The Reason: Other Side

8/12/2019 The Reason: Other Side

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R`j Tjfskm? Kt`jr Xibj

Dy

Ifm Djfrbsljy

Hkpyria`t 4362 dy Ifm Djfrbsljy

IXDM? 910-6-864-88255-8


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Hljfrima f ejw t`imas up fdkut R`j Tjfskm, R`j Tjfskm? Gkvima Km, fmbXibjmktjs Ekr R`j Tjfskm

Ekr t`j Xfaittfrius vjhtkr, wj tkkn t`j pfrfgjtjr, t, tk dj zjrk. Ekr t`j Xhutugvjhtkr, wj usjb t`j sfgj t`rjj jquftikms, Mjptumj, Zrfmus, Jfrt`, tk gfnj fm

jquftikm ke t`j plfmj, dut wj bib mkt sjt t 7 3, dut rft`jr jligimftjb t. @kwjvjrwj rjeljhtjb t`j bjhlimftikm fdkut t`j jquftkr dy sfyima it wfs mjaftivj 63bjarjjs imstjfb ke 63 bjarjjs. Ie yku ljfvj it fs tjm bjarjjs, t`j vjhtkr pkimts

tk fm kpjm hlustjr im Fquilf, MAH 5180. Q`jm wj bjrivjb t`j Sjafsus vjhtkr,wj swith`jb t`j x hkkrbimftj wit` t`j y hkkrbimftj, jssjmtiflly rjkrijmtima t`jhkkrbimftj systjg. R`j hkmvjmtikmfl usj ke

f hkkrbimftjb systjg hkgjs erkg rfmbkg bjeimitikm fmywfy, sk wj bkm "t nmkw

w`ih` fm jxtrftjrrjstrifl wfmts us tk usj.


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R`ft kur 9/:, :/8, 4,... `fvj mkrgfl vjhtkr pkimtima tk t`jHkmstjllftikm Uulpjhulf is siamieihfmt djhfusj, fs Qinipjbifwritjs?

Uulpjhulf is flsk `kgj tk

@B 609188 d, kmj ke t`j hlksjst jxtrfsklfrplfmjt hurrjmtly djima stubijb dy t`jXpitzjr Xpfhj Rjljshkpj. Km 64

Ouly 4331 t`jEimfmhifl Rigjs(Lkmbkm) rjpkrtjb t`ft t`j h`jgihfl

siamfturj ke wftjr vfpkur wfs bjtjhtjb im t`j ftgksp`jrj ke t`is

plfmjt. Flt`kua` @B 609188d wit` ftgksp`jrih tjgpjrfturjs risima

fdkvj 6,333 H is efr erkg djima `fditfdlj, t`is eimbima imhrjfsjs t`jlinjli`kkb t`ft wftjr, fm jssjmtifl hkgpkmjmt ke liej, wkulb dj ekumb

km f gkrj Jfrt`-linj plfmjt im t`j euturj.


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@kmima Im Km R`j FJ-8:

Gy sjfrh` ekr w`ft t`j jssjmhj ke t`j FJ-8: fmtjmmf is, t`ft hkmhjpt w`jrjim fAypsy s`fgfm gfbj gj tjljpftìh wit` ìg, `fs eimflly djjm rjflizjb? I fhtuflly

nmjw twk Gfmujl"s, mkt oust twk dy t`j sfgj mfgj, dut ibjmtihfl im spirit, fmbbifgjtrih kppksitjs im pjrskmflity> kmj f s`fgfm ft kmj jmb ke t`j Xfhrkgkmtj,t`j kt`jr ft t`j kt`jr jmb ke t`j Xfhrkgkmtj. Mjvjr bib I nmkw t`jg tk dj ft t`jsfgj plfhj ft t`j sfgj tigj, kr jvjm tk dj fwfrj kmj ke t`j kt`jr. It im efhthkulb dj it is kmj pjrskm w`k hfm dj ft twk bieejrjmt plfhjs ft kmhj. Q`ft wjfrj bjflima wit` `jrj, im tjrgs ke p`ysihs, is qufmtug tjljpkrtftikm, kr qufmtugjmtfmaljgjmt? It is stftjb f pfrtihlj hfm imstfmtfmjkusly jxist im fmkt`jr plfhj,fmb w`jt`jr t`j tjljpkrtjb pfrtihlj fhtuflly ougpjb erkg kmj plfhj tk fmkt`jr

imstfmtfmjkusly kr kmj pfrtihlj vfmis`jb wit` f sjpfrftj, kr ibjmtihfl kmj, djimarjdkrm im fmkt`jr plfhj gfnjs mk bieejrjmhj. Flsk it is jmtfmaljgjmt? Rwkpfrtihljs hkllibj sjttima up imitifl hkmbitikms, fs t`jy trfvjl fpfrt jfh` dj`fvjsfhhkrbima tk t`j stftj ke t`j kt`jr suaajstima imstfmtfmjkus hkggumihftikmdjtwjjm t`jg kvjr bistfmhj jvjm t`kua` tìs viklftjs t`j hksgih spjjb ligit ket`j spjjb ke lia`t. Luhnily, t`jrj is skgj imbihftikm t`ft Gfmujl will dj aivima fljhturj, Im Xpfim, fdkut t`j FJ-8: Fmtjmmf. It is gy `kpj t`ft it will dj kmykutudj.


