dmoide` o}j
ms mj oegi`h gs oh|th ve|e jjmae| ej g}smh. G|u}m`jh m` mj
vje`h.
Ve|tim`dh dmj E}dith|ih @eoih`ej* dmso|ilm vh| jh gm`hs dhs
t|eymoths e sitihs igvh|te`tms u}m `h sm beye` gm`oih`edh e`.
Dm jhs t|eymoths u}m mjmaistm* o}j ms mj gs je|ah8
O}j ms mj gs oh|th8
\mthE ve|ti| dmj vje`h dmtm|gi`e m`t|m u} oejjms
sm m`o}m`t|e je msteoi` dmj Gmt|h E}dith|ih.
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?>>?>
\mjeoih`ms dm v|hvh|oih`ejided\ms}mj~m v|hljmges dm ~ejh| nejte`tm m` jhs u}m sm de mj ~ejh|
}`ite|ih* h sm v|ma}`te vh| j* gmdie`tm disti`ths v|homdigim`ths.
E`jisis dm je i`nh|geoi`
a9Mj~ejh|
nejte`tmJh u}m oh`h{oh. \ms}mj~m jhssia}im`tms v|hljmges.e) J}ise t|eleke m` }`e nl|ioe dm
oegises. Ve|e oede oegise dm
ed}jth sm `momsite` 5= lhth`ms.
Ey}de e J}ise e m`oh`t|e|
jes oe`tidedms u}m nejte` m`je sia}im`tm telje. Dmsv}s*
oh`tmste jes v|ma}`tes.
Oegises dm ge`ae je|ae ve|e ed}jth
Oe`tidedms dm oegises 5 > 54 1= 5>6
Oe`tidedms dm lhth`ms 5=
O}`ths lhth`ms sm momsite` ve|e oh`nmooih`e| 56 oegises8 O}`ths lhth`ms sm `momsite` ve|e lhth`ms ve|e 2 oegises.Ey}de e J}ise e m`oh`t|e| jes oe`tidedms u}m nejte` m` je sia}im`tm
telje. Dmsv}s* oh`tmste je v|ma}`te.
Oegises ve|e `ih
Oe`tidedms dm oegises 5 2 56 5 446
U} v}mdm beom| J}ise ve|e selm| o}`ths lhth`ms sm `momsite` ve|e
546 oegises dm `ih8
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?1?1
5. M` mu}ivh* |ms}mj~e` mj v|hljmge sia}im`tm.
Je ohoi`e dm dh` Lmth ms neghse vh| s}s |iohs teohs dm ohobi`ite vilij.
E`htm` mj deth u}m nejte m` oede }`e dm jes sia}im`tms te|kmtes.
H|dm` dm ? teohs
vh| $
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?22?2
\mthJhs ej}g`hs dm o}e|th a|edh ohgv|e|h` n|}te. Eydm`jms e ohgvjmte|
mj sia}im`tm o}ed|h ve|e selm| o}`th ohgv|e|h`;
\m`e`sm m` mu}ivhs y
|ms}mj~e` mj v|hljmge sia}im`tm.
A|}vhCijha|eghs vh|
oeke
Vim{es m` thtej
Ge`{e`es Vm|es D}|e{`hs
4h. E 56 =6
4h. L 2 42 26
4h. O 5< >6
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?9?9
Oh` lesm m` je i`nh|geoi`dmj e`}`oih |msvh`de` jes
v|ma}`tes;
O}`th o}mste` t|ms oekes dm
vish jegi`edh dm > gg dm
a|hsh|8
O}`tes oekes dm vish
jegi`edh dm > gg o}l|m` }`
vish dm 5> g
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46646
5. \m`mtm oh` }` ohgvem|h y |mejiom` jh u}m smi`dioe m` oede oesh e ve|ti| dm je i`nh|geoi` dm je
igeam`.
