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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 tjljpft`ih wit` `ig, `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` t`is 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 `ig imstfll fm fmtjmmf ekr tjljvisikm
rjhjptikm ft `is mjp`jws `kusj im t`j Xfhrkgkmtj (Aypsy Hfvjs). Im t`j fht ke bkima
t`is I djhfgj tjljpft`ih wit` `ig. 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:. R`is 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. R`is 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 t`isfmtjmmf s`kulb mkt sudvjrt Gfmujls spjll, dut fltjr its fajmbf sk t`ft Gfmujl, I, fmb t`j
jxtrftjrrjstrifls frj fll wkrnima tkajt`jr tjljpft`ihflly wit` f mjw prkpksjb fajmbf, gy
aujss rkktjb im t`j hkmhjpt ke wjlhkgima `ugfmity 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, w`ih` 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 s`ip hkgputjr,rjpkrts it will efil im wit`im 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 `ills ekr rjsibjmhj w`jm t`jy wjrj duilbimat`j Fl`fgdrf Hfstlj km t`j `ill 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 `ig f mjw kmj.
@j hkgjs dy t`j hfvj f ejw bfys lftjr, wfnjs gj up fsns gj tk fhhkgpfmy`ig 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, w`ih` wfs f hkumtjr efhima t`j strjjt, mkt kmj t`ft yku hkulbjmtjr. @j sfys tk t`j gfm dj`imb t`j hkumtjr, aivj gj : gjtjrs ke `ksj. R`jgfm dj`imb 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 gfmdj`imb 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 `ishfvj 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 `ig 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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H`fptjr 4
Aypsijs `fvj f wfy ke nmkwima t`imas 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 `ig f `ksj, `j hfgj tk `is hfvjw`jrj I wfs stfyima, fmb fsnjb gj ie I wkulb dj fdlj tk imstfll fm fmtjmmf ekrtjljvisikm ft fm fpfrtgjmt w`jrj `is mjp`jw livjb.
Xk t`is 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 `ill 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 `is 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 H`ilbrjm 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 Frt`ur H. Hlfrnjs fmb Xtfmljy Nudrihns 4336? F XpfhjKbyssjy. R`j X`fgfm tjlls gj, tjljpft`ihflly, t`ft t`is tigj t`j gissikm wkmtefil.
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H`fptjr 2
I fg wfth`ima Xtfr Qfrs fmb sjj f spfhjs`ip, w`ih` is twk kdlkma hfpsuljselyima hkmmjhtjb im tfmbjg. R`j Aypsy X`fgfm sfys tk gj tjljpft`ihflly? 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 t`is 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) w`ih` 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 t`ishkgpfrjb tk t`ft, dut f prkpkrtikm is t`is is tk t`ft fs t`is 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 t`is 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 w`ih` 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-t`irbs.
Mimj-eiet`s wfs im t`j jljgjmts aklb tk silvjr, Xfturm tk Oupitjr, Xum tk gkkm.Q`jrj wfs eivj-t`irbs; Xflt ke hkursj. R`j Xflt Ke R`j Jfrt` is t`ft w`ih` 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, w`ih` isaklb tk silvjr. Dut gultiply yim wit` yfma, t`ft is mimj-eiet`s wit` eivj-t`irbs, fmbyku ajt 8, fmb t`j jfrt` is t`j t`irb 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-t`irbs. I sudtrfhtjb t`j twk fmb akt twk-eietjjmt`s! Rwk hkgpfrjb tk eietjjm!I `fb dkua`t t`j X`fgfm `is eietjjmt` ruddjr `ksj, fmb fetjr `j gfbj gj imtkt`j FJ8: Fmtjmmf kmj ke `is 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,
Q`ih` 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.
R`is 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 `ugfms, wj ljt m 78simhj t`j Jfrt` is t`j t`irb plfmjt kut erkg t`j Xum, im t`j jquftikm fmb t`j rjsultis f[m 7 61.5. R`is 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,
R`is is fm frit`gjtih sjqujmhj wit` hkggkm bieejrjmhj 8.8. It hfm dj writtjm?
(f[m) 7 8 + 8.8m
R`is 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 t`is is t`j gfss ke Zrfmus, w`ih` is 62.:2 jfrt` gfssjs. IeMjptumj is t`j Yim plfmjt, t`jm Zrfmus is t`j Yfma plfmjt. R`is is imtjrjstimadjhfusj I `fb ekumb t`ft Zrfmus fmb Mjptumj wjrj bieejrjmt gfmiejstftikms ket`j sfgj t`ima. 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, w`ih` wfs quitj eruiteul. Ljt us, `kwjvjr, t`imn 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 t`is 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. R`is 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 t`is jquftikm R`j Jfrt` Jquftikm.
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H`fptjr? 65? R`j Zmieihftikm Ke Si fmb S`i 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 p`i, 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 t`is mimj-eiet`s umieijs t`j twk gkst igpkrtfmt rftiks im gft`jgftihs pi
fmb t`j aklbjm rftik (p`i), im t`ft
pi + p`i 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 p`i t`j sjhkmb fmb t`irb 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 p`i fbb up tk gfnj 1, t`j fvjrfaj ke 9fmb :, fmb sudtrfht tk gfnj eivj, fmb t`j sjhkmb fmb t`irb biaits fetjr t`jbjhigfl fbb up tk mimj. Xk mkt kmly bkjs t`j sklfr systjg umiey pi fmb p`i
t`rkua` mimj-eiet`s, pi fmb p`i tfnjm flkmj jxprjss mimj-eiet`s im t`j djst pkssidljwfys.
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H`fptjr? 65? R`j Zmieihftikm Ke Si fmb S`i 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 p`i, 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 t`is mimj-eiet`s umieijs t`j twk gkst igpkrtfmt rftiks im gft`jgftihs pi
fmb t`j aklbjm rftik (p`i), im t`ft
pi + p`i 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 p`i t`j sjhkmb fmb t`irb 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 p`i fbb up tk gfnj 1, t`j fvjrfaj ke 9fmb :, fmb sudtrfht tk gfnj eivj, fmb t`j sjhkmb fmb t`irb biaits fetjr t`jbjhigfl fbb up tk mimj. Xk mkt kmly bkjs t`j sklfr systjg umiey pi fmb p`i
t`rkua` mimj-eiet`s, pi fmb p`i 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/:, w`ih` I `fvj ekumb jxists im Mfturj fmb t`jZmivjrsj, umieijs pi fmb t`j aklbjm rftik (p`i)?
(pi) + (p`i) 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`jt`irb 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 t`irb mugdjr
fetjr t`j bjhigfl is t`j 9 im mimj-eiet`s. R`j eirst mugdjr fetjr t`j bjhigfl isjia`t. R`is is siamieihfmt djhfusj t`j 0 is t`j 0 im 6.0, w`ih` 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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