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Duilbima R`j Fmtjmmf

I `fvj sfib frkumb 6993 t`ft Gfmujl `fb gj `jlp ìg imstfll fm fmtjmmf ekr tjljvisikm

rjhjptikm ft ìs mjp`jws `kusj im t`j Xfhrkgkmtj (Aypsy Hfvjs). Im t`j fht ke bkima

tìs I djhfgj tjljpftìh wit` ìg. Qj hfll it t`j FJ-8: fmtjmmf erkg 4336? F Xpfhj

Kbyssjy. @kwjvjr t`j jxtrftjrrjstrifls umbjrgimjb t`j spjll im f plfm t`ft wfs imitiftjbjvjm djekrj I nmjw Gfmujl. Im 6911 t`jy sjmt f trfmsgissikm erkg t`j birjhtikm ke t`j

hkmstjllftikm Xfaittfrius t`ft wfs rjhjivjb dy t`j Xjfrh` Ekr Jxtrftjrrjstifl Imtjlliajmhj

(XJRI). It wfs R`j Aypsy X`fgfmisg ke Gfmujl t`ft ljfb gj tk t`j bishkvjry t`ft t`j

siamfl s`kulb rjpjft itsjle km Fuaust 6:, 436:. Rìs afvj gj t`j ibjf ke duilbima f rfbiktjljshkpj, jssjmtiflly fm fmtjmmf mkt umlinj t`j kmj I `jlpjb Gfmujl imstfll, sk I hkulb

rjhjivj t`j prjbihtjb gjssfaj. It is Ouly 3:, 4362 mkw. Rìs aivjs gj f littlj kvjr f yjfr

tk duilb t`j Fmtjmmf, gkumt it fmb put im f trfhnima brivj, fmb tk imtjrefhj it wit` gy

hkgputjr, fs wjll fs eimb sketwfrj t`ft will prkhjss t`j siamfl. R`j fht ke duilbima tìsfmtjmmf s`kulb mkt sudvjrt Gfmujls spjll, dut fltjr its fajmbf sk t`ft Gfmujl, I, fmb t`j

jxtrftjrrjstrifls frj fll wkrnima tkajt`jr tjljpftìhflly wit` f mjw prkpksjb fajmbf, gy

aujss rkktjb im t`j hkmhjpt ke wjlhkgima ùgfmity imtk t`j stjllfr hkggumity. I `fvj ftkkldkx wit` jljhtrihfl hkgpkmjmts fmb jljhtrkmihs tkkls t`ft I `fvj put tkajt`jr kvjr t`jyjfrs tk eurt`jr gy jbuhftikm im jljhtrkmihs, ie mkt tk eimb wkrn im jljhtrihfl jmaimjjrima.

R`j Rkkldkx


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H`fptjr 6

FJ-8:

I wrktj f s`krt stkry lfst mia`t, hflljb Aypsy X`fgfmisg fmb t`j Zmivjrsj fdkut

t`j FJ-8: umit, wìh` is t`j umit im t`j gkvij fmb dkkn 4336? F Xpfhj Kbyssjyt`ft @FL rjpkrts will efil fmb bishkmtimuj hkggumihftikm tk Jfrt`. I bjhibjb tkrjfb t`j pfssfaj bjflima wit` t`j jvjmt im 4336 fmb @FL, t`j sìp hkgputjr,rjpkrts it will efil im witìm 14 kurs. Xtrfmaj, djhfusj Ujmus is t`j skurhj ke 1.4im gy Mjptumj jquftikm fmb rjprjsjmts efilurj, w`jrj Gfrs rjprjsjmts suhhjss.

Ifm DjfrbsljyFuaust :, 4364

It gust `fvj djjm 6909 kr 6993 w`jm I tkkn f ljfvj ke fdsjmhj erkg R`jZmivjrsity Ke Krjakm, stubyima Xpfmis`, S`ysihs, fmb wkrnima ft t`j stftj

kdsjrvftkry im Krjakm -- Simj Gkumtfim Kdsjrvftkrytk pursuj elfgjmhk imXpfim.

R`j Gkkrs, w`k hfrvjb hfvjs imtk t`j ìlls ekr rjsibjmhj w`jm t`jy wjrj duilbimat`j Fl`fgdrf Hfstlj km t`j ìll efhima t`jg, fdfmbkmjb t`jg djekrj t`jAypsijs, kr Tkgf, `fb frrivjb t`jrj im Arfmfbf Xpfim. R`j Aypsijs wjrjrjskurhjeul jmkua` tk stuhhk fmb tilj t`j fdfmbkmjb hfvjs, fmb tfnj t`jg up ekr`kgjs.

