ljrogoga 9= Jd udm jcprjsm sj emojd gcprjsgadjs jd hícgdms kj mojra quj kjspuçs sj oadvgjrtjd jd rjogpgjdtjs kj prakuotas kj atrms jcprjsms. Zd mspjota gcpartmdtj m vgnghmr jd kgoem gcprjsgÿd js hm tjcpjrmturm kj ‘eardjmka–, kadkj, jdtrj atrms oasms, sj prjsjdtmd mkejrjdogms y hm hícgdm sj sjom udm vjz quj em sgka gcprjsm. Hm tjcpjrmturm kj ogjrta earda kjij sjr 9:°O oad udm tahjrmdogm kj ½ :°O. M pjsmr kj quj mh earda sj hj pranrmcm hm tjcpjrmturm, par jxpjrgjdogm sj smij quj da hm cmdtgjdj6 par jhha, pmrm hhjvmr ud oadtrah mkjoumka kj hm tjcpjrmturm kjh praojsa sj kjogkj jcphjmr udm omrtm kj oadtrah kj gdkgvgkumhjs. Omkm kas earms sj cgkj hm tjcpjrmturm, jd hm tmihm >.7 sj cujstrmd has ühtgcas ;: kmtas jd jh arkjd quj sj aituvgjrad, oad jh rmdna cÿvgh pmrm bmoghgtmr has oíhouhas. _uinrupa = 9 ? ; : 2 > 75 =0 == =9 =? =; =: =2 => =5 =7 90 9= 99 9? [jcpjrmturm Ymdna cÿvgh 9>.; 92.5 0.2 9;.? 9.: 92.2 9.? 92.: 0.= 9:.2 0.7 9:.= 0.: 92.: =.; 9:.5 0.> 9;.> =.= 9?.? =.; 9?.? 0.0 9;.> =.; 9?.; =.? 9>.; ;.0 9;.> 9.> 9=.> ?.0 92.> :.0 9;.9 9.: 9:.: =.? 9:.? 0.9 9:.0 0.? 9?.5 =.9 _uinrupa 9; 9: 92 9> 95 97 ?0 [jcpjrmturm Ymdna cÿvgh 92.: 9.> 9?.? ?.9 9?.5 0.: 9:.: =.> 92.; 0.7 9>.: =.= 9>.> 0.9 95.: 0.5 97.5 =.? 9:.= ;.> 9:.0 0.= 99.7 9.= 9?.2 0.> 9;.> =.= 9;.; 0.? 9:.; =.0 9?.: =.7 9>.5 ;.? 9:.: 9.? 92.: 0.7 9;.: =.7 9?.: =.0 9:.?9 =.:> ?= ?9 ?? ?; ?: ?2 ?> ?5 ?7 ;0 ;= ;9 ;? ;; ;: Cjkgm m) ±Par qquç uç utghgzmr utghgzmr jjdd jstj oomsa msa ud udmm omrtm kj gdk gdkgvgku gvgkumhjs mhjs y ddaa udm om omrtm rtm U - Y1 » » ‟ Y quj sj jcphjm Parquj hm omrtm kj gdkgvgkumhjs sj mphgom m praojsas hjdtas, m kgbjrjdogm kj hm omrtm U jd praojsas cmsgvas y oad ud hmpsa cjdar rjqujrgka pmrm hm aitjdogÿd kj hm cujstrm, pujs jstas rjqugjrjd kj pjrgakas rjhmtgvmcjdtj hmrnas pmrm hm aitjdogÿd kj hm cujstrm kj prakuoogÿd. Jd jstj omsa sj jstí cgkgjdka hm tjcpjrmturm, y jd jstas praojsas hms cjkgogadjs ojromdms sÿha kgbgjrjd par jrrar kj cjkgogÿd,, kjigka m jsta sj oadsgkjrm oaca udm cjlar mhtjrdmtgvm cjkgogÿd mhtjrdmtgvm hm mphgomogÿd kj udm omrtm kj oadtrah kj gdkgvgkumhjs. i) stgcj has hãhãcgtjs cgtjs kj ooadtra adtrahh pm pmrm rm hm omrtm kj gd gdkgvgk kgvgkumhj umhjss j gd gdtjrpr tjrprçtjha çtjhas. s. Hãcgtjs kj jspjogbgomogÿd< Hm tjcpjrmturm kjh earda tgjdj udm tahjrmdogm kj ½ :°O, par ha oumh has hãcgtjs jspjogbgomkas sjríd< Hãcgtj kj jspjogbgomogÿd gdbjrgar< JG 39:∙ :390 ° O Ailjtgva< 9: °O Hãcgtj kj jspjogbgomogÿd gdbjrgar< J_ 39: + :3?0 ° O Jsta das gdkgom quj hm tjcpjrmturm quj sj jdoujdtrj kjdtra kj jstj rmdna sjrí oadsgkjrmka oaca mojptmihj y hm quj jstç bujrm kj jstas hãcgtjs sj oadsgkjrmrí gdmojptmihj. Hãcgtjs rjmhjs< Hãcgtj rjmh gdbjrgar HYG 3 θ∙? Ϗ ± 9:.?9∙? ( =.?7=5 )3 9:.?9∙;.