Preview only show first 10 pages with watermark. For full document please download

The Essentials Mathematics Sba Handbook - Glendon Steele

The Essential Mathematics SBA Handbook: A Guide for CSEC Examination, was designed specifically to provide assistance to teachers and students who are preparing for the NEW CSEC Mathematics Examina...

   EMBED


Share

Transcript

]HO OTTOA][email protected] IJ]HOIJ]BDT TEJ HJAMELLK J C _ B M O F L U D T O D O X J I B A J] B L A [email protected] T][email protected] MOMBDJ]BLA ]hbs ellk bs mombdjtom tl iy Djrbeeoja Oxjibajtblas Dluadb` (DXD) L‒ @ovo` Ijthoijtbds tojdhor, Ir. @`lym O``bltt, whl ijmo io fj`` ba `lvo wbth tho crojt suenodt, Ijthoijtbds. 7: [email protected]] B wlu`m `bko tl thjak Ir. Ttovo Hlpo flr prllfrojmbac tho TEJ prlnodts prosoatom ba thbs ellk jam lfforbac bavj`uje`o jmvbdo jam supplrt. B wlu`m j`sl `bko tl thjak jam jdkalw`omco tho wlrk lf Ibss Djambdo Ehjrjt ba prllfrojmbac tho ellk jam dlrrodtbac tho Oac`bsh @jacujco. ]hjak ylu! ]hbs ellk dlu`m alt hjvo eooa dlip`otom wbthlut tho supplrt jam mombdjtbla lf Ibss Rvotto Eost whl spoat ijay `lac hlurs rosojrdhbac, dl``odtbac jam propjrbac ijtorbj` flr tho TEJ prlnodts prosoatom ba thbs ellk. ]hjaks! ]hjaks! ]hjaks! @jst`y, B wlu`m `bko tl thjak Ir. Kuijr Ujisbach flr j`wjys oadlurjcbac io tl wrbto iy bmojs. ]hjaks flr eo`bovbac ba io. 75 WUOFJDO B jttoamom j Ijthoijtbds Tdhll` Ejsom Jssossioat (TEJ) Slrkshlp jpprlxbijto`y lao yojr jcl. Jt tho oam lf tho wlrkshlp, j auieor lf iy dl``ojcuos woro `lst, dlafusom jam mbm alt sooi tl uamorstjam whjt j Ijthoijtbds TEJ Wrlnodt shlu`m oatjb`. Jt thjt ilioat, B stjrtom thbakbac lf wrbtbac ja TEJ cubmo thjt dja ho`p tho stumoats jam tojdhors jt iy sdhll`. J fow ilaths `jtor ja bmoj strudk io, why alt wrbto j Ijthoijtbds TEJ Wrlnodt cubmo thjt dja wlrk flr j`` tojdhors jam stumoats whl jro bavl`vom ba tho DTOD Ijthoijtbds TEJ Wrlnodt< Jt thjt ilioat, tho dladopt lf thbs ellk wjs dladobvom jam thjt wjs tho coaosbs lf thbs pue`bdjtbla. ]ho Ossoatbj` Ijthoijtbds TEJ Hjamellk> J Cubmo flr DTOD Oxjibajtbla, wjs mosbcaom spodb﬊dj``y tl prlvbmo jssbstjado tl tojdhors jam stumoats whl jro propjrbac flr tho AOS DTOD Ijthoijtbds Oxjibajtbla ba Ijy 57:8 jam eoylam. Bt tjkos tho rojmor thrluch tho abao (2) sodtblas thjt dliprbso j DTOD Ijthoijtbds TEJ Wrlnodt jam wbth tho uso lf sbip`o `jacujco, ojdh sodtbla bs oxp`jbaom ba motjb`. J sjip`o prlnodt bs usom tl oxp`jba ojdh sodtbla lf j prlnodt. ]hbs bs mlao ba lrmor thjt stumoats soo oxjdt`y whjt bs roqubrom jt ojdh stjco lf j prlnodt. ]horo jro toa (:7) fu``y wlrkom prlnodts bad`umom ba tho ellk. ]hoso prlnodts woro wrbttoa js cubmos ba lrmor tl moilastrjto tl stumoats hlw ojdh sodtbla lf ja TEJ Wrlnodt dja eo strudturom jam wrbttoa js j roplrt. ]ho prlnodts woro batoatblaj``y wrbttoa ba lrmor tl stbiu`jto `bvo`y jam iojabacfu` d`jssrlli mbsdussblas eotwooa tho stumoat jam tojdhbac elmbos. Jt tho oam lf tho ellk, twoaty (57) mbfforoat roj`-wlr`m sdoajrbls jro prosoatom tlcothor wbth succostom prlnodt tbt`os jbiom tl jssbst stumoats wbth tho dhlbdo lf rosojrdh tlpbds flr ja TEJ Wrlnodt. ]ho ellk wjs wrbttoa ba lrmor tl mbsibss jay dlafusbla thjt tojdhors jam stumoats ijy oxporboado wbth rospodt tl wrbtbac j DTOD Ijthoijtbds TEJ Wrlnodt. Bt bs tho juthlr‒s hlpo thjt tojdhors jam stumoats drbtbquo tho prlnodts prosoatom ba thbs ellk, jmm jam suetrjdt whoro aodossjry, sl thjt ba tho oam stumoats prlmudo la thobr lwa, j wo`` rosojrdhom jam wrbttoa TEJ Wrlnodt thjt sjtbs﬊os tho roqubroioats lf tho Djrbeeoja Oxjibajtbla Dluadb` (DXD). Ml alt flrcot tl hjvo fua j`lac tho wjy. 74 [email protected]_DK! ][email protected] LF DLA]OA]T Todtbla......................................................................................................Wjco Auieor :. Mombdjtbla................................................................................................................: 5. Jdkalw`omcoioat ..................................................................................................5 4. Wrofjdo.....................................................................................................................4 =. ]je`o lf Dlatoats .....................................................................................................= ?. Hlw ]l _so ]hbs Ellk .............................................................................................? 6. Ujtblaj`o ..................................................................................................................6 3. Ttrudturo lf j DTOD Ijthoijtbds TEJ Wrlnodt .......................................................8 8. Wrosoatjtbla lf :7 Slrkom Ijthoijtbds TEJ Wrlnodts .........................................57 • Wrlnodt Lao ........................................................................................................5: • Wrlnodt ]wl .........................................................................................................43 • Wrlnodt ]hroo ......................................................................................................?5 • Wrlnodt Flur ........................................................................................................68 • Wrlnodt Fbvo.........................................................................................................85 • Wrlnodt Tbx ..........................................................................................................24 • Wrlnodt Tovoa ...................................................................................................:74 • Wrlnodt Obcht .....................................................................................................::6 • Wrlnodt Abao ......................................................................................................:47 • Wrlnodt ]oa ........................................................................................................:=3 2. 57 Bmojs flr j Ijthoijtbds TEJ wbth Tdoajrbls jam ]bt`os ................................:66 :7. Uoforoados...........................................................................................................:36 7= HLS ]L _TO ]HBT ELLK ]hbs ellk wjs wrbttoa js j cubmo; tho dlatoats jro alt djst ba stlao. Bt bs tho juthlr‒s wbsh thjt stumoats jam tojdhors cl thrluch ojdh prlnodt wbth drbtbdj` oyos, jaj`yzo ojdh sodtbla jam mbsduss wjys ba whbdh ojdh sodtbla dja eo biprlvom lr rowrbttoa ilro offodtbvo`y. Bt bs succostom thjt tojdhors j``ldjto twl (5) porblms por wook lvor j sot porblm lf tbio ba lrmor tl moj` wbth TEJ bssuos. Murbac thoso porblms, stumoats shlu`m eo oadlurjcom tl rojm jam jaj`yzo mbfforoat sodtblas lf tho prlnodts prosoatom ba tho ellk. ]hoy dja eo jskom tl rowrbto j sodtbla wbth tho uso lf thobr lwa wlrms. ]ojdhors jam stumoats dja mbsduss wjys ba whbdh ojdh prlnodt dja eo rowrbttoa sl thjt bt fj``s wbthba tho stbpu`jtom :777 wlrm cubmo`bao sot ey tho Djrbeeoja Oxjibajtblas Dluadb` (DXD). Ttumoats dja eo crlupom; ojdh crlup dja tjko j prlnodt jam mbsduss bt jilac tho bambvbmuj`s ba thjt crlup. Jftor stumybac tho toa (:7) prlnodts, stumoats shlu`m eo oadlurjcom tl cl tl tho oam lf tho ellk whoro thoro jro twoaty (57) plssbe`o sdoajrbls jam tbt`os frli whbdh thoy dja dhllso ba lrmor tl movo`lp thobr lwa prlnodts. Ttumoats shlu`m j`sl eo cbvoa tho froomli tl dhllso jay roj`-wlr`m sbtujtbla thjt thoy wbsh tl bavostbcjto flr ja TEJ Wrlnodt. [email protected]_DK! 7? UJ][email protected] FLU TEJ ‐]ho crojt ellk lf ajturo dja la`y eo uamorstllm ey thlso whl uamorstjam tho `jacujco ba whbdh bt bs sl wrbttoa jam thjt `jacujco bs Ijthoijtbds.’ [email protected]@OL Shoa Cj`b`ol wrlto thoso prlfluam wlrms yojrs jcl, ho wjs trybac tl sjy tl us thjt ajturo wjs cbvoa tl us wbth j ijauj` tl bts lporjtbla. Hlwovor, tho ijauj` bs wrbttoa ba j sdboatb﬊d `jacujco dj``om Ijthoijtbds whbdh iust eo uamorstllm bf wo wjat tl ua`ldk tho iystorbos lf ajturo. Ijthoijtbds bs tho `jacujco usom tl stumy tho prbadbp`os lf ajturo. Tbado ajturo rovoj`s btso`f tl us thrluch pjttoras, Ijthoijtbds bs j `jacujco thjt stumbos j`` plssbe`o pjttoras. Wjttoras ioja, jay rocu`jrbtbos whbdh tho erjba dja rodlcabzo. Hoado, jay stumy lf Ijthoijtbds shlu`m bavl`vo tho bavostbcjtbla lf pjttoras ba tho roj` wlr`m. Shoa rocu`jrbtbos jam pjttoras jro stumbom, tho `jacujco lf Ijthoijtbds dja ho`p us tl ostje`bsh ilmo`s whbdh dja thoa eo usom tl sl`vo ijay prle`ois ba tho roj` wlr`m. Hlwovor, trjmbtblaj``y,Ijthoijtbds bs tjucht frli toxtellks. Ttumoats jro thoa jssossom ey jasworbac quostblas frli toxtellks oxordbsos, wlrkshoots jam oxjibajtbla pjpors. Shoa tho suenodt bs prosoatom ba thbs wjy, stumoats jro coaorj``y dlafusom jam soo Ijthoijtbds js j TO] lf ru`os tl eo `ojrat ey rlto; thoy hjvo al bmoj lf hlw tl jpp`y Ijthoijtbds ba roj`-`bfo sbtujtblas. Js sudh, thoy jsk tho quostbla, ‐Shy ml wo pursuo Ijthoijtbds<’. ]ho Tdhll` Ejsom Jssossioat (TEJ) Wrlnodt bs ja oxdo``oat wjy tl `bak Ijthoijtbds tl roj`-wlr`m ovoats jam ho`p stumoats tl jpp`y tho dladopts thjt hjvo eooa tjucht ba tho d`jssrlli. 76 Wrlnodts ba Ijthoijtbds wb`` ho`p stumoats tl rodlcabzo thjt Ijthoijtbds bs j du`turj` pursubt; bt bs j `jacujco thjt porvjmos ovory du`turo. Wrlnodts wb`` ho`p stumoats cjba tho fl``lwbac skb``s> :. rojm jam thbak drbtbdj``y 5. motodt ſtjws ba jrcuioats 4. dlastrudt vbje`o jrcuioats =. bmoatbfy rbsks ?. ijko `lcbdj` modbsblas 6. tost jaodmltj` ovbmoado flr ro`bjeb`bty 3. prl﬊dboady ba lrj` jam wrbttoa dliiuabdjtbla Hoado, ja TEJ Wrlnodt wb`` ho`p stumoats tl jaswor tho quostbla, ‐Shoa ji B ovor clbac tl uso Ijthoijtbds<’. Ba rodoat yojrs, thoro hjs eooa j crlwbac rodlcabtbla thjt stumoats shlu`m `ojra Ijthoijtbds ba sudh j wjy thjt thoy dja soo bts ro`ovjado ba tho roj` wlr`m. ]ho Ijthoijtbds TEJ Wrlnodt hjs alw eodlio ja ossoatbj` pjrt lf tho DTOD Ty``jeus jam dlastbtutos 57% lf tho ﬊aj` DTOD Oxjibajtbla. ]ho TEJ Wrlnodts roqubro tho stumoats tl> :. To`odt j prle`oi flr rosojrdh frli tho roj` wlr`m. 5. To`odt tho ro`ovjat Ijthoijtbds tlpbd frli jay pjrt lf tho sy``jeus ba lrmor tl rosojrdh jam bavostbcjto tho dhlsoa prle`oi. 4. Srbto j d`ojr`y oxp`jbaom, `lcbdj` jam soquoadom prlnodt thjt sjtbs﬊os dortjba cubmo`baos stbpu`jtom ey tho Djrbeeoja Oxjibajtblas Dluadb` (DXD). 