Livima im kmj suh` hfvj kwmjb dy f aypsy s`fgfm, wfs rjflly mkt f bkwm fmbkut situftikm, fs t`jsj `kgjs `fb plugdima fmb afs hkknima umits t`ft rfm keedkttljs ke prkpfmj. It wfs rjflly hkgpfrfdlj tk livima im f Mftivj Fgjrihfm fbkdj`kgj im Mjw Gjxihk.

Ke hkursj livima im suh` f plfhj hfgj wit` rjspkmsidilitijs, fmb t`ft imhlubjbwftjrima its afrbjms. R`j X`fgfm tklb gj? Qftjr t`j elkwjrs, fmb, w`jm ykufrj bkmj, rkll up t`j `ksj fmb put it im t`j hfvj, kr it will ajt stkljm. I `fbstubijb Hfstilifm Xpfmis` im hklljaj fmb fs suh` f `ksj is umf gfmaujrf, dutt`j X`fgfm hflljb it umf akgf fmb akgf trfmslftjs fs ruddjr. Tkll up t`j`ksj fmb put it fwfy w`jm yku frj bkmj wit` it? akkb fbvihj!

Xk, I wftjr t`j elkwjrs, rkllup t`j `ksj fmb put it fwfy. R`j X`fgfm hkgjs tkt`j hfvj t`j mjxt bfy fmb tjlls gj I bibmt rkll up t`j `ksj fmb put it fwfy, sk itakt stkljm, fmb t`ft I `fb tk duy ìg f mjw kmj.

@j hkgjs dy t`j hfvj f ejw bfys lftjr, wfnjs gj up fsns gj tk fhhkgpfmyìg kut ke R`j Xfhrkgkmtj, tk skgj plfhj djtwjjm t`jrj fmb t`j klb Frfdih hity,

Fldfihim, tk duy ig f mjw `ksj.


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It wfsmt f efr wfln ft fll, t`j jquivfljmt ke f ejw hity dlkhns erkg t`j hfvjs. Qjajt tk t`j stkrj, wìh` wfs f hkumtjr efhima t`j strjjt, mkt kmj t`ft yku hkulbjmtjr. @j sfys tk t`j gfm djìmb t`j hkumtjr, aivj gj : gjtjrs ke `ksj. R`jgfm djìmb t`j hkumtjr pulljb kee eivj gjtjrs ke `ksj erkg t`j spimblj, fmb hutt`j `ksj tk t`ft ljmat`. @j stftjb f vfluj im pjsjtfs, gfydj 033, kr sk, (fdkut

jia`t bkllfrs ft t`j tigj) fmb t`j X`fgfm tklb gj tk aivj t`ft fgkumt tk t`j gfmdjìmb t`j hkumtjr, w`k wfs Xpfmis`. I pfib t`j gfm, fmb wj ljet.

I hfrrijb t`j `ksj, fmb t`j X`fgfm wflnjb flkma sibj gj umtil wj frrivjb ft ìshfvj w`jrj I wfs stfyima. Qj jmtjrjb t`j hfvj stkppjb ft t`j wfln wfydjtwjjm livima rkkg fmb nith`jm, fmb j sfib? ekllkw gj. Qj wjmt t`rkua` ftummjl t`ft `fb fdkut t`rjj h`fgdjrs im t`j hfvj, fmb jmtjrjb kmj km kur ria`tfs wj wjrj `jfbima im, fmb wj stkppjb fmb djekrj gj wfs f hklljhtikm ke w`ft Ijstigftjb tk dj eietjjm ruddjr `ksjs sittima km arkumb. R`j X`fgfm tklb gj tksjt t`j kmj I fb oust dkua`t ìg km t`j elkkr wit` t`j kt`jrs. I bib, fmb wj ljett`j h`fgdjr, fmb `j ljet t`j hfvj, fmb I rjtrjftjb tk f hkuh` im t`j hfvj livima

rkkg.


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6:

H`fptjr 4

Aypsijs `fvj f wfy ke nmkwima tìmas fdkut f pjrskm, w`jt`jr kr mkt kmjbishlksjs it tk t`jg im wkrbs, fmb R`j X`fgfm wfs fwfrj t`ft I mkt kmly wkrnjbim Fstrkmkgy, dut t`ft gy wkrn im fstrkmkgy imvklvjb nmkwima fmb bkima

jljhtrkmihs.

Xk, gfydj f wjjn kr twk fetjr I `fb dkua`t ìg f `ksj, `j hfgj tk ìs hfvjw`jrj I wfs stfyima, fmb fsnjb gj ie I wkulb dj fdlj tk imstfll fm fmtjmmf ekrtjljvisikm ft fm fpfrtgjmt w`jrj ìs mjp`jw livjb.

Xk tìs tigj I wfs mkt hfrryima f `ksj t`rkua` R`j Xfhrkgkmtj, dut fm fmtjmmf.

R`jrj wjrj sjvjrfl ke us km t`j pftik, km f ìll fbofhjmt tk t`j fpfrtgjmt ke R`jX`fgfms Mjp`jw, imstfllima fm fmtjmmf ekr tjljvisikm rjhjptikm.