=>:: 39=.=;;: Hãcgtj rjmh supjrgar HY_3 θ + ? Ϗ 39:.?9 + ? ( =.?7=5 )3 9:.?9+ ;.=>::397.;7:: Hm tjcpjrmturm (smhgkm kjh praojsa) sj jspjrm quj vmrãj jdtrj 9=.=;;: y 97.;7::. Jstms cjkgkms (hãcgtjs rjmhjs) omjd kjdtra kj has hãcgtjs jspjogbgomkas, par ha tmdta, jh praojsa js ompmz kj oucphgr oad kgoems jspjogbgomogadjs. Hãcgtjs kj oadtrah » ½ ?Ϗx Bÿrcuhm< U » Ϗ x3 θx3 U » Y k9 Kjsvgmogÿd jstídkmr m oarta phmza< Ϗ x 3 HO_39:.?9 + ? HOG 39:.?9∙? V V =.:> =.=95 =.:> =.=95 S3 S + ( » =.:> Y 3 3=.?7=5 k 9 =.=95 9:.?9 ? =.?7=5 )3 9:.?9+ ;.=>::397.;7:: 39:.?9∙? ( =.?7=5 ) 39:.?9∙;.=>:: 39=.=;;; Hãcgtjs kj rmdnas Bÿrcuhm< » 3 (0*=.:>) 3 0 Hãcgtj kj oadtrah gdbjrgar 3 K? Y » 3 =.:> Hãdjm ojdtrmh 3 Y » 3 (?.9252*=.:> Hãcgtj kj oadtrah supjrgar 3 K; Y ( ?.9252*=.:>)) 3 :.=?=>09 Has hãcgtjs kj oadtrah pmrm hm omrtm kj gdkgvgkumhjs rjbhjlmd hm vmrgmogÿd jspjrmkm jdtrj 9=.=; m 97.;7 °O jd hm tjcpjrmturm kj eardjmka. Oad udm cjkgm kj 9:.?9 °O y udm kjsvgmogÿd jstídkmr kj =.?7=5. o) Ait Aitjdn jdnmm hm hm omrtm omrtm j gdtj gdtjrpr rprçtj çtjhm. hm. Gdtjrprjtmogÿd kj hms Omrtms Jd hm nríbgom G sj pujkj aisjrvmr quj hm cjkgm kjh praojsa pakrãm da sjr jstmihj ym quj emy ud pudta bujrm kj has hãcgtjs kj oadtrah, jh oumh js jh dücjra ?9. Jsta rjprjsjdtm quj jh 9.9% kj has pudtas kj jh nrmbgoa sj jdoujdtrmd bujrm kj has hãcgtjs. Jd hm nríbgom CY sj pujkj aisjrvmr quj hm vmrgmogÿd js jstmihj ym quj da emy pudtas bujrm kj oadtrah. Jh praojsa js gdjstmihj, hm omrtm da prjsjdtm ud pmtrÿd kj sjoujdogm, sj pujkj aisjrvmr ud pmtrÿd kj tjdkjdogm kj omcigas rípgkas y quj vm kj cmdjrm msojdkjdtj, sus kmtas jstíd kj barcm mhjmtargm, pjra emy ud kmta quj smhj bujrm kj oadtrah. Bÿrcuhms< _t 3 Dücjra kj pudtas jspjogmhjs x =00 Dücjratatmh kj pudtas Ãdkgoj kj gdjstmighgkmk O ps3 J_ ∙ θ 3 ?Ϗ _t 3 = ;: x =0030.999∞=0039.99 _u ãdkgoj kj gdjstmighgkmk js kjh 9.99 %, ha quj rjprjsjdtm quj hm jstmighgkmk kj hm tjcpjrmturm js cakjrmkmcjdtj jstmihj. Ompmogkmk kjh praojsa pmrm hm jspjogbgomogÿd supjrgar O ps3 J_ ∙ θ 3 ?Ϗ ∙9:.?? 3 ;.2> 3=.==> ;.=5 ? ( =.?7=5 ) ?0 Jh ãdkgoj O ps3=.==>8 =.9: jh praojsa js pmrogmhcjdtj mkjoumka. Ompmogkmk kjh praojsa pmrm hm jspjogbgomogÿd gdbjrgar O pg3 θ ∙ JG 3 ?Ϗ ∙90 :.?? 