U} oe`tided dm ea}e oh`tim`m je lhtmjje8 O}`ths gijia|eghs "ga) dm shdih oh`tim`m8
E u} oe`tided dm ea}e oh||msvh`dm je
i`nh|geoi` `}t|igm`tej dm je mtiu}mte8
M` je igeam` dm je i{u}im|de eve|mom je mtiu}mte
dm }` o}edm|`h* hls|~eje y oh`tmste jesv|ma}`tes;
EA]E _IGVJM VHTELJM
OH@T. @MTH 5.= J
I@NH\GEOI@ @]T\IGM@TEJ
Vh| 566 gJ;
Oh`tm`idh m`m|atioh 6 coej
Oe|lhbid|eths 6 a
V|htm`es 6 a
A|eses "jvidhs) 6 a
_hdih = ga
O]EDM\@HN5
566BHKE_
O]ED\H1gg
VevmjLh d=>a
(g66 gs oe|e. O}`th jm
ohst je lioiojmte e _e`d|e8
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4 ms;
e) 56 666 # 966 # 4= # >
l) 56 666 # 9 666 # 4= # >
o) 56 666 # 966 # 466 # =6 # >
d) 56 666 # 9 666 # 466 # =6 # >
dm $ 5. O}`th di`m|h
tim`m m` thtej8
e)$ 4 52>l)$ 4 o)$ 4 d) $ 4 5
?. Oe|jhs tim`m ? le||es dm ege|e`th.
U}im|m |mve|ti|jes m`t|m j y s}s t|ms egiahs. U} n|eooi` dm jes
le||es dm ege|e`th jm oh||msvh`dm e oede }`h8
e) 5
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4?4?
4. \hd|iah ~m`dm m` s} vevmjm|e jhs
hlkmths sia}im`tms;
Ohgvjmte je telje dil}ke`dh m` mj jtigh|mo}ed|h mj di`m|h u}m jm shl|e h jm nejte e
oede u}im` ve|e ohgv|e| mj hlkmth.
Di`m|h u}mtim`m oede
`ih
Hlkmthu}m dmsmeohgv|e|
Jm nejte h jm shl|e
Gia}mj; $5>1 Oeke dm ohjh|ms
\}tb; $1< Jil|h
Mstbm|; $
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4444
=. _mjmooih`e je
nia}|e u}m tim`m
shjegm`tm }` ve|
dm jedhs ve|ejmjhs.
e)
o)
l)
d)
>. Dhe J}vite }tiji{e jhs sia}im`tms i`a|mdim`tms ve|e v|mve|e| }` ve`.
U} oe`tided dm i`a|mdim`tms `momsite|e ve|e v|mve|e| ? ve`ms8
Oe`tided I`a|mdim`tm
< te{es E{oe|
566 a|eghs Ge`tmu}ijje
4 vim{es B}m~h
? vim{es @e|e`kes
5 cijha|egh Be|i`e
e) > te{es dm e{oe|
?66 a dm ge`tmu}ijje
9 vim{es dm b}m~h
5< e|e`kes
4 ca dm be|i`e
l) > te{es dm e{oe|
?66 a dm ge`tmu}ijje
5< vim{es dm b}m~h
9 `e|e`kes
? ca dm be|i`e
o) > te{es dm e{oe|
526 a dm ge`tmu}ijje
9 vim{es dm b}m~h
9 `e|e`kes
? ca dm be|i`e
d) > te{es dm e{oe|
526 a dm ge`tmu}ijje
5< vim{es dm b}m~h
5< e|e`kes
4 ca dm be|i`e
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4=4=
aE}thm~ej}eoi`M` jes oesijjes oh||msvh`dim`tms* ge|oe oh` }`e vejhge jh u}m gmkh||mnjmkm jh u}m vim`ses.
Oh`tm`idhs v|homdigm`tejms
_imgv|m jh
beah
Jh beah e
~moms
Dinoijgm`tm
jh beah
\ms}mj~h v|hljmges u}m igvjioe`m`oh`t|e| mj ~ejh| nejte`tm m`
|mjeoih`ms dm v|hvh|oih`ejided.
Idm`tinioh jes ve|tms u}mohgvh`m` jhs o}m|vhs
amhgt|iohs.
Ohgv|m`dh je i`nh|geoi` u}m smv|msm`te m` di~m|shs vh|tedh|ms.
Oh`tm`idhs eotit}di`ejms
_imgv|m jh
beah
Jh beah e
~moms
Dinoijgm`tm
jh beah
Gm a}ste t|eleke| m` mu}ivh.
O}e`dh gis ohgvem|hsve|tioive`* mso}obh oh` |msvmth
s}s hvi`ih`ms.
O}e`dh t|elekh m` mu}ivh*
ev|m`dh dm gis ohgvem|hs.
O}e`dh t|elekh m` mu}ivh* mnmothgmkh| jes ohses u}m si jes jjm~h e
oelh i`di~id}ejgm`tm.