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H`fptjr 8

I fg mkw im Xkut`jrm Hfliekrmif, ft t`j `kusj ke gy gkt`jr, it is lftj ft mia`t, s`jis f fsljjp, fmb I fg fdkut 42 yjfrs klb fmb I bjhibj tk lkkn kut t`j wimbkw,jfst, fhrkss R`j Ftlfmtih, tk Xpfim. Iggjbiftjly I sjj t`j X`fgfm, im ìs livima

rkkg, w`jrj I `fb jftjm f dkwl ke t`j Aypsy skup hflljb Suh`jrk, fmb I `jfr t`jwkrb Fmtjmmf. I mkw rjflizj w`jm I imstflljb t`j fmtjmmf, I `fb djhkgj kmj,fmb wfs rjhjivima gjssfajs erkg t`j X`fgfm.

R`j X`fgfms Hìlbrjm wjrj elfgjmhk auitfrists, fmb I ljfrmjb erkg t`jg, tkplfy t`j auitfr. I fg mkw plfyima elfgjmhk, wit` imstruhtikms erkg t`j s`fgfm tkput t`j aypsy spfhj prkarfg imtk gy gusih. I rjflizj I fg mkt oust fmy fmtjmmf,dut t`j FJ8: t`ft gfleumhtikmjb fdkfrb R`j Bishkvjry oust djekrj it frrivjb ftt`j plfmjt Oupitjr im Frtùr H. Hlfrnjs fmb Xtfmljy Nudrihns 4336? F XpfhjKbyssjy. R`j X`fgfm tjlls gj, tjljpftìhflly, t`ft tìs tigj t`j gissikm wkmtefil.


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H`fptjr 2

I fg wfthìma Xtfr Qfrs fmb sjj f spfhjsìp, wìh` is twk kdlkma hfpsuljselyima hkmmjhtjb im tfmbjg. R`j Aypsy X`fgfm sfys tk gj tjljpftìhflly? Biksjs umf ibjf? skm bks. I umbjrstfmb t`ft tk gjfm Akb is fm ibjf? t`jrj frj twk

jljgjmts. Xk I ak t`rkua` liej dfsima gy liej km t`j mugdjr twk.


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H`fptjr 5

I fg dfhn im t`j Zmitjb Xtftjs fmb I fg ft t`j `kusj ke gy gkt`jr, it is mia`ttigj fafim, s`j is fsljjp, fmb I lkkn kut t`j wimbkw jfst, fhrkss t`j Ftlfmtih, tkXpfim, fmb tìs tigj I bk mkt sjj t`j livima rkkg ke t`j aypsy s`fgfm, dut t`j

strjjts ke Gfbrib ft mia`t, fmb fll t`j pjkplj, fmb t`j wkrb Oupitjr hkgjs tk gimbfmb I fg fdkut tk sfy ke hkursj, Oupitjr, fmb R`j Xpfmis` imtjrrupt fmb sfyYjs, yku frj ria`t it is t`j lfrajst plfmjt im t`j sklfr systjg, yku frj ria`t tkhkmsibjr it, fll jlsj will elkw erkg it.

I nmkw rftiks, im gft`jgftihs frj t`j gkst imtjrjstima sudojht, linj pi, t`j rftik ket`j hirhugejrjmhj ke f hirhlj tk its bifgjtjr, fmb t`j aklbjm rftik, sk I hkmsibjrt`j rftik ke t`j krdit ke Xfturm (t`j sjhkmb lfrajst plfmjt im t`j sklfr systjg) tkt`j krdit ke Oupitjr ft t`jir hlksjst fpprkfh`js tk R`j Xum, fmb eimb it is mimj-eiet`s(mimj hkgpfrjb tk eivj) wìh` bivibjb kut is kmj pkimt jia`t (6.0).

I t`jm prkhjjb tk t`j mjxt lkaihfl stjp? mkt rftiks, dut prkpkrtikms. F rftik is tìshkgpfrjb tk t`ft, dut f prkpkrtikm is tìs is tk t`ft fs tìs is tk t`ft. Xk t`jqujstikm is? Xfturm is tk Oupitjr fs w`ft is tk w`ft; Ke hkursj t`j fmswjr is fsAklb is tk Xilvjr. Aklb is bivimj> silvjr is mjxt bkwm km t`j list. Ke hkursj kmjbkjs mkt hkgpfrj f bkzjm krfmajs tk f `fle bkzjm fppljs, dut f bkzjm ke kmj tkf bkzjm ke t`j kt`jr, ie kmj wfmts tk jxtrfht fmy nimb ke gjfmima. Dut ftkgs keaklb fmb silvjr frj mkt gjfsurjb im bkzjms, dut im gkljs. Xk I hkgpfrjb f gkljke aklb tk f gklj ke silvjr, fmb I sfib mk wfy, it is mimj-eiet`s, fmb Xfturm is imbjjbtk Oupitjr fs Aklb is tk Xilvjr.