73 T]U_D]_UO LF J DTOD IJ]HOIJ]BDT TEJ WULNOD] Jftor ylu hjvo dhlsoa j Ijthoijtbds Wrlnodt tl rosojrdh, tho aoxt stop bs tl modbmo hlw tho prlnodt shlu`m eo prosoatom. ]ho lenodtbvo lf tho Ijthoijtbds TEJ Wrlnodt bs tl sook ja jaswor tl j prle`oi thjt wjs bmoatb﬊om jam tl coaorjto j wrbttoa roplrt la tho ﬊ambacs lf tho bavostbcjtbla. ]hbs roplrt iust eo propjrom jam prosoatom ba j pjrtbdu`jr lrmor ]ho DTOD Ijthoijtbds TEJ Wrlnodt dlasbsts lf sovoa (3) ijba sodtblas jam iust eo prosoatom ba tho fl``lwbac lrmor> TOD]BLA LF ]HO WULNOD] IJUKT [email protected]]OM ER D.X.D. :. ]bt`o lf Wrlnodt : 5. Batrlmudtbla = 4.IothlmlfMjtjDl``odtbla 5 =.WrosoatjtblalfMjtj ?. Jaj`ysbs lf Mjtj 5 6.MbsdussblalfFbambacs ? 5 Dlad`usbla 3. 5 ]ltj` :8 ]horo jro twl (5) ijrks thjt jro jwjrmom flr lvorj`` prosoatjtbla. ]horoflro, tho ijxbiui ijrk thjt dja eo letjbaom flr tho Ijthoijtbds TEJ Wrlnodt bs twoaty (57). AE> ]horo jro twl lthor sue-sodtblas lf tho Ijthoijtbds TEJ Wrlnodt thjt iust eo prosoatom jt tho oam lf tho prlnodt. ]hoso jro> :. tho Uoforoado 5. tho Jppoambx ]hoy jro dj``om sue-sodtblas eodjuso ijrks jro alt jwjrmom flr thoso twl sodtblas. 78 ]horoflro, j Ijthoijtbds TEJ Wrlnodt hjs abao (2) mbfforoat sodtblas; sovoa (3) sodtblas jro jwjrmom ijrks jam twl (5) sodtblas jro prosoatom flr dlip`otoaoss lf tho prlnodt hlwovor, al ijrks wb`` eo jwjrmom flr thoi. Eoflro wo dl``odt mjtj flr j prlnodt, wo iust kalw flr whjt purplso wo jro dl``odtbac tho mjtj; whjt bs tho prle`oi thjt wo wbsh tl sl`vo wbth tho mjtj< Hoado, tho ﬊rst stop lf tho prlnodt bs tl bmoatbfy j rosojrdh prle`oi thjt wo wlu`m `bko tl jaswor. Ba thbs babtbj` stjco, tho suenodt tojdhor shlu`m p`jy ja batocrj` rl`o ba jssbstbac tho stumoat tl bmoatbfy sbip`o roj`-wlr`m prle`ois thjt dja eo sl`vom usbac ejsbd Ijthoijtbdj` todhabquos. ]ho abao (2) sodtblas lf j prlnodt jro lut`baom jam oxp`jbaom eo`lw. J sjip`o prlnodt bs usom tl oxp`jba ojdh sodtbla lf tho prlnodt. CO]]BAC T]JU]OM (@llkbac flr mjtj tl sl`vo j sbip`o roj`-wlr`m prle`oi) [email protected] WULNOD] EOCBAT> @ot us supplso thjt j stumoat wjats tl motoribao tho `oacth lf tbio thjt hbs/hor poors spoam wjbtbac ba `bao flr sorvbdo jt tho sdhll`‒s djfotorbj murbac tho `uadh erojk. ]ho stumoat wb`` hjvo tl dl``odt qujatbtjtbvo mjtj ba lrmor tl bavostbcjto tho prle`oi. ]ho prlnodt dja eo prosoatom js fl``lws> TOD]BLA :> WULNOD] ]B]@O ]ho prlnodt tbt`o bs j d`ojr jam dliprohoasbvo stjtoioat thjt stjtos tho roj`-wlr`m prle`oi whbdh bs clbac tl eo bavostbcjtom lr oxp`jbaom. Bt to``s tho rojmor whjt tho prlnodt bs jelut. Flr oxjip`o, ba thbs sjip`o prlnodt tho prlnodt tbt`o dja rojm js fl``lws> ‐Ja bavostbcjtbla ba lrmor tl motoribao tho `oacth lf tbio stumoats spoam wjbtbac ba `bao flr sorvbdo jt tho sdhll`‒s djfotorbj murbac tho `uadh erojk.’ TOD]BLA 5> BA]ULM_D]BLA Ja batrlmudtbla bs j d`ojr`y wrbttoa pjrjcrjph thjt batrlmudos tho rojmor tl tho prlnodt. Bt shlu`m to`` tho rojmor why tho prlnodt wjs dhlsoa. Ba thbs sodtbla, tho stumoat iust d`ojr`y stjto tho lenodtbvo lf tho prlnodt. ]ho batrlmudtbla iust j`sl bad`umo j ]je`o lf Dlatoats flr tho prlnodt. ]ho ]je`o lf Dlatoats to``s tho rojmor whoro tl ﬊am tho mbfforoat sodtblas lf tho prlnodt. 72 Horo, tho stumoat shlu`m bmoatbfy tho pjco auieor la whbdh ojdh lao lf tho abao (2) sodtblas lf tho prlnodt dja eo fluam. ]ho ]je`o lf Dlatoats shlu`m eo p`jdom jftor tho hojmbac ‐Batrlmudtbla’ eut eoflro tho jdtuj` Batrlmudtbla bs wrbttoa. Flr oxjip`o,tho Batrlmudtbla flr tho sjip`o TEJ Wrlnodt shlu`m eo prosoatom jsfl``lws> BA]ULM_D]BLA ][email protected] LF DLA]OA]T> Wrlnodt ]bt`o .................................................................................................Wjco auieor Batrlmudtbla ...............................................................................................Wjco auieor Iothlm lf Mjtj Dl``odtbla .........................................................................Wjco auieor Wrosoatjtbla lf Mjtj ...................................................................................Wjco auieor Jaj`ysbs lf Mjtj..........................................................................................Wjco auieor Mbsdussbla lf Fbambacs ...............................................................................Wjco auieor Dlad`usbla..................................................................................................Wjco auieor Uoforoados .................................................................................................Wjco auieor Jppoambx ....................................................................................................Wjco auieor ‐Ijay lf iy poors usuj``y jrrbvo `jto flr d`jssos jftor tho `uadh erojk. Shoa tojdhors oaqubro jelut thbs hjebt, tho oxduso bs lftoatbios thjt tho stumoat spoat j `lac porblm lf tbio wjbtbac ba `bao flr sorvbdo jt tho sdhll`‒s djfotorbj. ]hbs oxduso bs alt j`wjys jddoptom ey tho tojdhors jam iy poors jro sliotbios puabshom. ]horoflro, B hjvo modbmom tl ml ja bavostbcjtbla ba lrmor tl motoribao bf tho wjbtbac tbio flr sorvbdo bs js `lac js bs roplrtom ey stumoats.’ TOD]BLA 4> IO]HLM LF MJ]J [email protected]@OD]BLA ]hbs bs j motjb`om mosdrbptbla thjt stjtos oxjdt`y hlw jam whoro tho mjtj flr j prlnodt wjs dl``odtom. Bt bs biplrtjat tl roioieor thjt tho rosojrdh bs sookbac tl jaswor j prle`oi thjt tho stumoat hjs bmoatb﬊om. Hoado, ba lrmor tl ho`p tho stumoat tl jaswor tho rosojrdh prle`oi, mjtj iust eo djrofu``y dl``odtom jam stumbom. Mjtj dja eo dl``odtom ba j auieor lf mbfforoat wjys. ]ho pjrtbdu`jr iothlm dhlsoa flr mjtj dl``odtbla wb`` vjry jam mopoams la whjt typo lf mjtj tho stumoat bs `llkbac flr. ]ho fl``lwbac jro j fow mbfforoat iothlms thjt dja eo usom tl dl``odt mjtj> (j) ]HO Z_OT]BLAAJBUO Ba thbs iothlm, tho stumoat cbvos tho rosplamoats wrbttoa quostblas la j quostbla shoot. ]ho quostblas jro stjamjrmbzom whbdh iojas thjt j`` tho rosplamoats iust jaswor tho sjio sot lf quostblas. ]hbs iothlm bs ja baoxpoasbvo wjy tl dl``odt mjtj frli j `jrco auieor lf porslas. Bt j`sl j``lws flr dl``odtbac mjtj ojsb`y wbthlut rovoj`bac tho rosplamoat‒s bmoatbty. :7 Hlwovor, slio mbsjmvjatjcos lf usbac quostblaajbros jro> • Uosplamoats jro sliotbios alt iltbvjtom tl jaswor j`` tho quostblas. • Bf slio rosplasos jro dlafusbac, thoy jro usuj``y mbf﬊du`t tl d`jrbfy. • Tliotbios quostblaajbros jro alt roturaom la tbio. (e) [email protected] BA]OUVBOST Horo, tho stumoat dja strudturo slio quostblas thjt ho lr sho wjats tl eo jasworom. ]ho stumoat dja thoa quostbla rosplamoats jam rodlrm tho jaswors la j shoot. Ba thbs iothlm, tho stumoat hjs tho ſtoxbeb`bty tl prleo tho rosplamoats ba lrmor tl d`jrbfy jaswors jam jsk fl``lw up quostblas. Hlwovor, sbado tho stumoat bs fjdo tl fjdo wbth tho rosplamoat, thbs ijy djuso mbsdliflrt tl tho rosplamoat jam ho lr sho ijy alt jaswor truthfu``y. Ba jmmbtbla, tho porslaj` ajturo lf tho batorvbow ijy djuso tho stumoat tl jsk suenodtbvo quostblas thjt dlu`m `ojm tho rosplamoat ba j pjrtbdu`jr mbrodtbla. (d) LETOUVJ]BLA Sbthlut dlamudtbac batorvbows tho stumoat dja batocrjto batl j plpu`jtbla jam qubot`y rodlrm mjtj la bt. ]hbs mjtj dja thoa eo stumbom ba lrmor tl ijko baforoados jelut tho plpu`jtbla. Alto, thjt ba thbs iothlm lf mjtj dl``odtbla, tho stumoat wb`` hjvo al dlatrl` lvor tho crlup thjt bs clbac tl eo lesorvom. (m) OXJIBAJ]BLA LF UODLUMT ]ho stumoat dja sook poribssbla tl poruso rodlrms, roplrts, stjtoioats jam rocu`jtblas ba lrmor tl dl``odt mjtj la j pjrtbdu`jr crlup. Hlwovor, tho mbsjmvjatjcos lf thbs iothlm jro> • Bt dja tjko j `lac tbio tl slrt jam dl``odt mjtj frli roplrts jam rodlrms. • ]ho stumoat ijy alt uamorstjam tho mjtj frli tho rodlrms jam jrrbvo jt fju`ty dlad`usblas. [email protected] Uoioieor, thjt j rosojrdh bavostbcjtos tho ro`jtblashbp eotwooa vjrbje`os. J vjrbje`o bs jay fjdtlr thjt hjs j qujatbty lr quj`bty thjt dja dhjaco. Flr oxjip`o> • J mopoamjat vjrbje`o bs j vjrbje`o thjt dja dhjaco ejsom la tho bipjdt lf jalthor vjrbje`o. • Ja bamopoamoat vjrbje`o bs j vjrbje`o thjt jffodts j mopoamjat vjrbje`o whbdh dja djuso bt tl dlatrbeuto tl j prle`oi. Flr oxjip`o, ba thbs sjip`o prlnodt> Torvbdo jt tho djfotorbj bs ja bamopoamoat vjrbje`o thjt dja bipjdt la tho wjbtbac tbio flr tho sorvbdo. Sjbtbac tbio bs tho mopoamjat vjrbje`o. Shoa dl``odtbac mjtj flr j prlnodt bt bs cllm prjdtbdo tl bmoatbfy tho mbfforoat typos lf vjrbje`os. :: Flr oxjip`o, ba thbs sjip`o prlnodt tho iothlm lf mjtj dl``odtbla dlu`m rojm js fl``lws> ]ho iothlm lf mjtj dl``odtbla dhlsoa wjs porslaj` batorvbows. ‐J flri d`jss wjs so`odtom frli ojdh yojr crlup frli Flris : tl ?. ]ho ajios lf j`` tho stumoats frli ojdh d`jss woro p`jdom batl ﬊vo (?) sopjrjto elxos. Ojdh elx wjs shjkoa jam thoa tho ajios lf twoaty (57) stumoats woro rjamli`y so`odtom frli ojdh elx. ]hbs drojtom j sjip`o sbzo lf lao huamrom (:77) stumoats flr tho purplso lf tho rosojrdh.’ ]ho lao huamrom (:77) stumoats woro thoa ojdh jskom tho stjamjrmbzom quostbla> ‐Hlw `lac mbm ylu spoam wjbtbac ba `bao flr sorvbdo jt tho sdhll`‒s djfotorbj murbac tho `uadh erojk<’ ]ho mjtj wjs dl``odtom frli Ilamjy tl Frbmjy, lvor j lao wook porblm. Woribssbla tl survoy tho stumoats murbac tho porblm biiombjto`y jftor tho `uadh erojk wjs crjatom ey iy tojdhor. TOD]BLA => WUOTOA]J]BLA LF MJ]J ]hbs bs j vory biplrtjat pjrt lf tho prlnodt whoro, tho stumoat prosoats tho mjtj thjt ho/ sho hjs dl``odtom. Coaorj``y, rojmors jro alt kooa la rojmbac thrluch `lac quj`btjtbvo prosoatjtblas lf mjtj jam jro ilro bad`baom tl poruso mbjcrjis sbado mbjcrjis, usuj``y suiijrbzo `jrco jiluats lf mjtj. Hoado, jftor dl``odtbac jam lrcjabzbac quj`btjtbvo mjtj, tho stumoat iust prosoat tho mjtj usbac jt `ojst twl djrofu``y `jeo`om mbjcrjis. ]hoso dja eo stjtbstbdj` mbjcrjis sudh js> • Froquoady ]je`os • Ejr Crjphs • Wbo Dhjrts • Dlipjrjtbvo Ejr Crjphs • Hbstlcrjis • Froquoady Wl`yclas • Duiu`jtbvo Froquoady Durvos. :5 ]ho fl``lwbac bs ja oxjip`o lf tho Wrosoatjtbla lf Mjtj flr tho sjip`o prlnodt> ]ho froquoady tje`o jam tho duiu`jtbvo froquoady tje`o shlw tho wjbtbac tbio ba ibautos thjt tho lao huamrom (:77) stumoats spoat wjbtbac ba `bao jt tho djfotorbj. Froquoady ]je`o Sjbtbac tbio ba ibautos ? - : Al. lf stumoats (f) 5 :7 - 6 :7 :?