3 3=.9>: ? ( =.?7=5 ) ;.=5 9:.?? Jh ãdkgoj O pg3=.9>: 4 =.9: jh praojsa js mkjoumka. Ãdkgoj kj ompmogkmk patjdogmh kjh praojsa O p3 HJ_∙ HJG 3 ?0∙90 3=.=7 2Ϗ 2 ( =.?7=5) Par ha quj jh praojsa sj oadsgkjrm pmrogmhcjdtj mkjoumka, mudquj rjqugjrj kj ud oadtrah jstrgota. _g jh praojsa jstuvgjrm ojdtrmka, jdtadojs jh oarrjspadkgjdtj praojsa prakuogrãm 0.072>% kj pgjzms bujrm kj jspjogbgomogÿd ha quj rjprjsjdtm 722.72: pmrtjs cmhms par omkm cghhÿd kj prakuota. Ãdkgoj kj ompmogkmk rjmh kjh praojsa O pf 3cgd V θ » ∙ HJG , HJ_ ∙ x» ?Ϗ ?Ϗ S _ustgtuogÿd O pf 3cgd V S ∙90 ?0∙ 9:.?? 3=.=9 , ? ( =.?7=5 ) ? ( =.?7=5) 9:.?? Jh ãdkgoj kj ompmogkmk rjmh kjh praojsa das cujstrm quj jh praojsa js ompmz ym quj O pf 4= , y oaca Op da jstm tmd mhjlmka kj Opf das gdkgom quj hm cjkgm kjh praojsa jstm cuy ojrom kjh pudta cjkga kj hms jspjogbgomogadjs. ÃDKGO ÃDKG O _ M HMYNA PHM\A D Kjsvgmogÿd jstídkmr m hmrna phmza< ∝ ( U ∙ U» ) 9 g g Ϗ H3 ∜ =9?.0? 3 D ∙= ∜ ;: ∙= =9?.0? 3 ∜ ;; 3∜ 9.503=.2>9 Ãdkgoj patjdogmh kj kjsjcpjýa P P3 J_∙ JG ?0∙ 90 30.772 3 2ϏH 2 ( =.2>9) ãdkgoj kj kjsjcpjýa rjmh kjh praojsa θ∙ JG J_∙ θ P 3 cgdãca ? Ϗ H , ? Ϗ H 3 V pf k) SV ∙90 ?0 ∙9:.?9 ? ( =.2>9= ) , ? ( =.2>9= ) 3 9:.?9 SV :.?9 :.0=2; ;.25 , :.0=2; S 3V =.020 , 0.7?0 S Has ãdkgojs P P30.772 y P pf 30.7?0, jstas sad cjdarjs m has ãdkgojs O p3=.=7 y O pf 30.7?0 par ha oumh da emy vmrgmogÿd kjdtra kj has suinrupas. d jh pudta ??99 sj kjogkg kjogkgÿÿ emojr ud ml mlustj ustj mh ea earda, rda, ±tg ±tgjdj jdj mhn mhnüd üd budk budkmcjd mcjdta ta jstmk jstmkãstgoa ãstgoa jst jstmm kjogsg kjogsgÿd1 ÿd1 ±Buj udm kjogsgÿd apartudm1 Js udm kjogsgÿd oarrjotm, ym quj jd jstj pudta jh vmhar sj smhj kj has hãcgtjs kj oadtrah y ha rjoacjdkmihj js rjmhgzmr ud mlustj pmrm oarrjngr jh praojsa y da njdjrmr pjrkgkms dg kjcarms. j) kjdtra Mhnu Mhnugjd gjdkjdajspjogbgomogadjs, jstí cu cuyy oadvjdo oadvjdogka gkaapgdm kj hm mhkjogs kjogsgÿd gÿd tac tacmkm mkm y mrnuc mrnucjdtm jdtm qu qujj hm tjcpjr tjcpjrmturm mturm tak takmvãm mvãm jstm jstmim im ±quç rjspjota1 _u mrnucjdta js gdoarrjota pujs jd hm nríbgom sj aisjrvm quj m pmrtgr kjh dücjra 9: emy 5 pudtas kj cmdjrm msojdkjdtj msojdkj dtj ha oumh jqugvmhj m ? pudtas jspjogmhjs, y hhjnmdka mh pudta ?9 sj jdoujdtrm bujrm kj has hãcgtjs kj oadtrah y mud quj saha js ud pudta jstj cujstrm udm tjdkjdogm msojdkjdtj par ha quj njdjrmrãm praihjcms jd hms gcprjsgadjs kj hms hícgdms kj mojra par hm tjcpjrmturm kj eardjmka. Mdíhgsgs kj Ompmogkmk jd Cgdgtmi