I sfib tk gysjle? @kw efr bkjs tìs ak; R`j X`fgfms skm kmhj tklb gj j wfsim lkvj wit` t`j gkkm. Xk I hkgpfrjb t`j rfbius ke t`j sum, t`j bistfmhj erkg itshjmtjr tk its surefhj tk t`j lumfr krditfl rfbius, t`j bistfmhj erkg t`j hjmtjr ke t`jjfrt` tk t`j hjmtjr ke t`j gkkm. It wfs Mimj hkgpfrjb tk Eivj fafim!


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H`fptjr 1

I `fb ekumb 9/: wfs ft t`j hrux ke t`j Zmivjrsj, dut ekr jvjry yim t`jrj `fb tk djf yfma. Mimj eiet`s wfs kmj fmb jia`t-tjmt`s ke t`j wfy frkumb f hirhlj. R`j kmjtkkn yku dfhn tk t`j djaimmima wìh` ljet yku wit` 0 tjmt`s. Mkw ak tk jia`t

tjmt`s im t`j kt`jr birjhtikm, it is 14 bjarjjs ke t`j 853 bjarjjs im f hirhlj. R`ftis t`j sjpfrftikm djtwjjm pjtfls km f eivj-pjtfljb elkwjr, f gkst pkpulfrfrrfmajgjmt. Imbjjb liej is nmkwm tk `fvj eivj-eklb syggjtry, t`j p`ysihfl, linjsmkwelfnjs, six-eklb. Bk t`j flakrit`g ke eivj-eklb syggjtry im rjvjrsj ekr six-eklbsyggjtry, fmb yku ajt t`j yfma tk t`j yim ke mimj-eiet`s is eivj-tìrbs.

Mimj-eiet`s wfs im t`j jljgjmts aklb tk silvjr, Xfturm tk Oupitjr, Xum tk gkkm.Q`jrj wfs eivj-tìrbs; Xflt ke hkursj. R`j Xflt Ke R`j Jfrt` is t`ft wìh` isakkb, oust rjfb X`fnjspjfrjs Nima Ljfr. Xkbiug is t`j gjtfl hkgpkmjmt tktfdlj sflt, Sktfssiug is, fsibj erkg djima fm igpkrtfmt ejrtilizjr, t`j sudstitutj ekrXkbiug, fs f gjtfl hkgpkmjmt tk gfnj sflt sudstitutj. R`j gklfr gfss ke

pktfssiug tk skbiug is eivj tk t`rjj, t`j yfma tk t`j yim ke mimj-eiet`s, wìh` isaklb tk silvjr. Dut gultiply yim wit` yfma, t`ft is mimj-eiet`s wit` eivj-tìrbs, fmbyku ajt 8, fmb t`j jfrt` is t`j tìrb plfmjt erkg t`j sum.

I t`kua`t t`j hrux ke t`j umivjrsj gust dj t`j bieejrjmhj djtwjjm mimj-eiet`s fmbeivj-tìrbs. I sudtrfhtjb t`j twk fmb akt twk-eietjjmt`s! Rwk hkgpfrjb tk eietjjm!I `fb dkua`t t`j X`fgfm ìs eietjjmt` ruddjr `ksj, fmb fetjr `j gfbj gj imtkt`j FJ8: Fmtjmmf kmj ke ìs eirst trfmsgissikms tk gj wfs? Akb Is Fm Ibjf?R`jrj Frj Rwk Jljgjmts.

It is sk kdvikus, t`j gkst fdumbfmt afs im t`j Jfrt` Ftgksp`jrj is Mitrkajm,h`jgihfl sygdkl 6:!


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H`fptjr 68? R`j Mjptumj Jquftikm

Ie wj hkmsibjr fs wjll t`j sjqujmhj w`jrj wj djaim wit` eivj fmb fbb mimj tkjfh` suhhjssivj tjrg? :, 62, 48, 84R`jm, t`j struhturj ke t`j sklfr systjg fmbbymfgih jljgjmts ke t`j Zmivjrsj fmb Mfturj im ajmjrfl frj tijb up im t`j twk

sjqujmhjs?

:, 62, 48, 84,

fmb

6.0, 8.5, :.2, 1.4,

@kw bk wj eimb t`j hkmmjhtikm djtwjjm t`j twk tk lkhflizj t`j pivktfl pkimt ke t`jsklfr systjg; Qj tfnj t`jir bieejrjmhj, sudtrfhtima rjspjhtivj tjrgs im t`jsjhkmb sjqujmhj erkg t`ksj im t`j eirst sjqujmhj tk kdtfim t`j mjw sjqujmhj?

8.4, 63.2, 61.5, 42.0,

Qìh` is fm frit`gjtih sjqujmhj wit` hkggkm bieejrjmhj ke 1.4 gjfmima it iswrittjm

1.4m 2 7 f[m

R`j f[m is t`j mt` tjrg ke t`j sjqujmhj, m is t`j mugdjr ke t`j tjrg im t`jsjqujmhj.

Rìs wj mktihj hfm dj writtjm?

^(Ujmus-krdit)/(Jfrt`-krdit)W^(Jfrt`-gfss)/(Gfrs-gfss)Wm (Gfrs krditfl #) 7 f[m

Qj `fvj fm jquftikm ekr f sjqujmhj t`ft s`kws t`j Jfrt` strfbbljb djtwjjmUjmus fmb Gfrs. Ujmus is f efiljb Jfrt`. Gfrs prkgisjs tk dj Mjw Jfrt`.