-:: :3 57-:6 :6 5?-5: 5? 47-56 58 4? - 4: 5 Duiu`jtbvo Froquoady ]je`o Sjbtbac tbio ba ibautos ? - Al. lf stumoats (f) : 5 :7 - Duiiu`jtbvo froquoady (df) 5 6 :7 :5 :? - :: :3 52 57 - :6 :6 =? 5? - 5: 5? 37 47 - 56 58 28 4? - 4: 5 :77 ]ho stumoats iust j`sl prosoat tho jpprlprbjto Ijthoijtbds dladopts usom tl jrrbvo jt tho rosojrdh rosu`ts. J`` ijthoijtbdj` rosu`ts iust eo prosoatom jddurjto`y usbac jpprlprbjto flriu`jo. Horo, tho fl``lwbac rosu`ts dja eo dj`du`jtom jam prosoatom> :4 • ijthoijtbdj` ioja • ilmo • • rjaco jroj • vl`uio • prl﬊t • `lss • Hbro Wurdhjso prbdo Flr oxjip`o, j`` dj`du`jtblas flr thbs sjip`o prlnodt jro prosoatom js fl``lws> :. Dj`du`jtbla lf tho ioja wjbtbac tbio. ? - Sjbtbac tbio Auieor lf D`jss ibmplbat ba ibautos stumoats f x 5: :7 - 4 6 :7 f Óx 6 8 87 :? - :: :3 :4 55: 57 - :6 :6 :8 588 5? - 5: 5? 54 ?3? 47 - 56 58 4? - 4: 58 5 38= 44 66 5757 √f 9 :77 √f Ó x ]ho jvorjco lr ioja 9 (tho sui lf f Ó x ) 9 (√fx) (tho sui lf (√f) Alto> f) 9 5757 :77 Τ bs tho Crook `ottor sbcij. Bt bs usom horo tl rop`jdo tho phrjso ‐tho sui lf’. ]ho Duiu`jtbvo Froquoady Durvo bs usom tl motoribao tho auieor lf stumoats whl wjbtom flr ilro thja j dortjba auieor lf ibautos flr sorvbdo jt tho sdhll`‒s djfotorbj. B motoribaom tho auieor lf stumoats whl wjbtom flr ilro thja twoaty (57) ibautos ey mrjwbac j vortbdj` `bao frli twoaty (57) ibautos la tho hlrbzlatj` jxbs tl ioot tho durvo jt plbat J js shlwa pjco :?. J hlrbzlatj` `bao wjs thoa mrjwa frli J tl ioot tho vortbdj` jxbs jt =5. Hoado, :77 - =5 9 ?8 stumoats frli tho sjip`o wjbtom flr ilro thja twoaty (57) ibautos flr sorvbdo. ]ho iombja wjbtbac tbio wjs motoribaom ey mrjwbac j hlrbzlatj` `bao frli ?7 la tho vortbdj` jxbs tl ioot tho durvo jt plbat E js shlwa. J vortbdj` `bao wjs thoa mrjwa tl ioot tho hlrbzlatj` jxbs jt twoaty twl (55) ibautos. Hoado, tho iombja wjbtbac tbio bs twoaty twl (55) ibautos. := Duiu`jtbvo froquoady durvo flr mjtj Tdj`o> 5di ≪ :7 stumoats la vortbdj` jxbs, 5di ≪ ? ibautos la hlrbzlatj` jxbs T ] A O M _ ] T F:77 L U O E I _ A ( 27 y 87 37 67 E ?7 J =7 47 57 :7 :? 7.? ?.? :7.? :?.? 57.? 5?.? 47.? 4?.? x (SJB]BAC ]BIO BA IBA_]OT) TOD]BLA ?> [email protected] LF MJ]J Ba thbs sodtbla, tho iojabac lf tho mjtj prosoatom iust eo mbsdussom ba j d`ojr jam `lcbdj` ijaaor. ]ho jaj`ysbs iust to`` tho rojmor whjt ho lr sho iust cot frli tho mjtj prosoatom. Bt iust sjy hlw tho ﬊ambacs jro ro`jtom tl tho prlnodt lenodtbvos. Flr oxjip`o, ba thbs sjip`o prlnodt, tho jaj`ysbs dja rojm js fl``lws> ‐]ho ioja wjbtbac tbio lf 57.5 ibautos jam tho iombja wjbtbac tbio lf 55 ibautos succost thjt j `jrco auieor lf stumoats frli tho sjip`o wjbtom flr ilro thja twoaty (57) ibautos. ]hbs bs supplrtom ey tho Duiu`jtbvo Froquoady Durvo whoro ﬊fty obcht (?8) stumoats wjbtom flr ilro thja twoaty (57) ibautos. ]hbs j`sl moilastrjtos thjt bf j stumoat bs dhlsoa jt rjamli frli tho sjip`o, tho prlejeb`bty thjt ho/sho wb`` wjbt flr ilro thja twoaty (57) ibautos bs ?8 .’ :77 TOD]BLA 6> MBTD_TTBLA LF FBAMBACT> Shoa mbsdussbac tho ﬊ambacs, tho stumoat shlu`m d`ojr`y stjto tho ﬊ambacs letjbaom frli tho jaj`ysbs lf tho mjtj jam mbsduss hlw thoy jro ro`jtom tl tho purplso lf tho prlnodt thjt wjs stjtom ba tho batrlmudtbla. ]ho mbsdussbla lf tho ﬊ambacs shlu`m j`wjys eo `bakom tl tho tbt`o jam tho batrlmudtbla lf tho prlnodt. Hoado, ba wrbtbac tho mbsdussbla, tho stumoat shlu`m j`wjys rotura tl tho prlnodt tbt`o jam batrlmudtbla flr cubmjado. Flr oxjip`o, ba thbs sjip`o prlnodt, tho mbsdussbla lf tho ﬊ambacs dja rojm js fl``lws> ‐]ho mjtj rovoj`om thjt tho ioja wjbtbac tbio flr sorvbdo jt tho sdhll`‒s djfotorbj bs 57.5 ibautos jam tho iombja wjbtbac tbio bs twoaty twl (55) ibautos. Fbfty obcht (?8) stumoats wjbtom ba `bao flr ilro thja twoaty (57) ibautos mjb`y. ]ho `uadh erojk bs lao hlur `lac jam stumoats sjbm thjt, bt tjkos ja jvorjco lf twoaty (57) ibautos tl dlasuio thobr `uadh. ]hbs `ojvos stumoats wbth :2.8 ibautos tl propjro thoiso`vos flr d`jssos jftor `uadh. ]hbs shlu`m cbvo stumoats oaluch tbio tl jrrbvo tl d`jss la tbio jftor tho `uadh erojk.’ :6 TOD]BLA 3> [email protected]_TBLA ]ho dlad`usbla bs j d`ojr`y wrbttoa jam dladbso pjrjcrjph thjt bs `bakom tl tho purplso lf tho prlnodt. Bt lffors tho stumoat j ﬊aj` dhjado tl moilastrjto thjt ho/sho hjs j dlip`oto uamorstjambac lf tho prlnodt‒s lenodtbvos. Shoa wrbtbac tho dlad`usbla, tho stumoat shlu`m rotura tl tho batrlmudtbla lf tho prlnodt jam `llk jt tho purplso flr whbdh tho rosojrdh wjs dlamudtom. ]ho dlad`usbla shlu`m mbsduss jam jaswor tho purplso lf tho prlnodt. Flr oxjip`o, ba thbs sjip`o prlnodt tho dlad`usbla dja rojm js fl``lws> ‐]ho rosojrdh shlws thjt tho stumoats‒ d`jbi lf j `lac wjbtbac tbio flr sorvbdo jt tho djfotorbj murbac tho `uadh erojk bs rojslaje`o. Hlwovor, ja jvorjco wjbtbac tbio lf 57.5 ibautos stb`` `ojvos thoi wbth oaluch tbio flr ojr`y jrrbvj` tl d`jssos flr tho jftoralla sossbla.’ Jftor tho sovoa (3) ijba sodtblas lf tho prlnodt jro prosoatom, thoro jro twl lthor sodtblas thjt iust eo prosoatom flr dlip`otoaoss. Hlwovor, ijrks wb`` alt eo jwjrmom flr thoso twl sodtblas. ]hoso twl sodtblas jro> :. Uoforoado 5. Jppoambx TOD]BLA 8> UOFOUOADOT J roforoado bs tho poau`tbijto sodtbla lf tho prlnodt. Bt dlatjbas j `bst lf j`` tho slurdos sudh js> ellks, aowspjpors, ijcjzbaos jam woesbtos whbdh tho stumoat wlu`m hjvo usom ba lrmor tl jssbst ba hbs/hor rosojrdh flr tho prlnodt. Flr oxjip`o, tho roforoados flr tho sjip`o prlnodt jro `bstom eo`lw. Croor, J & @jyao, D.O, Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja. 5am Om. www.ijthbsfua.dli www.purp`oijth.dli www.hlio.juvjatj.dli TOD]BLA 2> JWWOAMBX Ja Jppoambx bs tho sodtbla jt tho oam lf tho prlnodt thjt dlatjbas supplrtbac mlduioats thjt woro usom ey tho stumoat ba tho wrbtbac lf tho prlnodt. ]hoso supplrtbac mlduioats jro ossoatbj` flr tho dlip`otoaoss lf tho prlnodt eut ibcht eo dlasbmorom tll `lac jam duieorslio flr tho rojmor tl poruso. Ujw mjtj, tje`os, dhjrts, crjphs, quostblaajbros jam mo﬊abtblas jro slio lf tho thbacs thjt dja eo bad`umom ba tho jppoambx. Bf ylu hjvo ilro thja lao jppoambx, ijko suro thjt ojdh lao eocbas la j aow :3 pjco jam bs tbt`om; Jppoambx J, Jppoambx E, Jppoambx D otd. Flr oxjip`o, tho Jppoambx flr tho sjip`o prlnodt shlu`m eo prosoatom js fl``lws> JWWOAMBX Ujw mjtj shlwbac tho tbio thjt tho lao huamrom (:77) stumoats spoat wjbtbac flr sorvbdo jt tho djfotorbj. 4:, 4=, :6, 57, 5, :7, ?, :6, :3, ::, :5, :?, :=, 8, 3, :7, 5:, 5?, 53, 52, 58, 53, :6, ::, :?, :4, 5:, 5=, 55, :4, :=, :?, 52, 47, 53, :4, :?, :6, :2, :8, 56, 52, 47, 3, :7, 6, 8, 8, 2, :7, :5, :=, :?, :5, ::, :6, :3, :?, 57, :=, :?, :6, 57, 55, 54, 5=, 5?, 5:, 54, 55, 5=, 5?, 5:, 5?, 5=, 5:, 55, 54, 5=, 5?, 55, 54, 5=, 5?, 47, 52, 56, 53, 5?, 47, 53, 47, 52, 58, 52, 56, 53, 56, 47, 52. // WUOTOA]J]BLA LF [email protected] WULNOD] OAMT // [email protected] LF ]HO ]OJDHOU> ]ho ejsbd rl`o lf tho tojdhor bs tl> • Jssbst stumoats wbth tho so`odtbla lf tlpbds tl eo bavostbcjtom flr prlnodts. • Wrlvbmo iojabacfu` cubmjado thrluchlut tho murjtbla lf tho prlnodt. ]ho tojdhor wb`` sot mojm`baos flr stumoats tl dlip`oto ojdh pjrt lf tho prlnodt. ]ho tojdhor iust oasuro thjt stumoats jmhoro tl roqubrom mojm`baos. • J``lw tho stumoats tl prlmudo j auieor lf mrjfts lf tho dhlsoa prlnodt. ]ho tojdhor shlu`m rojm tho mrjfts, lffor foomejdk jam cbvo cubmjado thrluchlut tho dyd`o lf tho prlnodt. Bt shlu`m eo altom thjt, tho tojdhor‒s rl`o bs thjt lf j fjdb`btjtlr jam js sudh ho/sho shlu`m la`y lffor cubmjado rjthor thja cbvo sl`utblas tl tho prle`oi eobac bavostbcjtom ba tho prlnodt. • Mombdjto jt `ojst lao porblm por wook ba lrmor tl fjdb`btjto mbsdussblas la bssuos ro`jtbac tl tho prlnodt. • Mbsduss stumoats‒ prle`ois wbth tho Hojm lf Mopjrtioat ba lrmor tl jrrbvo jt sl`utblas. :8 [email protected] LF ]HO T]_MOA] ]ho ejsbd rl`o lf tho stumoat bs tl> • Slrk d`lso`y wbth tho tojdhor ba lrmor tl so`odt ja TEJ Wrlnodt rosojrdh tlpbd. • Jmhoro tl j`` mojm`baos sot ey tho tojdhor. • Took jmvbdo frli tho tojdhor la j`` tho mbfforoat pjrts lf tho prlnodt. • Uojm aowspjpors, nluraj`s, ijcjzbaos jam ellks ba lrmor tl cot baflrijtbla la tho tlpbd dhlsoa flr bavostbcjtbla. ]ho batoraot bs j`sl ja bavj`uje`o tll` ba tho propjrjtbla lf j prlnodt. • Wrlmudo mrjfts lf tho prlnodt flr tho tojdhor‒s porusj` eoflro tho ﬊aj` prlnodt bs sueibttom. ]hbs wb`` j``lw tho tojdhor tl cbvo iojabacfu` jam tbio`y foomejdk tl stumoats eoflro tho dlip`otbla lf prlnodts jam ﬊aj` sueibssbla. J SLUM LF DJ_]BLA • J Ijthoijtbds TEJ Wrlnodt bs iojat tl tost dortjba skb``s lf j pjrtbdu`jr djambmjto. ]horoflro, whoa mlbac ja TEJ prlnodt, lao iust ijko ovory offlrt tl oasuro thjt lao‒s lrbcbaj` wlrk bs prlmudom jam prosoatom. Bf tho stumoat bs usbac jalthor porsla‒s wlrk, thoa drombt iust eo cbvoa tl tho prlmudor lf tho lrbcbaj` wlrk. Ttumoats ijy wlrk ba sij`` crlups whoa dl``odtbac mjtj flr j prlnodt. Hlwovor, ojdh stumoat bs oxpodtom tl wrbto hbs lr hor lwa jaj`ysbs jam dlad`usbla lf mjtj dl``odtom. • ]ho Ijthoijtbds TEJ Wrlnodt hjs j `bibt lf lao thlusjam (:,777) wlrms jam ovory offlrt iust eo ijmo tl stjy wbthba tho stbpu`jtom `bibt. Fjb`uro tl ml sl wb`` rosu`t ba j momudtbla lf ijrks frli tho stumoat‒s ﬊aj` TEJ Wrlnodt ijrk. Ba lrmor tl jvlbm oxdoombac tho wlrm `bibt lao shlu`m put oxtrj ijtorbj`s sudh js dhjrts, tje`os, rjw mjtj, pbdturos jam mo﬊abtblas ba ja jppoambx. • Shoa wrbtbac j prlnodt, ml alt uso tho jdtuj` ajios lf eusbaossos, sdhll`s, polp`o jam clvoraioat bastbtutblas. • Shoa wlrkbac la prlnodts oasuro thjt wlrk bs dlatbauj``y ejdkom up jam sjvom. ]hbs wb`` ho`p stumoats tl ojsb`y rop`bdjto wlrk ba tho ovoat lf thoft lr j mbsjstor. Bt wb`` j`sl ho`p ba tho sueibssbla lf tho ﬊aj` Ijthoijtbds TEJ prlnodt tl DXD js thbs wb`` eo prosoatom vbj slft dlpy. • ]wl ijrks jro jwjrmom flr tho lvorj`` prosoatjtbla lf tho prlnodt. Hoado, ovory offlrt iust eo ijmo ba lrmor tl oasuro thjt tho baflrijtbla prosoatom ba tho prlnodt bs crjiijtbdj``y dlrrodt jam iust eo wrbttoa d`ojr`y jam `lcbdj``y. ]ho stumoat dja jsk ja Oac`bsh tojdhor tl jssbst hbi lr hor wbth prllfrojmbac tho Ijthoijtbds TEJ Wrlnodt eoflro bts ﬊aj` sueibssbla. :2 WUOTOA]J]BLA LF :7 SLUKOM IJ]HOIJ]BDT TEJ WULNOD]T 57 WULNOD] : TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla batl tho wjbtbac tbio flr sorvbdo jt j hoj`th doatro ba ]rbabmjm jam ]lejcl. 