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hu}mII
Ev|m`di{ekms msvm|edhs \ms}mj~mv|hljmgesdh`dmdmtm|gi`m
u}n|eooi`ms}`eve|tmdededm}`e
gea`it}d Jmm*mso|ilmyohgve|e`gm|hsdmoigejms
besteom`tsighsm`oh`tmrthsdmdi`m|h
ygmdioi`
\ms}mj~mv|hljmgesu}mmgvjme`s}ges
h|mstesdmn|eooih`ms
\ms}mj~mv|hljmgesu}mi`~hj}o|e`
disti`thssia`inioedhsdmjedi~isi`dm
`gm|hs`et}|ejms
Idm`tinioeo}m|vhsamhgt|iohsgmdie`tmjedmso|ivoi`dms}soe|eotm|stioes
]tiji{emjt|e`svh|tedh|ve|egmdi|
`a}jhs
\ms}mj~mv|hljmgesdm~ejh|nejte`tm
gmdie`tmmjojo}jhdmj~ejh|}`ite|ihh
evjioe`dhv|hvimdedmsdm}`e|mjeoi`dm
v|hvh|oih`ejided
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41
Igeai`e u}m mj |mot`a}jh
ms je o}e|te ve|tm dm }`e
veje`u}mte dm oeoeb}etm.
Dil}ke je le||e ohgvjmte.
5. Hlsm|~e jes igam`msy oh`tmste jes v|ma}`tes.
Nia}|eE Nia}|eL
Nia}|eO Nia}|eD
M` u} nia}|e h nia}|es mst
ohjh|mede je gited dm je s}vm|nioim8
M` u} nia}|e h nia}|es mst
ohjh|mede je tm|om|e ve|tm dm je
s}vm|nioim8
M` u} nia}|e h nia}|es mst vi`tede
je o}e|te ve|tm dm je s}vm|nioim8
@gm|hsn|eooih`e|ihs
Oejo}je n|eooih`ms dm gea`it}dms oh`ti`}es "jh`ait}d*s}vm|nioim dm nia}|es) y* |mov|hoegm`tm* msteljmomu} n|eooi` ms }`e ve|tm dede dm }`e gea`it}d.
_ia`inioedhy}shdmjhs`gm|hs
a55Oejo}je
n|eooih`msJh u}m oh`h{oh. \meji{e je eoti~ided sia}im`tm.
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42
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49
?E oh`ti`}eoi` sm dmso|ilm` eja}`es dm jes ~m`te`es dm jes oelees dmj|e`obh dh`dm ~i~m Ge}|ioih. Dil}ke m` jhs msveoihs }`e |mv|msm`teoi`
dm oede ~m`te`e.
]`e ~m`te`e |mote`a}je| di~idide
bh|i{h`tejgm`tm m` ? ve|tms ia}ejms y
sjh }`e tm|om|e ve|tm sm v}mdm gh~m|
ve|e el|i| h om||e|. Je ~m`te`e gidm
4 g dm je|ah y 5 g dm ejth. O}`th
gidm je ve|tm u}m sm v}mdm el|i| h
om||e|8
]`e ~m`te`e u}m gidm 526 og dm je|ah y
=6 og dm ejth y tim`m nh|ge |mote`a}je|
mst di~idide m` 9 ve|tms ia}ejms. O}`th
v}mdm gmdi| oede }`e dm jes ve|tms* ve|e
u}m thdes sme` ia}ejms8
]`e ~m`te`e dm
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=6
Ve|e
o}eju}im|
vm|sh`e
$
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=
G}jtivjioh
vh|
56
G}jtivjioeoi`ydi~isi`
Dmtm|gi`e |majes v|otioes ve|e g}jtivjioe||videgm`tm vh| 56* 566* 5666* mtotm|e.a54
_ia`inioedhy}shdmjeshvm|eoih`ms
M` mj sej` dm _hne mst` h|ae`i{e`dh }`e |ine dm < veu}mtms
dm v|ha|eges dho}gm`tejms m` nh|geth D^D. Mj lhjmth ve|e
ve|tioive| m` je |ine dmj v|igm| veu}mtm o}mste $2.66 y mj dmj
sma}`dh* $5?.66. Jh u}m hltm`ae` dm je ~m`te dm jhs lhjmths*
}`e ~m{ u}m e mse oe`tided sm jm |mstm jh u}m ohste|h` jhs dhs
veu}mtms* sm }tiji{e| ve|e |meji{e| }` oh`~i~ih e ni` dm eh. M`
thtej sm igv|igim|h` =66 lhjmths ve|e oede }`h dm jhs veu}mtms.