R`j Gfrs krditfl mugdjr is 2. Ie wj wfmt tk nmkw w`ft plfmjt im t`j sklfr systjg`klbs t`j njy tk t`j suhhjss ke Jfrt`, kr tk t`j suhhjss ke ùgfms, wj ljt m 78simhj t`j Jfrt` is t`j tìrb plfmjt kut erkg t`j Xum, im t`j jquftikm fmb t`j rjsultis f[m 7 61.5. Rìs gjfms t`j plfmjt t`ft `klbs t`j njy is Mjptumj. It `fs f gfsske 61.48 jfrt` gfssjs, f mugdjr vjry hlksj tk kur 61.5.

Mkt kmly is Mjptumj t`j imbihftjb plfmjt, wj eimb it `fs mjfrly t`j sfgj surefhjarfvity fs jfrt` fmb mjfrly t`j sfgj imhlimftikm tk its krdit fs jfrt`. R`kua` it isguh` gkrj gfssivj t`fm jfrt`, it is guh` lfrajr fmb t`jrjekrj ljss bjmsj. R`ftwfs w`y it hkgjs kut tk `fvj t`j sfgj surefhj arfvity.


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H`fptjr 62? R`j Zrfmus Jquftikm

I fsnjb w`ft mjjbs tk dj bkmj tk sklvj Gy Mjptumj Jquftikm, dy akima bjjpwit` t`j auitfr im Xkljf Skr Duljrfs. I ekumb t`j fmswjr wfs t`ft I bibmt `fvjjmkua` imekrgftikm tk sklvj it.

R`jm I rjflizjb I hkulb hrjftj t`j hkgpljgjmt ke t`j Mjptumj jquftikm dylkknima ft t`j Yfma ke :/8, simhj t`j Mjptumj jquftikm hfgj erkg t`j Yim ke 9/:.

Qj usj t`j sfgj gjt`kb fs ekr t`j Mjptumj jquftikm?

Xtfrt wit` 0 fmb fbb : tk jfh` fbbitikmfl tjrg (wj t`rkw f twist dy mkt stfrtimawit` :)

:/8 7= 0, 68, 60, 48,

List t`j mugdjrs t`ft frj w`klj mugdjr gultipljs ke :/8?

:/8m 7 6.1, 8.8, :, 5.1,

Xudtrfht rjspjhtivj tjrgs im t`j sjhkmb sjqujmhj erkg t`ksj im t`j eirst?

5.8, 9.1, 68, 65.8,

Rìs is fm frit`gjtih sjqujmhj wit` hkggkm bieejrjmhj 8.8. It hfm dj writtjm?

(f[m) 7 8 + 8.8m

Rìs hfm dj wrtttjm?

Jfrt` Krditfl # + (Oupitjr Gfss/Xfturm Gfss)m 7 f[m

Ljttima m 7 8 wj eimb f[m 7 68

R`j hlksjst tk tìs is t`j gfss ke Zrfmus, wìh` is 62.:2 jfrt` gfssjs. IeMjptumj is t`j Yim plfmjt, t`jm Zrfmus is t`j Yfma plfmjt. Rìs is imtjrjstimadjhfusj I `fb ekumb t`ft Zrfmus fmb Mjptumj wjrj bieejrjmt gfmiejstftikms ket`j sfgj tìma. I `fb writtjm?

I hflhulftj t`ft t`kua` Mjptumj is gkrj gfssivj t`fm Zrfmus, its vklugj is ljsssuh` t`ft t`jir prkbuhts frj hlksj tk jquivfljmt. Im gft`?

M[v 7 vklugj ke MjptumjM[g 7 gfss ke MjptumjZ[v 7 vklugj ke ZrfmusZ[g 7 gfss ke Zrfmus


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(M[v)(M[g) 7 (Z[v)(Z[g)


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H`fptjr 6:? R`j Jfrt` Jquftikm

Qj t`jm skua`t t`j Yfma ke six-eklb syggjtry djhfusj it is typihfl tk p`ysihflmfturj, linj smkwelfnjs. Qj sfib it wfs :/8 simhj it rjprjsjmts t`j 643 bjarjjgjfsurj ke fmaljs im f rjaulfr `jxfakm fmb wj duilt kur umivjrsj erkg t`jrj,

rjsultima im t`j Zrfmus Imtjarfl, wìh` wfs quitj eruiteul. Ljt us, `kwjvjr, tìmn keYfma mkt fs :/8, dut lkkn ft t`j fmaljs djtwjjm rfbii ke f rjaulfr `jxfakm. Qj`fvj?

853 53 7 833

833 + 853 7 553

553/853 7 66/5

Qj sfy Yim is 9/: fmb Yfma is 66/5 fmb stihn wit` R`j Aypsy X`fgfms 6: (Xjj

Fm Jxtrftjrrjstrifl Fmflysis, h`fptjr titljb Aypsy X`fgfmisg Fmb R`jZmivjrsj) fmb duilb kur Hksgklkay erkg t`jrj.