5: WULNOD] : TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................ Wjco Auieor ?. Jaj`ysbs lf Mjtj ......................................................................Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Wolp`o dlip`jba vbj tho iombj (rjmbl, tj`k shlws, abcht`y aows, aowspjpor jrtbd`os, otd.) jelut tho `lac tbio thoy iust wjbt flr sorvbdo jt clvoraioat bastbtutblas sudh js hoj`th doatros, oiorcoady rllis jt hlspbtj`s, jam biibcrjtbla lf﬊dos. Sjbtbac j `lac tbio flr sorvbdo dja eo frustrjtbac, badlavoaboat jam ijy djuso ovoa tho ilst tl`orjat porsla tl eodlio jaalyom, jaxblus lr ovoa `lso oiltblaj` dlatrl`. ]hobr jddluat lf `lac wjbtbac tbio ijy, hlwovor, eo rocjrmom js obthor uaro`bje`o lr hojrsjy. ]ho purplso lf thbs prlnodt bs tl uso stjtbstbdj` todhabquos tl bavostbcjto tho d`jbi thjt polp`o wjbt j `lac tbio flr sorvbdo jt clvoraioat bastbtutblas. J hoj`th doatro wjs dhlsoa eodjuso ilst lf tho dlip`jbats woro lf tjrmy hoj`th djro mo`bvory. 55 WULNOD] : TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA J hoj`th doatro wjs vbsbtom frli Ilamjy tl Frbmjy eotwooa tho hlurs lf 3>77 ji tl =>77 p.i. ]ho mjtj djpturom woro thjt lf tho ﬊rst thbrty porslas whl oatorom flr sorvbdo ojdh mjy. ]ho rocbstorbac d`ork bssuom j dlasodutbvo auieor tl ojdh pjtboat js ho lr sho wjs sojtom. J iothlm lf mjtj dl``odtbla dj``om ala-pjrtbdbpjat lesorvjtbla wjs usom. ]ho mjtj woro coaorjtom ey mbrodt`y lesorvbac jam rodlrmbac tho jdtbvbtbos lf ojdh mjy js fl``lws> • mjys lf tho wook thjt porslas jrrbvom flr sorvbdo • dlasodutbvo auieors lf 47 porslas whl oatorom tho rlli flr sorvbdo • jrrbvj` tbios lf ojdh porsla • tho tbios jt whbdh thoy woro dj``om tl rodobvo sorvbdo. ]horo wjs al batorjdtbla wbth tho porslas eobac lesorvom. (Too Jppoambx flr rjw mjtj) 54 WULNOD] : TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Jftor tho mjtj woro dl``odtom flr tho ﬊vo mjys, tho rjw mjtj woro thoa lrcjabzom usbac ﬊vo froquoady mbstrbeutbla tje`os. ]ho tje`os dlasbst lf sbx d`jss batorvj`s ojdh hjvbac j wbmth lf ?7 ibautos. ILAMJR Sjbtbac tbio ba ibautos ]_OTMJR Auieor lf pjtboats (f) Sjbtbac tbio ba ibautos SOMAOTMJR Auieor lf pjtboats (f) Sjbtbac tbio ba ibautos Auieor lf pjtboats (f) :77:=2 - 7 :77:=2 - : :77:=2 - 7 :?7:22 - 4 :?7:22 - 2 :?7-:22 :4 5775=2 - ? 577-5=2 :7 5775=2 - 8 5?7522 - ? 5?7-522 :7 5?7522 - = 477-4=2 4?7422 - :3 7 4774=2 4?7422 - 7 7 4774=2 4?7422 - ? 7 ]L][email protected] 47 ]L][email protected] ]H_UTMJR Sjbtbac tbio ba ibautos 47 47 FUBMJR Auieor lf pjtboats (f) Sjbtbac tbio ba ibautos Auieor lf pjtboats (f) :77:=2 - 3 :77:=2 - : :?7:22 - 2 :?7:22 - = 5775=2 - = 5775=2 - 8 5?7522 - 8 5?7522 - 3 4774=2 - 5 4774=2 - 8 4?7422 - 7 4?7422 - 5 ]L][email protected] ]L][email protected] 47 ]L][email protected] 47 5= Ejr crjph shlwbac jvorjco wjbtbac tbio por mjy ba hlurs (5 di ≪ : hlur la vortbdj` jxbs ) ? =.? = O T U _ 4.? L H A B O 4 BI ] C A B 5.? ] B J S O C 5 J U O V J :.? : 7.? 7 ILAMJR ]_OTMJR SOMAOTMJR ]H_UTMJR FUBMJR ]ho ioja lr jvorjco wjbtbac tbio wb`` alw eo dj`du`jtom flr ojdh mjy. ILAMJR Sjbtbac tbio ba ibautos Auieor lf pjtboats (f) D`jss ibmplbat (x) :?7 :22 - 4 :3=.? ?54.? 577 5=2 - ? 55=.? ::55.? 5?7 522 - ? 53=.? :435.? 477 4=2 - :3 45=.? ??:6.? ]L][email protected] 47 ]ho jvorjco lr ioja 9 ]L][email protected] 5? 8?4? (tho sui lf f Ó x ) 9 (√fx) f) (tho sui lf 9 58=.? ibautos 9 f Óx =.3= hlurs (√f) 9 8?4? 47 ]_OTMJR Sjbtbac tbio ba ibautos Auieor lf pjtboats (f) D`jss ibmplbat (x) : :5=.? :5=.? :?7 :22 - 2 :3=.? :?37.? 577 5=2 - :7 55=.? 55=?.7 5?7 522 - :7 53=.? 53=?.7 :77 :=2 - ]L][email protected] 47 ]ho jvorjco lr ioja 9 ]L][email protected] 668? (tho sui lf f Ó x ) 9 (√fx) (tho sui lf 9 9 f Óx f) 9 668? (√f) 47 555.84 ibautos 4.3: hlurs SOMAOTMJR Sjbtbac tbio ba ibautos Auieor lf pjtboats (f) D`jss ibmplbat (x) f Óx :?7 :22 577 5=2 - :4 8 :3=.? 55=.? 5568.? :326 5?7 522 - = 53=.? :728 477 4=2 - ? ]L][email protected] 45=.? 47 ]ho jvorjco lr ioja 9 9 638? (tho sui lf f Ó x ) 9 (√fx) (tho sui lf 9 :655.? ]L][email protected] f) (√f) 9 638? 47 556.:3 ibautos 4.33 hlurs 56 ]H_UTMJR Sjbtbac tbio ba ibautos :77 :=2 :?7 :22 - Auieor lf pjtboats (f) D`jss ibmplbat (x) 3 :5=.? 83:.? :3=.? :?37.? 2 5=2 577 - = f Óx 55=.? 828 5?7 522 - 8 53=.? 5:26 4=2 477 - 5 45=.? 6=2 ]L][email protected] 47 ]ho jvorjco lr ioja 9 ]L][email protected] (tho sui lf f Ó x ) 9 (√fx) (tho sui lf 9 9 6:8? f) 9 6:8? (√f) 47 576.5 ibautos 4.== hlurs FUBMJR Sjbtbac tbio ba ibautos :77 :=2 - Auieor lf pjtboats (f) : D`jss ibmplbat (x) :5=.? :22 :?7 - = :3=.? 577 5=2 - 8 55=.? 5?7 522 - 3 :5=.? 628 :326 53=.? :25:.? 477 4=2 - 8 45=.? 5?26 422 4?7 - 5 43=.? 3=2 ]L][email protected] 47 ]ho jvorjco lr ioja 9 ]L][email protected] 9 9 388? (tho sui lf f Ó x ) 9 (√ fx) (tho sui lf f) (√ f) 9 388? 47 565.8 ibautos =.48 hlurs Alto> 53 f Óx Τ bs tho Crook `ottor sbcij. Bt bs usom horo tl rop`jdo tho phrjso ‐tho sui lf’ WULNOD] : TOD]BLA 7? [email protected] LF MJ]J ]ho mjtj dl``odtom frli thbs rosojrdh rovoj`om> :. ]ho jvorjco wjbtbac tbio la Ilamjy wjs =.3= hlurs ]ho jvorjco wjbtbac tbio la ]uosmjy wjs 4.3: hlurs ]ho jvorjco wjbtbac tbio la Somaosmjy wjs 4.33 hlurs ]ho jvorjco wjbtbac tbio la ]hursmjy wjs 4.== hlurs ]ho jvorjco wjbtbac tbio la Frbmjy wjs =.48 hlurs 5. ]ho ejrcrjph shlws thjt tho jvorjco wjbtbac tbio la ]uosmjy, Somaosmjy jam ]hursmjy woro jpprlxbijto`y tho sjio (b.o. jelut 4.6 hlurs). Wjtboats wjbtom iudh `lacor la Ilamjy jam Frbmjy flr sorvbdo. La elth lf thoso mjys thoy wjbtom jpprlxbijto`y ja hlur `lacor thja tho lthor throo mjys. La jay cbvoa mjy thoy wjbtom ja jvorjco lf jt `ojst throo hlurs flr sorvbdo. 4. ]ho jvorjco mjb`y wjbtbac tbio 9 (=.3=+4.3:+4.33+4.==+=.48) ? 9 57.7= ? 9 =.778 hlurs ≈ = hlurs ]hbs succosts thjt bf j`` tho pjtboats woro tl wjbt flr tho sjio auieor lf hlurs flr sorvbdo ojdh mjy, thjt wjbtbac tbio wb`` eo = hlurs. 58 WULNOD] : TOD]BLA 76 MBTD_TTBLA LF FBAMBACT ]ho mjtj wjs dl``odtom usbac porslaj` lesorvjtbla lvor j lao wook porblm rovoj`om thjt, la jvorjco, pjtboats wjbtom flr jpprlxbijto`y flur hlurs eoflro eobac jttoamom tl jt thbs pjrtbdu`jr hoj`th doatro. 52 WULNOD] : TOD]BLA 73 [email protected]_TBLA Ejsom la thbs rosojrdh, tho pue`bd‒s pordoptbla thjt porslas wjbt j `lac tbio flr sorvbdo jt clvoraioat bastbtutblas, ajio`y hoj`th doatros, bs truo. Jt thbs bastbtutbla ba pjrtbdu`jr, porslas wjbtom ja jvorjco lf = hlurs mjb`y flr sorvbdo. ]hbs supplrts tho jaodmltj` d`jbi thjt polp`o spoam j `lac tbio wjbtbac flr sorvbdo. ]hbs sbtujtbla bs uatoaje`o jam roqubros urcoat jttoatbla ey thlso ba juthlrbty. 47 WULNOD] : TOD]BLA 78 UOFOUOADOT ]ll`sbo, U.; Ijthoijtbds> J Dlip`oto Dlurso wbth DXD Zuostblas. Vl`. 5 www.dlipjss.plrt.jd.uk www.ylurjrtbd`o`berjry.dli 4: WULNOD] : TOD]BLA 72 JWWOAMBX ILAMJR Wjtboat Al. Jrrbvj` ]bio flr Torvbdo ]bio Dj``om flr Torvbdo : 3>77j.i. 2>47j.i. ]bio Sjbtom flr Torvbdo 5hlurs47ibautos 5 3>77j.i. 2>=:j.i. 5hlurs=:ibautos 4 3>74j.i. :7>77j.i. 5hlurs?3ibautos = 3>7?j.i. :7>57j.i. 4hlurs5=ibautos ? 3>:7j.i. :7>=7j.i. 4hlurs47ibautos 6 3>:?j.i. :7>?7j.i. 4hlurs4?ibautos 3 3>:8j.i. ::>75j.i. 4hlurs==ibautos 8 3>57j.i. ::>57j.i. =hlurs7ibautos 2 3>54j.i. ::>4?j.i. =hlurs:5ibautos :7 3>58j.i. ::>==j.i. =hlurs:6ibautos :: 3>47j.i. ::>?8j.i. =hlurs58ibautos :5 3>48j.i. :5>:?p.i. =hlurs43ibautos :4 3>=5j.i. :5>48p.i. =hlurs?6ibautos := 8>77j.i. :>77p.i. ?hlurs7ibautos :? 8>:7j.i. :>:?p.i. ?hlurs?ibautos :6 8>:5j.i. :>47p.i. ?hlurs:8ibautos :3 8>47j.i. :>48p.i. ?hlurs8ibautos :8 8>44j.i. :>=?p.i. ?hlurs:5ibautos :2 8>48j.i. :>?7p.i. ?hlurs:5ibautos 57 8>=7j.i. 5>77p.i. ?hlurs57ibautos 5: 8>=?j.i. 5>:5p.i. ?hlurs53ibautos 55 8>?6j.i. 5>57p.i. ?hlurs5=ibautos 54 2>7:j.i. 5>5?p.i. ?hlurs5=ibautos 5= 2>:?j.i. 5>4?p.i. ?hlurs:7ibautos 5? 2>58j.i. 5>48p.i. ?hlurs:5ibautos 56 2>47j.i. 5>=?p.i. ?hlurs:?ibautos 53 2>46j.i. 5>=8p.i. ?hlurs:5ibautos 58 2>42j.i. 5>?7p.i. ?hlurs::ibautos 52 47 2>==j.i. 2>=?j.i. 5>??p.i. 4>77p.i. ?hlurs::ibautos ?hlurs:?ibautos 45 ]_OTMJR 44 Wjtboat Al. Jrrbvj` ]bio flr Torvbdo : 3>77j.i. ]bio Dj``om flr Torvbdo 2>57j.i. ]bio Sjbtom flr Torvbdo 5hlurs57ibautos 5 3>:7j.i. 2>=7j.i. 5hlurs47ibautos 4 3>::j.i. 2>=8j.i. 5hlurs43ibautos = 3>:8j.i. :7>7:j.i. 5hlurs=4ibautos ? 3>5?j.i. :7>:?j.i. 5hlurs?7ibautos 6 3>52j.i. :7>5:j.i. 5hlurs?:ibautos 3 3>47j.i. :7>47j.i. 4hlurs7ibautos 8 2 3>4?j.i. 3>42j.i. :7>42j.i. :7>?7j.i. 4hlurs=ibautos 4hlurs:ibautos :7 3>=4j.i. ::>7:j.i. 4hlurs:8ibautos :: 3>=2j.i. ::>:?j.i. 4hlurs56ibautos :5 3>?4j.i. ::>57p.i. 4hlurs53ibautos :4 3>?2j.i. ::>58j.i. 4hlurs52ibautos := 8>7?j.i. ::>4?j.i. 4hlurs47ibautos :? 8>78j.i. ::>=4j.i. 4hlurs4?ibautos :6 8>:?j.i. ::>=2j.i. 4hlurs4=ibautos :3 8>:8j.i. ::>?4j.i. 4hlurs4?ibautos :8 8>54j.i. :5>57p.i. 4hlurs?3ibautos :2 8>52j.i. :5>4?p.i. =hlurs6ibautos 57 8>47j.i. :5>=7p.i. =hlurs?ibautos 5: 8>42j.i. :5>=2p.i. =hlurs:7ibautos 55 8>=5j.i. :5>?4p.i. =hlurs::ibautos 54 8>?7j.i. :>:7p.i. =hlurs57ibautos 5= 8>??j.i. :>:?p.i. =hlurs57ibautos 5? 2>7:j.i. :>47p.i. =hlurs52ibautos 56 2>78j.i. :>48p.i. =hlurs57ibautos 53 2>::j.i. :>==p.i. =hlurs44ibautos 58 2>:?j.i. :>??p.i. =hlurs=7ibautos 52 2>:8j.i. 5>:7p.i. =hlurs?5ibautos 47 2>44j.i. 5>:?p.i. =hlurs=5ibautos SOMAOTMJR Wjtboat Al. Jrrbvj` ]bio flr Torvbdo : 3>77j.i. ]bio Dj``om flr Torvbdo 2>7?j.i. ]bio Sjbtom flr Torvbdo 5hlurs?ibautos 5 3>77j.i. 2>5?j.i. 5hlurs5?ibautos 4 3>77j.i. 2>58j.i. 5hlurs58ibautos = 3>7?j.i. 2>42j.i. 5hlurs4=ibautos ? 3>:5j.i. 2>=?j.i. 5hlurs44ibautos 6 3>:=j.i. 2>??j.i. 5hlurs=:ibautos 3 3>:?j.i. :7>7?j.i. 5hlurs?7ibautos 8 2 3>:8j.i. 3>54j.i. :7>:?j.i. :7>4:j.i. 5hlurs?3ibautos 4hlurs8ibautos :7 3>47j.i. :7>42j.i. 4hlurs2ibautos :: 3>44j.i. :7>?7j.i. 4hlurs:3ibautos :5 3>42j.i. :7>??j.i. 4hlurs:6ibautos :4 3>=:j.i. ::>77j.i. 4hlurs:2ibautos := 3>?7j.i. ::>::j.i. 4hlurs5:ibautos :? 3>?