O}`th di`m|h hltm`d|` dm je ~m`te dm jhs lhjmths8
Mrvjioe ogh hlt}~istm mj |ms}jtedh. Mj v|igm| de ~m`dim|h` 56 lhjmths ve|e mj v|igm| veu}mtm y 566
lhjmths ve|e mj sma}`dh veu}mtm. O}`th di`m|h k}`te|h` msm
de8
Jh u}m oh`h{oh. Dm nh|gei`di~id}ej* |ms}mj~m je
sia}im`tm eoti~ided.
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=1
Ve|e mj u}i`th de sjh jms u}mdele` 56 lhjmths dmj sma}`dh veu}mtm
y 566 lhjmths dmj v|igm| veu}mtm. O}`th di`m|h k}`te|h` ve|e mj
u}i`th de8
Dmso|ilm dm u} ge`m|e hlt}~istm je |msv}mste.
_i mj v|igm| veu}mtm ohst $266.66 y mj sma}`dh* $5 ?66.66* o}`th
di`m|h u}md ve|e h|ae`i{e| mj oh`~i~ih8
\mth
V|igm|h dmoidi|` u}i` ohgim`{e je eoti~ided y oh`ti`}e| mj ohg'
vem|h dm je dm|mobe.
Oede k}aedh| je`{e| jhs dedhs y mj `gm|h u}m hltm`ae dm s}ge|
jhs v}`ths dm eglhs sm| g}jtivjioedh vh| mj `gm|h u}m sejae ej
ai|e| je vm|i`hje.
E`hte mj |ms}jtedh dm g}jtivjioe| msths dhs `gm|hs.
Mkmgvjh; Ej je`{e| jhs dedhs sm hltim`m < y ej ai|e| je vm|i`hje sm hl'
tim`m 56* vh| jh u}m mj |ms}jtedh ms
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=2
V|hljmgesediti~hs
\ms}mj~m v|hljmges u}m igvjiu}m` s}ge h |mste dm n|eooih`ms* m`oeshs sm`oijjhs* oh` disti`ths v|homdigim`ths. Mjelh|e m i`tm|v|mte
|mv|msm`teoih`ms a|nioes dm jes n|eooih`ms.
_ia`inioedhy}shdmjeshvm|eoih`ms
a5=_}ge h |mstedm
n|eooih`msJh u}m oh`h{oh. \meji{e je sia}im`tm eoti~ided ymso|ilm m` t} o}edm|`h jhs ojo}jhs u}m mnmot}estm.
Mj dmvh|tm ne~h|ith dm Geade ms mj n}tlhj y ohgh
thdhs m` s} negijie jh selm`* simgv|m jm |maeje`
lejh`ms y vmjhtes* u}m a}e|de m` s} oese. Ve|e
h|dm`e|jhs jhs eohghd vh| ohjh|ms y tegehs. Ej
tm|gi`e| sm dih o}m`te dm u}m;
5= dmj thtej dm jhs lejh`ms* sh` dm ohjh| |hkh* sh` gs obioes u}m }` lej` dm
n}tlhj v|hnmsih`ej y 5> ms gs a|e`dm. Mj |msth sh` dmj
gisgh tegeh u}m }` lej`.
U} n|eooi` |mv|msm`te` jhs lejh`ms dm ohjh|
lje`oh dmj thtej dm lejh`ms8 O}j ms je n|eooi` u}m |mv|msm`te jes vmjhtes u}m
sh` dmj gisgh tegeh u}m }` lej`8 U}m hvm|eoih`ms |meji{estm ve|e oh`tmste| jes
v|ma}`tes8 Dmso|ilm jh u}m beoms ve|e |meji{e| s}ges dm
n|eooih`ms.
Dmso|ilm jh u}m beoms ve|e |meji{e| |mstes dm
n|eooih`ms.
8/6/2019 Matemticas 4 RIEB Alumno 2011-2012
61/202
=9
5\ms}mj~m jhs mkm|oioihs sia}im`tms;
e) Ohjh|me jes s}ges u}m sh` ia}ejms e .
l) _i jh `momsites* }se jes ti|es dm je eoti~ided < ljhu}m 5 ve|eoh`tmste| mj sia}im`tm mkm|oioih. Hlsm|~e mj mkmgvjh;
E = ti|es dm 52 dm jh`ait}d jm u}iteghs ? ti|es dm52 * m`th`oms `hs
u}mde` < ti|es dm 52 * oede }`e.
54 #
54 7
5? #
54 7
54 #
52 7
5> #
7
5? #
5> 7
?2 #
#
?> 7
?4 #
?4 7
8/6/2019 Matemticas 4 RIEB Alumno 2011-2012
62/202
>6
7
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