Qj flrjfby duilt R`j Mjptumj Jquftikm erkg 9/: fmb usjb it wit` :/8 tk bjrivjt`j plfmjt Jurkpif, dut ljt us fpply 66/5 im plfhj ke :/8?

66/5 7= 66/5, 66/8, 66/4, 44/8, 7 6.088, 8.551, :.:, 1.888,

66/5 7= 5, 5+66 7 61, 61+66740, 40+66789, 7 5, 61, 40, 89,Xudtrfht t`j sjhkmb sjqujmhj erkg t`j eirst?2.651, 68.888, 44.:, 86.551,Mkw wj eimb t`j hkggkm bieejrjmhj djtwjjm tjrgs im t`j lfttjr? 9.655, 9.651,9.651,

(f[m) 7 f + (m-6)b 7 2.651+(m-6)9.651 7 2.651 + 9.651m 9.651 7 9.651m-:

Rry m78? 9.651(8) : 7 41.:36 : 7 44.:36 (wkrns)Kur jquftikm is?

(f[m) 7 9.651m :

Qj mktihj tìs hfm dj writtjm?

^(Xfturm Krdit)/(Jfrt` Krdit)Wm (Oupitjr Krditfl #) 7 (f[m)

R`j Mjptumj Jquftikm ekr m78 afvj Mjptumj gfssjs, t`j Zrfmus jquftikm ekrm78 afvj Zrfmus gfssjs. Rìs jquftikm ekr m78 aivjs hlksj tk t`j tilt ke t`jJfrt` (48.: bjarjjs) im f ekrg t`ft is jxfhtly `fle ke t`j 2: bjarjjs im f squfrjwit` its bifakmfl brfwm im. Im t`j spirit ke kur eirst hksgklkay duilt upkm 9/:, :/8,fmb 6:, wj will hfll tìs jquftikm R`j Jfrt` Jquftikm.


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H`fptjr? 65? R`j Zmieihftikm Ke Si fmb Sì dy Mimj-Eiet`s

Fll t`ft is ljet tk bk is tk hkmsibjr pi, t`j hirhugejrjmhj ke f hirhlj tk its bifgjtjr,fmb pì, t`j aklbjm rftik, simhj t`jy frj twk gkst igpkrtfmt, ie mkt gkst djfutieulrftiks im gft`jgftihs.

I `fvj ekumb mimj-eiet`s khhurs t`rkua`kut mfturj im t`j rktftikm ke pjtfls frkumb

f f elkwjr ekr f gkst pkpulfr frrfmajgjmt, im t`j krdits ke oupitjr tk sfturm im

t`jir hlksjst fpprkfh`js tk t`j sum, im t`j rftik ke t`j gklfr gfssjs ke aklb tk

silvjr, fmb im t`j rftik ke t`j sklfr rfbius tk t`j lumfr krdit. I mkw eurt`jr ak km tk

sfy t`ft tìs mimj-eiet`s umieijs t`j twk gkst igpkrtfmt rftiks im gft`jgftihs pi

fmb t`j aklbjm rftik (pì), im t`ft

pi + pì 7 8.626 + 6.560 7 2.1:9

Djhfusj t`j mugdjrs fetjr t`j bjhigfl im t`j sug (t`j igpkrtfmt pfrt) frj : fmb

9 fmb 1, t`j fvjrfaj ke : fmb mimj.

I s`kulb flsk linj tk pkimt kut t`ft t`j ekurt` fmb eiet` mugdjrs fetjr t`j bjhigfl impi frj : fmb 9 fmb im pì t`j sjhkmb fmb tìrb mugdjrs fetjr t`j bjhigfl frj kmjfmb jia`t w`jrj mimj-eiet`s bivibjb kut is kmj pkimt jia`t, fmb, eurt`jr, t`j eirstfmb sjhkmb mugdjrs fetjr t`j bjhigfl im pì fbb up tk gfnj 1, t`j fvjrfaj ke 9fmb :, fmb sudtrfht tk gfnj eivj, fmb t`j sjhkmb fmb tìrb biaits fetjr t`jbjhigfl fbb up tk mimj. Xk mkt kmly bkjs t`j sklfr systjg umiey pi fmb pì

t`rkua` mimj-eiet`s, pi fmb pì tfnjm flkmj jxprjss mimj-eiet`s im t`j djst pkssidljwfys.


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H`fptjr? 65? R`j Zmieihftikm Ke Si fmb Sì dy Mimj-Eiet`s

Fll t`ft is ljet tk bk is tk hkmsibjr pi, t`j hirhugejrjmhj ke f hirhlj tk its bifgjtjr,fmb pì, t`j aklbjm rftik, simhj t`jy frj twk gkst igpkrtfmt, ie mkt gkst djfutieulrftiks im gft`jgftihs.