=j.i. ::>57j.i. 4hlurs56ibautos :6 8>77j.i. ::>52j.i. 4hlurs52ibautos :3 8>7?j.i. ::>=7j.i. 4hlurs4?ibautos :8 8>78j.i. ::>=2j.i. 4hlurs=:ibautos :2 8>:5j.i. ::>??j.i. 4hlurs=4ibautos 57 8>:8j.i. :5>57p.i. =hlurs5ibautos 5: 8>54j.i. :5>47p.i. =hlurs3ibautos 55 8>52j.i. :5>=?p.i. =hlurs:6ibautos 54 8>44j.i. :>:7p.i. =hlurs43ibautos 5= 8>42j.i. :>47p.i. =hlurs?:ibautos 5? 8>==j.i. :>42p.i. =hlurs??ibautos 56 8>=8j.i. :>=8p.i. ?hlurs7ibautos 53 8>??j.i. 5>77p.i. ?hlurs?ibautos 58 8>?8j.i. 5>:?p.i. ?hlurs:3ibautos 52 2>7:j.i. 5>5?p.i. ?hlurs:=ibautos 47 2>7?j.i. 5>47p.i. ?hlurs5?ibautos 4= ]H_UTMJR 4? Wjtboat Al. Jrrbvj` ]bio flr Torvbdo : 3>77j.i. ]bio dj``om flr Torvbdo 2>74j.i. ]bio wjbtom flr Torvbdo 5hlurs4ibautos 5 3>77j.i. 2>:7j.i. 5hlurs:7ibautos 4 3>7?j.i. 2>57j.i. 5hlurs:?ibautos = 3>:7j.i. 2>47j.i. 5hlurs57ibautos ? 3>:5j.i. 2>48j.i. 5hlurs56ibautos 6 3>:?j.i. 2>?7j.i. 5hlurs4?ibautos 3 3>47j.i. 2>??j.i. 5hlurs5?ibautos 8 2 3>4?j.i. 3>42j.i. :7>:?j.i. :7>57j.i. 5hlurs4?ibautos 5hlurs=:ibautos :7 8>77j.i. :7>58j.i. 5hlurs58ibautos :: 8>7?j.i. :7>4?j.i. 5hlurs47ibautos :5 8>78j.i. :7>=2j.i. 5hlurs=:ibautos :4 8>::j.i. ::>??j.i. 5hlurs==ibautos := 8>:4j.i. ::>::j.i. 5hlurs?8ibautos :? 8>5?j.i. ::>57j.i. 5hlurs??ibautos :6 8>42j.i. ::>47j.i. 5hlurs?:ibautos :3 8>?7j.i. :5>:7j.i. 4hlurs57ibautos :8 8>??j.i. :5>5?j.i. 4hlurs47ibautos :2 2>77j.i. :>77p.i. =hlurs7ibautos 57 2>78j.i. :>:7p.i. =hlurs5ibautos 5: 2>:7j.i. :>52p.i. =hlurs:2ibautos 55 2>:?j.i. :>47p.i. =hlurs:=ibautos 54 2>5:j.i. :>42p.i. =hlurs:8ibautos 5= 2>54j.i. 5>77p.i. =hlurs43ibautos 5? 2>5?j.i. 5>::p.i. =hlurs=6ibautos 56 2>58j.i. 5>57p.i. ?hlurs?5ibautos 53 2>47j.i. 5>5?p.i. ?hlurs??ibautos 58 2>4:j.i. 5>52p.i. ?hlurs?8ibautos 52 2>4=j.i. 5>4?p.i. ?hlurs:ibautos 47 2>4?j.i. 5>=:p.i. ?hlurs6ibautos FUBMJR Wjtboat Al. Jrrbvj` ]bio flr Torvbdo : 3>77j.i. ]bio dj``om flr Torvbdo 2>:?j.i. ]bio wjbtom flr Torvbdo 5hlurs:?ibautos 5 3>77j.i. 2>47j.i. 5hlurs47ibautos 4 3>77j.i. 2>4?j.i. 5hlurs4?ibautos = 3>7?j.i. :7>77j.i. 5hlurs??ibautos ? 3>78j.i. :7>4?j.i. 4hlurs:3ibautos 6 3>:5j.i. :7>==j.i. 4hlurs45ibautos 3 3>:2j.i. :7>??j.i. 4hlurs46ibautos 8 2 3>5?j.i. 3>47j.i. ::>47j.i. ::>4?j.i. =hlurs?ibautos =hlurs?ibautos :7 3>4?j.i. ::>48j.i. =hlurs4ibautos :: 3>42j.i. ::>==j.i. =hlurs?ibautos :5 3>==j.i. ::>=2j.i. =hlurs?ibautos :4 3>=8j.i. ::>??j.i. =hlurs6ibautos := 3>??j.i. :5>78p.i. =hlurs:4ibautos :? 8>77j.i. :5>57p.i. =hlurs57ibautos :6 8>7?j.i. :5>4?p.i. =hlurs57ibautos :3 8>:7j.i. :5>=2p.i. =hlurs42ibautos :8 8>:8j.i. :>77p.i. =hlurs=5ibautos :2 8>5?j.i. :>57p.i. =hlurs??ibautos 57 8>47j.i. :>58p.i. =hlurs?8ibautos 5: 8>44j.i. :>42p.i. ?hlurs6ibautos 55 8>=7j.i. :>=?p.i. ?hlurs?ibautos 54 8>=?j.i. 5>77p.i. ?hlurs:?ibautos 5= 8>=2j.i. 5>57p.i. ?hlurs4:ibautos 5? 8>?5j.i. 5>52p.i. ?hlurs43ibautos 56 8>??j.i. 5>48p.i. ?hlurs=4ibautos 53 8>?2j.i. 5>=?p.i. ?hlurs=6ibautos 58 2>7:j.i. 5>?7p.i. ?hlurs=2ibautos 52 2>74j.i. 4>77p.i. ?hlurs?3ibautos 47 2>7?j.i. 4>:7p.i. 6hlurs6ibautos 46 WULNOD] 5 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla batl vjrblus Hbro Wurdhjso p`jas frli flur mbfforoat stlros ba ]rbabmjm jam ]lejcl. 43 WULNOD] 5 TOD]BLA 7: BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................ Wjco Auieor ?. Jaj`ysbs lf Mjtj ......................................................................Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Jt lao tbio lr jalthor ovorylao purdhjsos sliothbac frli j stlro. Tliotbios pjyioat ijy eo ba fu`` jt tho tbio lf purdhjso roforrom tl js djsh. Hlwovor, tho euyor ijy dhllso tl oator batl ja jrrjacoioat whoroey pjyioats dja eo ijmo ba oquj` ilath`y bastj`ioats. ]hbs jrrjacoioat jam bts prldoss bs roforrom tl js Hbro Wurdhjso. Flr oxjip`o> iy pjroats jro p`jaabac tl purdhjso j `bvbac rlli sot flr Dhrbstijs eut thoy ml alt hjvo oaluch ilaoy tl pjy djsh flr tho btoi. Js sudh thoy iust oator batl j hbro purdhjso jrrjacoioat wbth tho stlro. Hjvbac stumbom dlasuior jrbthiotbd ba sdhll`, B hjvo modbmom tl uso iy kalw`omco lf Hbro Wurdhjso tl jssbst thoi ba bavostbcjtbac vjrblus Hbro Wurdhjso p`jas. ]ho purplso lf thbs prlnodt bstl bavostbcjto vjrblus Hbro Wurdhjso p`jas ba lrmor tl motoribao hlw thoso p`jas jro dj`du`jtom jam thobr dlst offodtbvoaoss. 48 WULNOD] 5 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA Flur (=) stlros woro vbsbtom. Ttlro J — Ojst ]rbabmjm Ttlro E — Sost ]rbabmjm Ttlro D — Alrth ]rbabmjm Ttlro M — Tluth ]rbabmjm Ja batorvbow wbth tho suporvbslr lf ojdh stlro prlvbmom tho mjtj rocjrmbac tho djsh prbdo jam tho vjrblus Hbro Wurdhjso p`jas la tho sjio `bvbac rlli sot ba hbs/hor rospodtbvo stlro. ]ho mjtj dl``odtom jro js fl``lws> (b) Djsh Wrbdo (bb) Hbro Wurdhjso W`jas> (j) 4 ilaths flr djsh (e) : yojr jt rocu`jr prbdo (d) mlwa pjyioat jam 5= oquj` ilath`y bastj`ioats (m) al mlwa pjyioat jam 5= ilath`y bastj`ioats 42 WULNOD] 5 TOD]BLA 7= WUOTOA]J]BLA LF MJ]J T]LUO J ]ypolfW`ja Djsh ]ypo lf W`ja Dlst lf `bvbac rlli sot ($) IothlmlfWjyioatW`ja lao-lff fu`` pjyioat Iothlm lf Wjyioat W`ja :5,472.67 Uocu`jr Wrbdo ($) Dlst lf `bvbac rlli sot ($) Hbro Wurdhjso W`ja j 4ilathsflrdjsh :?,483.77 :6,:?6.4? Hbro Wurdhjso W`ja e :yojrjtrocu`jrprbdo :?,483.77 :8,=6=.=7 Hbro Wurdhjso W`ja d Mlwa pjyioat jam 5= oquj` ilath`y bastj`ioats :?,483.77 5:,?=:.87 Hbro Wurdhjso W`ja m Al mlwa pjyioat jam 5= ilath`y bastj`ioats :?,483.77 5:,?=:.87 T]LUO E ]ypolfW`ja Djsh ]ypo lf W`ja Dlst lf `bvbac rlli sot ($) IothlmlfWjyioatW`ja lao-lff fu`` pjyioat Iothlm lf Wjyioat W`ja :5,877.77 Uocu`jr Wrbdo ($) Dlst lf `bvbac rlli sot ($) Hbro Wurdhjso W`ja j 4ilathsflrdjsh :6,777.77 :6,877.77 Hbro Wurdhjso W`ja e :yojrjtrocu`jrprbdo :6,777.77 :2,577.77 Hbro Wurdhjso W`ja d Mlwa pjyioat jam 5= oquj` ilath`y bastj`ioats :6,777.77 55,=77.77 Hbro Wurdhjso W`ja m Al mlwa pjyioat jam 5= ilath`y bastj`ioats :6,777.77 55,=77.77 =7 T]LUO D ]ypolfW`ja Djsh ]ypo lf W`ja Hbro Wurdhjso W`ja j Dlst lf `bvbac rlli sot ($) IothlmlfWjyioatW`ja lao-lfffu`` pjyioat Iothlm lf Wjyioat W`ja :5,472.67 Uocu`jr Wrbdo ($) Dlst lf `bvbac rlli sot ($) 4ilathsflrdjsh :=,877.77 :?,?=7.77 :yojrjtrocu`jrprbdo :=,877.77 :3,367.77 Hbro Wurdhjso W`ja e Hbro Wurdhjso W`ja d Mlwa pjyioat jam 5= oquj` ilath`y bastj`ioats :=,877.77 57,357.77 Hbro Wurdhjso W`ja m Al mlwa pjyioat jam 5= ilath`y bastj`ioats :=,877.77 57,357.77 T]LUO M ]ypolfW`ja Djsh ]ypo lf W`ja =: Dlst lf `bvbac rlli sot ($) IothlmlfWjyioatW`ja lao-lfffu`` pjyioat Iothlm lf Wjyioat W`ja ::,577.77 Uocu`jr Wrbdo ($) Dlst lf `bvbac rlli sot ($) Hbro Wurdhjso W`ja j 4ilathsflrdjsh :=,777.77 :=,377.77 Hbro Wurdhjso W`ja e :yojrjtrocu`jrprbdo :=,777.77 :6,877.77 Hbro Wurdhjso W`ja d Mlwa pjyioat jam 5= oquj` ilath`y bastj`ioats :=,777.77 :2,677.77 Hbro Wurdhjso W`ja m Al mlwa pjyioat jam 5= ilath`y bastj`ioats :=,777.77 :2,677.77 ]ho crjph shlws hlw tho djsh prbdo dlipjros tl tho mbfforoat Hbro Wurdhjso p`jas jt stlro J. 57 :8 7 7 ,7 : Ó $ :6 B A O D B U W :7 := :5 78 76 7= 75 jedm ]RWO LF HBUO W_UDHJTO [email protected] DW HWWUBDO J`` flur stlros lffor tho sjio pjyioat strudturo uamor djsh jam Hbro Wurdhjso, js sudh, tho mjtj frli lao stlro wb`` eo usom tl moilastrjto tho coaorj` prbadbp`o lf Hbro Wurdhjso p`jas. W`ojso alto thjt tho rocu`jr prbdo bs tho prbdo thjt bs usom tl dj`du`jto tho mbfforoat Hbro Wurdhjso p`jas. ]ho rocu`jr prbdo bs letjbaom ey ijrkbac up tho djsh prbdo ey 5?%. Ba lrmor tl dj`du`jto tho mbfforoat Hbro Wurdhjso p`jas, flr ovory 4 ilaths, ? % batorost bs jmmom tl tho rocu`jr prbdo. (o.c.) 4 ilaths flr djsh> 6 ilaths flr djsh> ?% batorost bs jmmom tl tho rocu`jr prbdo. :7% batorost bs jmmom tl tho rocu`jr prbdo. :5 ilaths flr djsh> 57% batorost bs jmmom tl tho rocu`jr prbdo. 5= ilaths flr djsh> =7% batorost bs jmmom tl tho rocu`jr prbdo. =5 _sbac Mjtj Frli Ttlro J Dj`du`jtbla lf dlst lf `bvbac rlli sot uamor twl mbfforoat p`jas W`ja # : Djsh> j lao-lff fu`` pjyioat lf tho djsh prbdo jt tho tbio lf purdhjso. DJTH WUBDO 9 $:5,472.67 W`ja #5 HBUO W_UDHJTO> ]horo woro flur Hbro Wurdhjso p`jas lfforom> j, e, d, m W`ja j> 4 Ilaths flr Djsh ]hbs dlasbsts lf tho rocu`jr prbdo p`us ?% batorost lf tho rocu`jr prbdo. ]hbs jiluat iust eo pjbm ba 4 ilaths. Uocu`jr prbdo 9 $:?,483.77 Batorost 9 ?% lf rocu`jr prbdo 9 ? Ó $:?,483 9 $362.4? :77 ∽ Dlst lf @bvbac Ulli sot 9 Uocu`jr Wrbdo + Batorost 9 $:?,483 + $362.4? 9 $:6,:?6.4? Auieor lf ilath`y bastj`ioats 9 4 ∽ Jiluat lf ojdh ilath`y bastj`ioat 9 Dlst lf sot 4 9 $:?,:?6.4? 4 9 $?,48?.=? ]horoflro, bf tho `bvbac rlli sot bs purdhjsom usbac thbs p`ja, iy pjroats wb`` pjy $:6,:?6.4? ba 4 oquj` ilath`y bastj`ioats lf $?,48?.=?. =4 W`ja e> Lao Rojr jt Uocu`jr Wrbdo ]hbs dlasbsts lf tho rocu`jr prbdo p`us 57% batorost lf tho rocu`jr prbdo. ]hbs jiluat iust eo pjbm ba :5 ilaths. Uocu`jr prbdo 9 $:?,483.77 Batorost 9 57% lf rocu`jr prbdo 9 57 Ó $:?,483 9 $4,733.=7 :77 ∽ Dlst lf `bvbac rlli sot 9 9 Uocu`jr Wrbdo + Batorost $:?,483 + $4,733.=7 9 $:8,=6=.=7 Auieor lf ilath`y bastj`ioats 9 :5 ∽ Jiluat lf ojdh ilath`y bastj`ioat 9 Dlst lf sot :5 9 $:8,=6=.=7 :5 9 $:,?48.37 ]horoflro, bf tho `bvbac rlli sot bs purdhjsom usbac thbs p`ja, iy pjroats wb`` pjy $:8,=6=.=7 ba :5 oquj` ilath`y bastj`ioats lf $:,?48.37. W`ja d> Mlwa Wjyioat jam 5= Ilath`y Bastj`ioats Uocu`jr prbdo 9 Batorost 9 9 $:?,483.77 =7% lf rocu`jr prbdo =7 Ó $:?,483 9 $6,:?=.87 :77 ∽ Dlst lf `bvbac rlli sot 9 9 Uocu`jr Wrbdo + Batorost $:?,483 + $6,:?=.87 9 $5:,?=:.87 Mlwa pjyioat 9 5?% lf dlst lf sot 9 5? Ó 5:,?=:.8 7 :77 9 $?,48?.=? Ej`jado tl eo pjbm ba ilath`y bastj`ioat 9 9 dlst lf sot — mlwa pjyioat $5:,?=:.87 — $?,48?.=? 9 $:6,:?6.4? Auieor lf ilath`y bastj`ioats 9 5= ∽ Jiluat lf ojdh ilath`y bastj`ioat 9 Ej`jado 5= 9 $5:,?=:.87 5= 9 $634.57 ]horoflro, bf tho `bvbac rlli sot bs purdhjsom usbac thbs p`ja, iy pjroats wb`` pjy $5:,?=:.87 ba 5= oquj` ilath`y bastj`ioats lf $634.57 jam ja babtbj` mlwa pjyioat lf $?,48?.=?. == W`ja m> Al Mlwa Wjyioat jam 5= Ilath`y Bastj`ioats Uocu`jr prbdo 9 Batorost 9 =7% lf rocu`jr prbdo =7 Ó 9 $:?,483.77 $:?,483 9 $6,:?=.87 :77 ∽ Dlst lf `bvbac rlli sot 9 9 Uocu`jr Wrbdo + Batorost $:?,483 + $6,:?=.87 9 $5:,?=:.87 Auieor lf ilath`y bastj`ioats 9 5= ∽ Jiluat lf ojdh ilath`y bastj`ioat 9 Dlst lf sot 5= 9 5:,?=:.87 5= 9 $823.67 ]horoflro, bf tho `bvbac rlli sot bs purdhjsom usbac thbs p`ja, iy pjroats wb`` pjy $5:,?=:.87 ba 5= oquj` ilath`y bastj`ioats lf $823.67. =? WULNOD] 5 TOD]BLA 7? [email protected] LF MJ]J Ojdh Hbro Wurdhjso p`ja wb`` alw eo jaj`ysom jam dlipjrom tl tho djsh prbdo flr dlst offodtbvoaoss. Hbro Wurdhjso W`ja j Hbro Wurdhjso prbdo lf `bvbac rlli sot 9 $:6,:?6.4? Djsh prbdo 9 $:5,472.67 Mbfforoado ba prbdo 9 ($:6,:?6.4? — $:5,472.67) 9 $ 4,8=6.3? ]horoflro, uamor W`ja j tho dlasuior pjys $ 4,8=6.3? ilro thja tho djsh prbdo. ]hbs badrojso ba prbdo js j pordoatjco 9 4,8=6.3? Ó :77% :5,472.67 9 4:.5?% Hbro Wurdhjso W`ja e Hbro Wurdhjso prbdo lf `bvbac rlli sot 9 $:8,=6=.=7 Djsh prbdo 9 $:5,472.67 Mbfforoado ba prbdo 9 ($:8,=6=.=7— $:5,472.67) 9 $ 6,:?=.87 ]horoflro, uamor W`ja e tho dlasuior pjy $ 6,:?=.87 ilro thja tho djsh prbdo. ]hbs badrojso ba prbdo js j pordoatjco 9 6,:?=.87 Ó :77% :5,472.67 9 ?7% Hbro Wurdhjso W`ja d Hbro Wurdhjso prbdo lf `bvbac rlli sot 9 $ 5:,?=:.=7 Djsh prbdo 9 $:5,472.67 Mbfforoado ba prbdo 9 ($5:,?=:.=7 — $:5,472.67) 9 $ 2,54:.87 ]horoflro, uamor W`ja d tho dlasuior pjy $ 2,54:.87 ilro thja tho djsh prbdo. ]hbs badrojso ba prbdo js j pordoatjco 9 2,54:.87 Ó :77% :5,472.67 9 3?% =6 Hbro Wurdhjso W`ja m Hbro Wurdhjso prbdo lf `bvbac rlli sot 9 $5:,?=:.87 Djsh prbdo 9 $:5,472.67 Mbfforoado ba prbdo 9 ($5:,?=:.=7 — $:5,472.67) 9 $ 2,54:.87 ]horoflro, uamor W`ja m tho dlasuior pjy $ 2,54:.87 ilro thja tho djsh prbdo. ]hbs badrojso ba prbdo js j pordoatjco 9 2,54:.87 Ó :77% :5,472.67 9 3?% AE> ]l quj`bfy flr j Hbro Wurdhjso p`ja, iy pjroats wb`` eo suenodtom tl j Iojas ]ost. (Too Jppoambx) =3 WULNOD] 5 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT Frli tho mjtj dl``odtom, bt bs sooa thjt> :. j`` stlros hjvo tho sjio pjyioat strudturo js stjtom ba tho prosoatjtbla lf mjtj. 5. j`` Hbro Wurdhjso prbdos lrbcbajtom frli tho djsh prbdo. 4. purdhjsbac tho `bvbac rlli sot uamor tho djsh p`ja bs tho dhojpost lptbla. =. flr ojdh iothlm lf Hbro Wurdhjso tho badrojso ba batorost vjrbos badroioatj``y frli 4:% up tl 3?%. ?. thoro bs j dlrro`jtbla eotwooa tho `oacth lf tbio lf ropjyioat, tho jiluat lf ilath`y bastj`ioats, jam tho batorost dhjrcom uamor ojdh p`ja. (o.c. tho `lacor iy pjroats tjko tl ropjy, tho sij``or tho ilath`y bastj`ioats jam tho hbchor tho batorost) 6. ]ho la`y truo djsh prbdo bs j lao-lff fu`` pjyioat ijmo jt tho tbio lf purdhjsbac tho btoi. J`` lthor prbdos jro morbvom frli tho rocu`jr prbdo, whbdh bs 5?% ilro thja tho djsh prbdo. (o.c. 4 ilaths flr djsh bs j tori usom ey stlros tl ibs`ojm dlasuiors batl eo`bovbac thjt thoy jro pjybac djsh flr tho btoi). ]horo jro ijay pjyioat p`jas jvjb`je`o tl iy pjroats ba purdhjsbac tho `bvbac rlli sot vbj Hbro Wurdhjso. Hlwovor, j`` thoso p`jas dlio wbth oxtrj dhjrcos eodjuso hbro purdhjso bs j flri lf elrrlwbac jam thoro bs j dlst jttjdhom tl elrrlwbac. Ey usbac dlasuior jrbthiotbd, B wjs je`o tl dliputo tho pordoatjco badrojso la tho djsh prbdo lf tho `bvbac rlli sot thrluch tho flur mbfforoat Hbro Wurdhjso p`jas. _sbac thoso dj`du`jtblas iy pjroats dja motoribao eoflrohjam tho jmvjatjcos jam mbsjmvjatjcos lf ojdh p`ja eoflro oatorbac batl j Hbro Wurdhjso jcrooioat. ]ho ijba jmvjatjco bs thjt bt j``lws iy pjroats tl ijko uso lf tho `bvbac rlli sot whb`st stb`` pjybac flr bt. La tho lthor hjam, iy pjroats ijy eo fjdom wbth tho mbsjmvjatjco lf pjybac oxlrebtjat prbdos flr tho `bvbac rlli sot. Ba slio djsos j`ilst mlue`o tho djsh prbdo. =8 WULNOD] 5 TOD]BLA 73 [email protected]_TBLA ]ho bavostbcjtbla lf tho mbfforoat Hbro Wurdhjso pjyioat p`jas rovoj` tho fl``lwbac dj`du`jtblas> :. Dlst lf tho `bvbac rlli sot uamor W`ja j> 4 ilaths flr djsh bs $:6,:?6.4?, whbdh roprosoats j 4:% badrojso ba batorost la tho djsh prbdo. 5. Dlst lf tho `bvbac rlli sot uamor W`ja e> : yojr jt rocu`jr prbdo bs $:8,=6=.=7 whbdh roprosoats j ?7% badrojso ba batorost la tho djsh prbdo. 4. Dlst lf tho `bvbac rlli sot uamor W`ja d> mlwa pjyioat jam 5= ilath`y bastj`ioats bs $5:,?=:.=7 whbdh roprosoats j 37% badrojso ba batorost la tho djsh prbdo. =. Dlst lf tho `bvbac rlli sot uamor W`ja m> 5= ilath`y bastj`ioats bs $5:,?=:.=7 whbdh roprosoats j 37% badrojso ba batorost la tho djsh prbdo. Ejsom la tho jelvo, tho ilst dlst offodtbvo p`ja bs W`ja j> 4 ilaths flr djsh. =2 WULNOD] 5 TOD]BLA 78 UOFOUOADOT Croor, J. & @jyao, D. O. (:22:) Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja. ]ll`sbo, U, (:222).J Dlip`oto Dlurso wbth DXD Zuostblas. www.ovorythbacijths.dl.zj www.wbkbOmudjtlr.lrc ?7 WULNOD] 5 TOD]BLA 72 JWWOAMBX ]oris usom ba thbs prlnodt Djsh Wrbdo > Hbro Wurdhjso/Uocu`jr prbdo > Lao fu`` pjyioat jt tho tbio lf purdhjso tho Hbro Wurdhjso prbdo bs j`sl roforrom tl js tho Uocu`jr Wrbdo. Bt dlasbsts lf 5?% badrojso la tho djsh prbdo Mlwa pjyioat > ]ho ﬊rst pjyioat tho euyor ijkos la tho btoi tl eocba Bastj`ioats > Sook`y lr ilath`y pjyioats wbthba tho purdhjso p`ja Hbro Wurdhjso Jcrooioat > Ja jcrooioat eotwooa tho euyor jam tho stlro lut`babac tho Hbro Wurdhjso prldoss. tho toris jam dlambtblas lf tho pjyioat p`ja. Bt j`sl lut`baos iojsuros tl eo tjkoa rocjrmbac ala-pjyioat la tho euyor‒s pjrt. Iojas ]ost > ]hbs bs usom tl motoribao whothor tho euyor wb`` quj`bfy flr j pjrtbdu`jr Hbro Wurdhjso p`ja. Uoqubroioats flr Iojas ]ost jro> Nle `ottor jam pjys`bp Bmoatb﬊djtbla Djrm _tb`bty eb`` ]wl (5) roforoados Ejak Ttjtoioat flr `jst 6 ilaths bf so`f-oip`lyom. ?: WULNOD] 4 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla batl tojdhors‒ puadtuj`bty jam rocu`jrbty jt j clvoraioat sdhll`. ?5 WULNOD] 4 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................Wjco Auieor ?. Jaj`ysbs lf Mjtj ...................................................................... Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Ttjkohl`mors sudh js W]J, `ojmors wbthba tho Ibabstry lf Omudjtbla jam stumoats thoiso`vos, dlip`jba jelut hjebtuj` tjrmbaoss jam jesoatoobsi la tho pjrt lf tojdhors wbthba tho clvoraioat sdhll` systoi. ]ho d`jssrlli tojdhor bs j`sl j ijnlr stjkohl`mor ba tho omudjtbla systoi. ]ho suddoss lf tho mo`bvory lf tho durrbdu`ui jam mbsdbp`bao jro mopoamoat la tho tojdhor eobac ba tho d`jssrlli, js sudh, tojdhor puadtuj`bty jam rocu`jrbty jro ijnlr fjdtlrs wbthba tho systoi. ]ho d`jbi lf tojdhor jesoatoobsi jam hjebtuj` tjrmbaoss bs usuj``y morbvom frli jaodmltj` ovbmoado rjthor thja mjtj mrbvoa d`jbis. ]ho purplso lf thbs prlnodt bs tl oxjibao tho rodlrms lf tojdhor puadtuj`bty jam rocu`jrbty flr lao ilath jt j clvoraioat sodlamjry sdhll` ba lrmor tl motoribao whothor tho `jtos jam jesoados jro js hbch js tho jaodmltj` roplrts succost. ?4 WULNOD] 4 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA Woribssbla wjs crjatom ey tho sdhll`‒s prbadbpj` tl poruso tho ]ojdhors‒ Jttoamjado Uocbstor wook`y flr j porblm lf lao ilath ba lrmor tl oxtrjdt mjtj la rocu`jrbty jam puadtuj`bty flr thjt spodb﬊d ilath. ]ho sjip`o sbzo dlasbstom lf =? tojdhors. ?= WULNOD] 4 TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Jftor tho mjtj woro dl``odtom, thoy woro lrcjabzom usbac j tje`o, dlipjrjtbvo ejr dhjrts jam froquoady tje`os js fl``lws> ]ho tje`o shlws tho auieor lf tojdhors whl woro `jto jam jesoat flr tho pjrtbdu`jr ilath Sook Mjy @jto Jesoat Wrosoat Ilamjy :7 :: 4= : ]uosmjy k o Somaosmjy o S :5 := 4: := 78 43 ]hursmjy :3 := 4: Frbmjy := := 4: Ilamjy :: 74 =5 ]uosmjy :4 73 48 o k o Somaosmjy S 5 :6 72 46 ]hursmjy :6 76 42 Frbmjy :5 :3 58 Ilamjy 72 :5 44 ]uosmjy :6 :: 4= 4 k o Somaosmjy o S :7 72 46 ]hursmjy :5 74 =5 Frbmjy :: := 4: Ilamjy :5 :5 44 ]uosmjy :5 78 43 72 72 46 ]hursmjy 78 75 =4 Frbmjy :7 57 5? = k o Somaosmjy o S ]je`o Lao ?? Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook Lao ] A O T E J / O ] J @ T O 57 B] I F L U O E I _ A :7 :8 :6 := :5 78 76 7= 75 ILA ]_OT SOM ]H_U FUB MJRT LF ]HO SOOK @J]O JETOA] Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook ]wl ] A O T E J / O ] J @ T O BI ] F L U O E I _ A 57 :8 :6 := :5 :7 78 76 7= 75 ILA ]_OT SOM ]H_U FUB MJRT LF ]HO SOOK @J]O JETOA] ?6 Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook ]hroo ] A O T E /J O ] J @ T O 57 B] I F L U O E I _ A :7 :8 :6 := :5 78 76 7= 75 ILA ]_OT SOM ]H_U FUB MJRT LF ]HO SOOK @J]O JETOA] Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook Flur ] A O T E /J O ] J @ T O I B ] F L U O E I _ A 57 :8 :6 := :5 :7 78 76 7= 75 ILA ]_OT SOM ]H_U FUB MJRT LF ]HO SOOK @J]O ?3 JETOA] Ujw mjtj shlwbac tho auieor lf ibautos tho =? tojdhors woro `jto ba j ilath 4, :7, 8, 3, :5, :6, 4, :7, :, 57, 42, 5, :=, 5:, 8, 2, =4, =2, ?7, ?5, =7, :, ?, 6, :5, :3, ?8, 67, ??, =?, =8, =:, =?, 4?, 44, 42, 5?, 55, 47, 5=, 47, 5:, 47, 55, 47 ]je`o ]wl> Froquoady tje`o shlwbac hlw tho rjw mjtj woro lrcjabsom ]bio ba ibautos Auieor lf ]ojdhors :7 —: :4 57 :: — 76 47 5: — :7 =7 4: — 7? ?7 =: — 73 67 ?: — 7= ]je`o ]hroo> ]je`o shlwbac tho dj`du`jtbla lf tho ioja auieor lf ibautos `jto ey tojdhors ba j ilath ]bio ba Ibautos :7— : Auieor lf ]ojdhors (f) :4 Ibmplbat x ?.? fÓx 3:.? 57 :: — 76 :?.? 24 47—5: :7 5?.? 5?? =7—4: 7? 4?.? ?7—=: 73 =?.? 67—?: = ??.? √ f 9 =? :33.? 4:8.? 555 √fx 9 :,:43.? ]ho sui lf f 9 =? ]ho sui lf fx9 :,:43.7 ]ho ioja x̍̍ 9 √fx 9 ::43.? 9 5?.4 ibautos √f =? ?8 Tdj`o> :di ≪: tojdhor la tho vortbdj` jxbs 5di ≪:7 ibautos la tho hlrbzlatj` jxbs := :4 :5 :: :7 T U O H D J O ] F L U O E I _ A 2 8 3 6 ? = 4 5 : 7 7.? :7.? 57.? 47.? =7.? ?7.? 67.? A_IEOU LF IBA_]OT @J]O Hbstlcrji shlwbac tho auieor lf ibautos thjt tho =? tojdhors hjvo eooa `jto flr tho ilath. ?2 ]je`o Flur> ]ho tje`o shlws j suiijry lf jesoados jam `jto ba pordoatjcos Sook Lao Mjy ]ltj` al. lf Al. lf Al. lf Wordoatjco Wordoatjco tojdhors tojdhors tojdhors lf tojdhors lf tojdhors la rl``, jesoat la `jto la mjy, jesoat la J mjy, x y mjy. `jto la mjy y Ó:77% J x J Ó:77% 5= Ilamjy =? :: :7 ]uosmjy =? := :5 4: 55 53 Somaosmjy =? 8 := :8 4: ]hursmjy =? := :3 4: 48 Frbmjy =? := := 4: 4: Sook ]wl Mjy ]ltj` al. lf Al. lf Al. lf Wordoatjco Wordoatjco tojdhors la tojdhors tojdhors lf tojdhors lf tojdhors rl``, jesoat la `jto la mjy, jesoat la J mjy, y mjy. `jto la mjy y J Ó:77% x J Ó:77% x Ilamjy ]uosmjy =? =? 4 3 :: :4 3 :6 5= 52 Somaosmjy =? 2 :6 57 46 ]hursmjy =? 