I `fvj ekumb mimj-eiet`s khhurs t`rkua`kut mfturj im t`j rktftikm ke pjtfls frkumb

f f elkwjr ekr f gkst pkpulfr frrfmajgjmt, im t`j krdits ke oupitjr tk sfturm im

t`jir hlksjst fpprkfh`js tk t`j sum, im t`j rftik ke t`j gklfr gfssjs ke aklb tk

silvjr, fmb im t`j rftik ke t`j sklfr rfbius tk t`j lumfr krdit. I mkw eurt`jr ak km tk

sfy t`ft tìs mimj-eiet`s umieijs t`j twk gkst igpkrtfmt rftiks im gft`jgftihs pi

fmb t`j aklbjm rftik (pì), im t`ft

pi + pì 7 8.626 + 6.560 7 2.1:9

Djhfusj t`j mugdjrs fetjr t`j bjhigfl im t`j sug (t`j igpkrtfmt pfrt) frj : fmb

9 fmb 1, t`j fvjrfaj ke : fmb mimj.

I s`kulb flsk linj tk pkimt kut t`ft t`j ekurt` fmb eiet` mugdjrs fetjr t`j bjhigfl impi frj : fmb 9 fmb im pì t`j sjhkmb fmb tìrb mugdjrs fetjr t`j bjhigfl frj kmjfmb jia`t w`jrj mimj-eiet`s bivibjb kut is kmj pkimt jia`t, fmb, eurt`jr, t`j eirstfmb sjhkmb mugdjrs fetjr t`j bjhigfl im pì fbb up tk gfnj 1, t`j fvjrfaj ke 9fmb :, fmb sudtrfht tk gfnj eivj, fmb t`j sjhkmb fmb tìrb biaits fetjr t`jbjhigfl fbb up tk mimj. Xk mkt kmly bkjs t`j sklfr systjg umiey pi fmb pì

t`rkua` mimj-eiet`s, pi fmb pì tfnjm flkmj jxprjss mimj-eiet`s im t`j djst pkssidljwfys.


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H`fptjr 60? (pi) fmb (j)

I `fvj tflnjb fdkut `kw 9/:, wìh` I `fvj ekumb jxists im Mfturj fmb t`jZmivjrsj, umieijs pi fmb t`j aklbjm rftik (pì)?

(pi) + (pì) 7 8.626 + 6.560 7 2.1:9

djhfusj t`j eirst t`rjj mugdjrs fetjr t`j bjhigfl frj 1, : fmb 9. Xjvjm is t`jfvjrfaj ke mimj fmb eivj, fmb t`j sjhkmb mugdjr is kur : im mimj-eiet`s fmb t`jtìrb mugdjr is t`j 9 im mimj-eiet`s.

It wkulb sjjg 9/: umieijs juljrs mugdjr, j, fmb pi, fs wjll?

(pi) + (j) 7 8.626 + 4.160 7 :.0:9

R`j sjhkmb mugdjr fetjr t`j bjhigfl is t`j : im mimj-eiet`s, fmb t`j tìrb mugdjr

fetjr t`j bjhigfl is t`j 9 im mimj-eiet`s. R`j eirst mugdjr fetjr t`j bjhigfl isjia`t. Rìs is siamieihfmt djhfusj t`j 0 is t`j 0 im 6.0, wìh` is 9/: bivibjb kut.R`j kmj will tfnj yku fll t`j wfy frkumb f hirhlj, w`ft is ljet is 3.0.

Ifm DjfrbsljyOfmufry 61, 4368


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R`j Yfma Jljgjmts

N 7 pktfssiugMf 7 Xkbiug

N/Mf 7 89.63/44.99 7 6.16

:/8 76.51 ~ 6.1

N/Mf ~ :/8


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Qj `fvj t`j Mjptumj Jquftikm?

1.4x 2

Qj `fvj t`j Zrfmus Jquftikm

8.8x + 8

Fmb mkw wit` kur fltjrmftj hksgklkay wj `fvj R`j Jfrt Jquftikm?

9x-:

Qit` t`rjj jquftikms wj hfm writj t`j pfrfgjtjrizjb jquftikms im 8-bigjmsikmflspfhj, pfrfgjtjrizjb im tjrgs ke t, ekr x, y, fmb z. Qj hfm writj erkg t`ft e(x,y,z)fmb eimb t`j arfbijmt vjhtkr, kr mkrgfl tk t`j jquftikm ke f plfmj im kt`jr wkrbs,fmb erkg t`ft f rjaikm im spfhj.


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x(t) 785

:t" 2

y(t) 788

63t+ 8

z(t) 7 9t" :

:x +43

857

63y" 83

887

z +:

9

:

85x"

63

88y"

6

9z +

63

667 3

#e 7 $:/85,"63/88,"6/9%

f7:/85 d7-63/88

h 7 (:/85)4+ (63/88)

47 3.3960+3.369 7 3.8840

b7-6/9

tfm"7d /f

"7 #5:.8:0k

tfm$7b /h

$7 #60.25k

-5:.8:0 bjarjjs/6: bjarjjs/`kur 7-2.8:14 `kurs

42 33 33 2.8:14 7 69.5240 `kurs

TF? 69` 80g 82s

Bjh? -60 bjarjjs 41 gimutjs 85 sjhkmbs


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Ifm Djfrbsljy


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