6 :6 :4 46 Frbmjy =? :3 :5 48 4: 67 Sook ]hroo Mjy ]ltj` al. lf Al. lf Al. lf Wordoatjco Wordoatjco tojdhors la tojdhors tojdhors lf tojdhors lf tojdhors rl``, jesoat la jesoat la J mjy, `jto la mjy, y `jto la mjy y Ó:77% J mjy. x Ó:77% J x Ilamjy =? :5 2 53 57 ]uosmjy =? :4 :6 52 46 Somaosmjy =? 2 :7 57 55 ]hursmjy =? 4 :5 3 53 Frbmjy =? := :: 4: 5= Sook Flur Mjy 6: ]ltj` al. lf Al. lf Al. lf Wordoatjco Wordoatjco tojdhors la tojdhors tojdhors lf tojdhors lf tojdhors rl``, jesoat la `jto la mjy, jesoat la J mjy, x y mjy. `jto la mjy y Ó:77% J x Ó:77% J Ilamjy =? :5 :5 53 53 ]uosmjy Somaosmjy =? =? 8 2 :5 2 :8 57 53 57 ]hursmjy =? 5 8 7= :8 Frbmjy =? 57 :7 == 55 Sook Lao Jvorjco pordoatjco lf tojdhors `jto > 55+53+4:+48+4: 9 52.8% ? Jvorjco pordoatjco lf tojdhors jesoat > 5=+4:+:8+4:+4: 9 53% ? Sook ]wl Jvorjco pordoatjco lf tojdhors `jto > Jvorjco pordoatjco lf tojdhors jesoat > 5=+52+56+56+4: ? 9 4:.5% 3+:6+57+:4+48 9 :8.8% ? Sook ]hroo Jvorjco pordoatjco lf tojdhors `jto > 57+46+55+53+5= 9 5?.8% ? Jvorjco pordoatjco lf tojdhors jesoat > 53+52+57+3+4: 9 55.8% ? Sook Flur Jvorjco pordoatjco lf tojdhors `jto > 53+53+57+:8+55 9 55.8% ? Jvorjco pordoatjco lf tojdhors jesoat > 53+:8+57+=+== 9 55.6% ? 65 WULNOD] 4 TOD]BLA 7? [email protected] LF MJ]J ]je`o Flur shlws thjt frli j stjff lf =? tojdhors> :. Ba Sook Lao, jpprlxbijto`y 53% lf tho tojdhbac stjff wjs jesoat mjb`y jam 47% lf tojdhors woro `jto mjb`y 5. Ba Sook ]wl, jpprlxbijto`y :2% lf tho tojdhbac stjff wjs jesoat mjb`y jam 4:% lf tojdhors woro `jto mjb`y 4. Ba Sook ]hroo, jpprlxbijto`y 54% lf tho tojdhbac stjff wjs jesoat mjb`y jam 56% lf tojdhors woro `jto mjb`y =. Ba Sook Flur, jpprlxbijto`y 54% lf tho tojdhbac stjff wjs jesoat mjb`y jam 54% lf tojdhors woro `jto mjb`y ]ho jvorjco pordoatjco lf tojdhors jesoat flr tho flur wooks bs> 53 + :2 + 54 + 54 9 25 = ≈ 54% = ]ho jvorjco pordoatjco lf tojdhors `jto flr tho flur wook bs> 47 + 4: + 56 + 54 9 = ≈ ::7 58% = ]horoflro, tho mjtj rovoj`om thjt flr tho ilath uamor dlasbmorjtbla> :. 54% lf tojdhor woro jesoat la j mjb`y ejsbs 5. 58% lf tojdhor woro `jto la j mjb`y ejsbs ]je`o ]wl jam tho hbstlcrji shlw thjt :2 tojdhors woro `jto flr : tl 57 ibautos flr tho ilath, whorojs 56 tojdhors woro `jto flr 5: tl 67 ibautos flr tho ilath. 64 ]ho flur dlipjrjtbvo ejr crjphs rovoj`om thjt ba jay cbvoa wook, ilro tojdhors woro `jto thja jesoat. ]hbs bs sooa ba> Ejrcrjph (:) — whoro 5 lut lf tho ? mjys, ilro tojdhors woro `jto thja jesoat Ejrcrjph (5) — whoro = lut lf ? mjys, ilro tojdhors woro `jto thja jesoat Ejrcrjph (4) — whoro 4 lut lf ? mjys, ilro tojdhors woro `jto thja jesoat. Ejrcrjph (=) — whoro 5 lut lf ? mjys, ilro tojdhors woro `jto thja jesoat jam jam la lao mjy tho sjio auieor wjs `jto js jesoat flr 5 mjys tho sjio auieor wjs `jto js jesoat. ]ho crjphs j`sl shlw thjt tojdhors woro ilro `bko`y tl eo jesoat la j Frbmjy thja jay lthor mjy. ]hbs bs ovbmoat ba tho fjdt thjt la tho Frbmjy lf> (j) Sook Lao — (e) Sook ]wl — := tojdhors woro jesoat :3 tojdhors woro jesoat (d) Sook ]hroo — := tojdhors woro jesoat (m) Sook Flur — 57 tojdhors woro jesoat ]je`o ]hroo cbvos tho ioja auieor lf ibautos `jto ey tojdhors ba tho ilath tl eo 5?.4 ibautos. ]hbs iojas thjt bf j`` tho tojdhors woro tl eo jesoat flr tho sjio auieor lf ibautos ovory mjy thjt auieor wb`` eo 5?.4 ibautos. 6= WULNOD] 4 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT ]ho mjtj shlwom thjt la jvorjco, 54% lf tojdhors jro jesoat ovorymjy whbdh bs jelut :7 tojdhors frli j stjff lf =?. J`sl, ja jvorjco lf 58% lf tojdhors jro `jto ovory mjy flr ja jvorjco lf 5?.4 ibautos por mjy. ]hbs dliputos tl ?76 ibautos lf tojdhbac tbio por ilath lr jelut :3 porblms por ilath. ]horo jro 8 (4? ibauto) porblms ba j tojdhbac mjy jt tho sdhll`, thoroflro 5?.4 ibautos por mjy `jto, trjas`jto tl 5 mjys jesoados por ilath ba `jto ibautos por tojdhor. 6? WULNOD] 4 TOD]BLA 73 [email protected]_TBLA ]ho ﬊ambacs rovoj`om thjt 54% lf tho tojdhors woro `jto ovory mjy jam 58% woro jesoat ovorymjy lvor tho porblm lf lao ilath. ]hbs succosts, thjt la jvorjco, lut lf j stjff lf =? tojdhors, jpprlxbijto`y :7 lf thoi jro `jto ovor mjy jam :4 jro jesoat ovory mjy. ]hbs supplrts tho jaodmltj` d`jbi thjt jt thbs pjrtbdu`jr sdhll`, tojdhors jro tjrmy ba cottbac tl sdhll` jam tho jesoatoobsi rjto bs hbch. 66 WULNOD] 4 TOD]BLA 78 UOFOUOADOT Croor, J. & @jyao, D.O. Dortb﬊djto ba Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja. 5am Ombtbla. www.omuſtlw.wlrmpross.dli/tjrmbaoss www.thojstlfom.dli 63 WULNOD] = TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla ba lrmor tl motoribao bf tho Tdhll` Foombac Wrlcrjiio badrojsos puadtuj`bty jam rocu`jrbty jt j pjrtbdu`jr sdhll`. 68 WULNOD] = TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................Wjco Auieor ?. Jaj`ysbs lf Mjtj ...................................................................... Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor ]ho Tdhll` Foombac Wrlcrjiio wjs batrlmudom ba sodlamjry sdhll`s js j sjfoty aot, jbiom jt jssbstbac dhb`mroa lf `lw sldbl-odlalibd hlusohl`ms. Bts ijba fldus bs tl> • prlvbmo autrbtblus ioj`s flr dhb`mroa • • badrojso oarl`ioat prlilto jdjmoibd suddoss • romudo jesoatoobsi jam biprlvo rocu`jrbty jam puadtuj`bty ba sdhll`s. ]ho purplso lf thbs prlnodt bs tl motoribao whothor tho Tdhll` Foombac Wrlcrjiio bs fu`﬊``bac lao lf bts ijamjtos lf romudbac jesoatoobsi jam biprlvbac puadtuj`bty ba sdhll`s. 62 WULNOD] = TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA ]ho mjtj wjs dl``odtom vbj j quostblaajbro. ]ho quostblaajbro dlasbstom lf obcht (8) pro-sot stjamjrmbzom quostblas, ba lrmor tl j``lw tho sjio baflrijtbla tl eo coaorjtom frli ojdh stumoat. ]ho quostblas woro jskom ba tho sjio lrmor. ]ho sjip`o dlasbstom lf :77 stumoats, 57 lf whli woro dhlsoa frli ojdh flri `ovo`. ]horo jro = d`jssos jt ojdh flri `ovo` whoro tho stumoats woro j`` jskom bf thoy wjatom tl tjko pjrt ba j survoy. Frli tho crlup lf stumoats whl cjvo j plsbtbvo rosplaso, ﬊vo stumoats woro rjamli`y dhlsoa frli ojdh flri d`jss. ]ho survoy wjs dlamudtom murbac tho `uadh erojk jftor stumoats wlu`m hjvo dlasuiom tho erojkfjst jam `uadh. (Too jppoambx flr quostblaajbro usom ba survoy) Bt tllk flur (=) wooks tl dl``odt tho mjtj frli tho sjip`o sbzo. 37 WULNOD] = TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Jftor tho mjtj wjs dl``odtom, bt wjs lrcjabzom jam prosoatom usbac tje`os, dlipjrjtbvo ejr dhjrts jam pbo dhjrts js fl``lws. :. ]ho tje`o eo`lw shlws tho auieor lf stumoats pjrtbdbpjtom ba tho sdhll` foombac prlcrjiio Flri Auieor Wjrt jkbac Auieor Alt Wjrtjkbac : :8 5 5 :? ? 4 := 6 = :5 8 ? :7 :7 62 4: ]je`o : ]ho dlipjrjtbvo ejr dhjrt dlipjros stumoats whl pjrtbdbpjtom jam whl mbm alt pjrtbdbpjto ba tho Tdhll` Foombac Wrlcrjiio ] A O T E J / O ] J @ T O I B ] F L U O E I _ A 57 :8 :6 := :5 :7 78 76 7= 75 :54=? FLUI [email protected] 3: Fbcuro : ROT AL 5. ]ho tje`o eo`lw shlws tho auieor lf stumoats ey flri whl jrrbvom ojr`y flr erojkfjst jam pjrtbdbpjtom ba tho Tdhll` Foombac Wrlcrjiio Ojr`y flr Alt ojr`y flr erojkfjst erojkfjst : :8 5 57 5 :? ? 57 4 := 6 57 = :5 8 57 ? :7 :7 57 62 4: :77 Flri ]ltj` ]je`o 5 4. ]ho tje`o eo`lw shlws tho auieor lf stumoats whl hjm erojkfjst ovorymjy ey flri Auieor Hjvbac Auieor Alt Hjvbac Erojkfjst Ovorymjy Erojkfjst Ovorymjy : 57 7 57 5 57 7 57 4 57 7 57 = 57 7 57 ? 57 7 57 :77 7 :77 Flri ]ltj` ]je`o 4 =. ]ho tje`o eo`lw shlws tho auieor lf stumoats whl letjbaom erojkfjst frli tho Tdhll` Foombac Wrlcrjiio, hlio jam tho djfotorbj ey flri. Shoro erojkfjst bs letjbaom Flri Hlio Tdhll` Foombac Wrlcrjiio Djfotorbj ]ltj` :: :8 : 57 54 :? 5 57 45 := = 57 =5 :5 6 57 ?4 :7 3 57 62 57 :77 :: ]je`o = 35 ]ho pbo dhjrt shlws tho prlplrtbla lf stumoats whl letjbaom erojkfjst frli tho Tdhll` Foombac Wrlcrjiio, hlio jam djfotorbj. Hlio Djfotorbj Tdhll` Foombac Wrlcrjiio ?. ]ho tje`o eo`lw shlws tho auieor lf stumoats whl jttoamom sdhll` rocu`jr`y flr `uadh frli tho Tdhll` Foombac Wrlcrjiio Jttoam Tdhll` Ml Alt Jttoam flr @uadh Tdhll` flr @uadh : :8 5 5 :? ? 4 := 6 = :5 8 ? :7 :7 Flri 62 4: ]je`o ? 34 6. ]ho tje`o eo`lw shlws tho auieor lf stumoats whl hjm `uadh ovory mjy ey flri. Auieor Hjvbac Auieor Alt Hjvbac @uadh Ovory Mjy @uadh Ovory Mjy : 57 7 5 57 7 4 57 7 = ? 57 57 7 7 :77 7 Flri ]je`o 6 3. ]ho tje`o shlws tho auieor lf stumoats whl letjba `uadh frli tho Tdhll` Foombac Wrlcrjiio Shoro `uadh bs letjbaom Flri Hl io Tdhll` Foombac Wrlcrjiio Djfotorbj ]ltj` :: :8 : 57 54 45 :? := 5 = 57 57 =5 :5 6 57 ?4 :7 3 57 62 57 :77 :: 3= ]ho pbo dhjrt shlws tho prlplrtbla lf stumoats whl letjbaom `uadh frli tho Tdhll` Foombac Wrlcrjiio, hlio jam djfotorbj. Hlio Djfotorbj Tdhll` Foombac Wrlcrjiio 3? WULNOD] = TOD]BLA 7? [email protected] LF MJ]J ]je`o : shlws thjt lut lf tho :77 stumoats whl woro survoyom, 62 woro pjrtbdbpjats lf tho Tdhll` Foombac Wrlcrjiio, whbdh iojas thjt 62% lf tho sjip`o woro rodbpboats lf ioj`s frli tho Tdhll` Foombac Wrlcrjiio. ]je`o : jam tho dlipjrjtbvo ejr dhjrt (Fbcuro :) shlw thjt tho stumoats ba tho `lwor flris (:, 5 jam 4) woro ilro `bko`y tl pjrtbdbpjto ba tho Tdhll` Foombac Wrlcrjiio thja dhb`mroa frli tho uppor flris. ]hbs bs supplrtom ey tho fl``lwbac dj`du`jtblas> Frli ]je`o B> (b) tho auieor lf `lwor flri stumoats whl pjrtbdbpjtom ba tho Tdhll` Foombac Wrlcrjiio wjs (:8 + :? + :=) 9 =3. ]ho tltj` auieor lf `lwor flri stumoats ba tho survoy wjs 67. Hoado, tho pordoatjco lf `lwor flri stumoats whl pjrtbdbpjtom ba tho Tdhll` Foombac Wrlcrjiio wjs =3 Ó :77% 9 38.4% 67 (bb) tho auieor lf uppor flri stumoats whl pjrtbdbpjtom ba tho Tdhll` Foombac Wrlcrjiio (:5 + :7) 9 55. ]ho tltj` auieor lf uppor flri stumoats ba tho survoy wjs =7. ]horoflro, tho pordoatjco lf uppor flri stumoats whl pjrtbdbpjtom ba tho prlcrjiio wjs 55 Ó :77% 9 ??% =7 ]je`o 4 jam 6 shlw thjt :77% lf tho stumoats survoyom hjm erojkfjst jam `uadh ovory mjy. Hlwovor, tje`os 5 jam = shlw thjt 62% clt erojkfjst jam `uadh frli tho Tdhll` Foombac Wrlcrjiio; whb`st ::% clt frli hlio jam 57% frli tho djfotorbj. ]hbs bs b``ustrjtom ba Fbcuro 5 jam 4. Ba dlastrudtbac tho pbo dhjrts, jac`os woro dj`du`jtom tl roprosoat tho sodtlrs> - Tdhll` Foombac Wrlcrjiio - hlio - djfotorbj ]hbs wjs mlao js fl``lws> Tdhll` Foombac Wrlcrjiio 62 Hlio :: Djfotorbj 57 :77 36 Jac`o roprosoatbac Tdhll` Foombac Wrlcrjiio 9 62 Ó 467· 9 5=8.=· :77 Jac`o roprosoatbac Hlio 9 :: Ó 467· 9 42.6· :77 Jac`o roprosoatbac Djfotorbj 9 57 Ó 467· 9 35· :77 Frli tho :77 stumoats whl woro survoyom 62 djio ojr`y flr erojkfjst jam jttoamom sdhll` rocu`jr`y flr `uadh frli tho sdhll` foombac prlcrjiio. ]horoflro, bf j stumoat bs dhlsoa jt rjamli frli tho sjip`o, tho prlejeb`bty lf thjt dhb`m jrrbvbac ojr`y flr erojkfjst jam rocu`jr`y flr `uadh bs 62% lr 7.62 33 WULNOD] = TOD]BLA 76 MBTD_TTBLA LF FBAMBACT J`thluch j`` lf tho stumoats survoyom hjm erojkfjst jam `uadh ovory mjy, tho ijnlrbty lf thoi (62%) djio ojr`y jam rocu`jr`y tl sdhll` ba lrmor tl letjba thobr ioj`s frli tho sdhll` foombac prlcrjiio. ]ho stumoats frli flris :, 5, jam 4 oxprossom crojtor batorost ba jrrbvbac ojr`y jam rocu`jr`y tl pjrtbdbpjto ba tho Tdhll` Foombac Wrlcrjiio. 38 WULNOD] = TOD]BLA 73 [email protected]_TBLA Cbvoa tho hbch prlplrtbla lf stumoats whl jrrbvo ojr`y jam rocu`jr`y flr tho Tdhll` Foombac Wrlcrjiio, lao dja dlad`umo thjt tho Tdhll` Foombac Wrlcrjiio hjs j plsbtbvo bipjdt la tho `bvos lf stumoats whbdh rosu`tom ba ja badrojso ba puadtuj`bty jam rocu`jrbty. 32 WULNOD] = TOD]BLA 78 UOFOUOADOT www.wbkbhlw.dli www.ttdlaaodt.clv.tt www.cujrmbja.dl.tt 87 WULNOD] = TOD]BLA 72 JWWOAMBX Z_OT]BLAAJBUO FLU T_UVOR :. W`ojso tbdk lao rosplaso la`y Flri D`jss  :  5  4  =  ? 5. Ml ylu pjrtjko ba tho sdhll` foombac prlcrjiio<  Ros  Al 4. Ml ylu jrrbvo ojr`y tl rodobvo erojkfjst frli tho sdhll` foombac prlcrjiio<  Ros  Al =. Ml ylu hjvo erojkfjst ovory mjy<  Ros  Al ?. Bf tho jaswor tl quostbla = bs yos, thoa whoro ml ylu cot erojkfjst<  Hlio  Tdhll`  Djfotorbj 6. Ml ylu jttoam sdhll` rocu`jr`y tl rodobvo `uadh<  Ros  Al 3. Ml ylu hjvo `uadh ovory mjy<  Ros  Al 8. Bf tho jaswor tl quostbla 3 bs yos, thoa whoro ml ylu cot `uadh<  Hlio 8:  Tdhll`  Djfotorbj WULNOD] ? TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla tl motoribao tho auieor lf ebrms thjt iust eo purdhjsom ba lrmor flr j sij`` eusbaoss tl roj`bzo j ijxbiui prl﬊t. 85 WULNOD] ? TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................Wjco Auieor ?. Jaj`ysbs lf Mjtj ...................................................................... Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Iy mjm hjs modbmom tl stjrt j sij`` eusbaoss tl supp`oioat hbs ilath`y badlio. Ho p`jas tl purdhjso dhbdkoas jam mudks wook`y tl rotjb` jt j prl﬊t. Jftor hojrbac mjm‒s p`ja, B modbmom tl uso j erjadh lf Ijthoijtbds dj``om `baojr prlcrjiibac tl ho`p hbi ilmo` hbs eusbaoss p`ja. @baojr prlcrjiibac bs j ijthoijtbdj` todhabquo thjt bs usom tl ijxbibzo prl﬊t lr ibabibzo `lss wbthba j spodb﬊om systoi, cbvoa j`` tho dlastrjbats ba tho systoi. ]hbs todhabquo wb`` j``lw mjm tl prombdt tho oxjdt auieor lf ebrms ho shlu`m purdhjso wook`y ba lrmor tl ijxbibzo prl﬊t la hbs bavostioat, wbthlut vbl`jtbac dortjba dlastrjbats. Shb`o trybac tl ostje`bsh tho eusbaoss, mjm ijy oadluator `bibtjtblas jam rostrbdtblas. ]hoso `bibtjtblas jam rostrbdtblas jro dj``om dlastrjbats. 84 WULNOD] ? TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA :. B vbsbtom j plu`try fjri jam dl``odtom mjtj js fl``lws> (b) whl`osj`o prbdos la dhbdkoas jam mudks (bb) tho ibabiui auieor lf ebrms thjt iust eo purdhjsom ba lrmor tl letjba tho whl`osj`o prbdo. (bbb) tho succostom prbdos jt whbdh tho ebrms dja eo rotjb`om. (bv) tho ijxbiui auieor lf ebrms thjt dja eo stlrom ba tho flw` rua jt hlio. 5. B j`sl clt mjm‒s wook`y eumcot flr tho purdhjso lf ebrms. 8= WULNOD] ? TOD]BLA 7= WUOTOA]J]BLA LF MJ]J ]ho mjtj dl``odtom shlws, thjt ba lrmor tl letjba whl`osj`o jam rotjb` prbdos, mjm iust sjtbsfy tho fl``lwbac flur dlastrjbats> :. Ho iust euy jt `ojst :7 mudks; thbs iojas thjt tho ibabiui jiluat lf mudks thjt ho dja purdhjso bs :7 5. Ho iust euy jt `ojst 57 dhbdkoas; thbs iojas thjt ho iust euy 57 lr ilro dhbdkoas 4. Ho hjs stlrjco spjdo flr la`y 34 ebrms; thbs iojas thjt ho djaalt euy ilro thja 34 ebrms. =. Ho la`y hjs $4,777.77 tl spoam la ebrms. Mudks dlst $87.77 ojdh jam dhbdkoas dlst $47.77 ojdh. ]ho mjtj j`sl shlws thjt jt tho oam lf thbs voaturo, mjm bs oxpodtom tl ijko j prl﬊t lf $37.77 la ojdh mudk jam $47.77 la ojdh dhbdkoa. Ba `baojr prlcrjiibac, wo uso baoquj`btbos tl roprosoat roj` wlr`m dlastrjbats whbdh dja thoa eo roprosoatom crjphbdj``y ey rocblas. Flr mjm‒s eusbaoss ilmo`, ojdh dlastrjbat wb`` cbvo rbso tl ja baoquj`bty. Ba lrmor tl wrbto baoquj`btbos, wo iust batrlmudo vjrbje`os. Flr thbs ilmo`, B wb`` uso twl vjrbje`os, x jam y. B wb`` `ot x roprosoat tho auieor lf mudks jam y roprosoat tho auieor lf dhbdkoas thjt mjm wjats tl purdhjso. :. Mjm iust euy jt `ojst :7 mudks ]hoa x iust eo crojtor thja lr oquj` tl :7 ]hbs bs wrbttoa js x ≯ :7 5. Ho iust euy jt `ojst 57 dhbdkoas ]hoa y iust eo crojtor thja lr oquj` tl 57 ]hbs bs wrbttoa js y ≯ 57 4. Ho hjs stlrjco flr la`y 34 ebrms ]hoa tho tltj` auieor lf ebrms iust eo `oss thja lr oquj` tl 34 ]hbs bs wrbttoa js x + y ≭ 34 8? =. ]ho dlst lf x mudks jt $87.77 ojdh bs $87 x ]ho dlst lf y dhbdkoas jt $47.77 ojdh bs $47 y Ho hjs la`y $4,777.77 tl spoam la ebrms ]hoa tho tltj` jiluat lf ilaoy tl eo spoat iust eo `oss thja lr oquj` tl $4777.77 ]hbs bs wrbttoa js 87 x + 47y ≭ $4,777.77 Ojdh lf tho jelvo baoquj`btbos wb`` roprosoat j rocbla la j crjph shoot. ]l bmoatbfy rocblas, wo iust hjvo eluamjrbos. ]ho oquj`bty pjrt lf ojdh baoquj`bty wb`` eo usom js j eluamjry `bao flr ojdh baoquj`bty. :. Flr tho rocbla x ≯ :7; tho strjbcht `bao x 9 :7 wb`` eo mrjwa js j eluamjry `bao 5. Flr tho rocbla y ≯ 57; tho strjbcht `bao y 9 57 wb`` eo mrjwa js tho eluamjry `bao. 4. Flr tho rocbla x + y ≭ 34; tho strjbcht `bao x + y 9 34 wb`` eo mrjwa js tho eluamjry `bao =. Flr tho rocbla 87x + 47y ≭ 4777; tho strjbcht `bao 87 x + 47y 9 4777 wb`` eo mrjwa js j eluamjry `bao ]l mrjw tho `bao x + y 9 34 ; tho twl plbats (7, 34) jam (34, 7) wb`` eo usom x y 7 34 34 7 Eoflro tho `bao 87x + 47y 9 4777 bs mrjwa, tho oqujtbla wb`` eo sbip`b﬊om ey mbvbmbac ey :7. ]ho oqujtbla bs alw 8x + 4y 9 477; jam tho twl plbats (7, :77) jam (47, 57) wb`` eo usom tl mrjw tho eluamjry `bao. x 7 47 y :77 57 ]ho crjph eo`lw roprosoats tho systoi lf tho flur baoquj`btbos. ]ho shjmom rocbla T roprosoats mjm‒s mocroo lf froomli. Ba thbs rocbla ho bs froo tl purdhjso j dliebajtbla lf mudks jam dhbdkoas wbthlut vbl`jtbac jay lf tho flur dlastrjbats. 86 Thjmom rocbla T roprosoats mjm‒s mocroo lf froomli y Tdj`o> 5di ≪:7 mudks la hlrbzlatj`, 5di ≪:7 dhbdkoas la vortbdj` :77 x 9 :7 27 87 ) T A O K 37 BD H D F L U O 67 E I _ (A E (:7, 64) D (:6, ?3) y ?7 =7 s 47 M (47, 57) 57 y 9 57 J (:7, 57) x + y 9 34 :7 x 8x + 4 y 9 477 :7 83 57 47 =7 ?7 67 x (A_IEOU LF M_DKT) 37 WULNOD] ? TOD]BLA 7? [email protected] LF MJ]J Mjm bs oxpodtom tl ijko j prl﬊t lf $37.77 la ojdh mudk jam $47.77 la ojdh dhbdkoa. x mudks jt $37.77 ojdh wb`` ybo`m j prl﬊t lf $37 x jam y dhbdkoas jt $47 ojdh wb`` ybo`m j prl﬊t lf $47 y. ]horoflro tho prl﬊t oqujtbla flr mjm‒s eusbaoss ilmo` bs wrbttoa js> W 9 37x + 47y ]ho jbi bs tl motoribao tho auieor lf mudks jam dhbdkoas thjt mjm shlu`m purdhjso tl jdhbovo tho ijxbiui prl﬊t. Alw, tho flur baoquj`btbos cjvo rbso tl j pl`ycla wbth tho vortbdos J (:7, 57); E (:7, 64); D (:6, ?3); M (47, 57) js shlwa la tho crjph. ]ho fuamjioatj` tholroi lf `baojr prlcrjiibac stj tos thjt lao lf tho flur vortbdos wb`` cbvo vj`uos lf x jam y thjt wb`` ijxbibzo tho oqujtbla W 9 37x + 47y ]ostbac flr tho ijxbiui prl﬊t wo cot> :. Jt J (:7, 57); whoro x 9 :7, y 9 57 W 9 37 Ó :7 + 47 Ó 57 9 377 + 677 9 $:,477.77 ]hbs iojas thjt bf mjm purdhjsos :7 mudks jam 47 dhbdkoas, ho wb`` ijko j prl﬊t lf $:,477.77 por wook. 5. Jt E (:7, 64); whoro x 9 :7, y 9 64 W 9 37 Ó :7 + 47 Ó 64 9 377 + :,827 9 $5,?27.77 ]hbs iojas thjt bf mjm purdhjsos :7 mudks jam 64 dhbdkoas, ho wb`` ijko j prl﬊t lf $5,?27.77 por wook. 4. Jt D (:6, ?3); whoro x 9 :6, y 9 ?3 W 9 37 Ó :6 + 47 Ó ?3 9 :,:57 + :,3:7 9 $5,847.77 ]hbs iojas thjt bf mjm purdhjsos :6 mudks jam ?3 dhbdkoas, ho wb`` ijko j prl﬊t lf $5,847.77 por wook. 88 =. Jt D (47, 57); whoro x 9 47, y 9 57, W 9 37 Ó 47 + 47 Ó 57 9 5,:77 + 677 9 $5,377.77 ]hbs iojas thjt bf mjm purdhjsos 47 mudks jam 57 dhbdkoas, ho wb`` ijko j prl﬊t lf $5,377.77 por wook. ]horoflro, ba lrmor flr mjm tl letjba j ijxbiui prl﬊t lf $5,847, ho iust purdhjso :6 mudks jam ?3 dhbdkoas ojdh wook. 82 WULNOD] ? TOD]BLA 7? MBTD_TTBLA LF FBAMBACT ]hbs sbip`o `baojr prlcrjiibac ilmo`, cbvos mjm j cubmo sl ho dja ijko ja baflriom modbsbla whoa purdhjsbac tho ebrms tl rotjb` jt j prl﬊t. Bt ho`ps hbi tl jvlbm uaaodossjry spodu`jtblas jam ostbijtos ejsom la cuosswlrk. Flr oxjip`o, ejsom la hbs mocroo lf froomli, mjm kalws thjt> :. bf ho purdhjsos :7 mudks jam 57 dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $:,477.77 por wook. 5. bf ho purdhjsos :7 mudks jam 64 dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,?27.77 por wook. 4. bf ho purdhjsos :6 mudks jam ?3 dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,847.77 por wook. =. bf ho purdhjsos 47 mudks jam 57 dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,377.77 por wook. Hoado, mjm alw kalws tho oxjdt auieor lf mudks jam dhbdkoas ho iust purdhjso wook`y wbthba tho cbvoa dlastrjbats ba lrmor tl ijxbibzo prl﬊t la hbs bavostioat. 27 WULNOD] ? TOD]BLA 76 [email protected]_TBLA Ejsom la tho ﬊ambacs, bt dja eo dlad`umom thjt mjm iust purdhjso :6 mudks jam ?3 dhbdkoas, j tltj` lf 34 ebrms ba lrmor tl coaorjto j ijxbiui prl﬊t lf $5,847.77 por wook. 2: WULNOD] ? TOD]BLA 78 UOFOUOADOT Croor, J. & @jyao, D. O., (:287);Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja. ]ll`sbo, U.; Ijthoijtbds> J Dlip`oto Dlurso wbth DXD Zuostblas. Vl`. 5 www.ijth.ud`j.omu www.ijthswlrk.dli 25 WULNOD] 6 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla tl motoribao tho ijxbiui jroj lf j vocotje`o cjrmoa thjt dja eo dlastrudtom frli j cbvoa p`lt lf `jam. 24 WULNOD] 6 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................ Wjco Auieor ?. Jaj`ysbs lf Mjtj ......................................................................Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor ]l moj` wbth rbsbac prbdos, iy pjroats jam B hjvo modbmom tl drojto j vocotje`o cjrmoa jt tho ejdk lf lur hlio. Tbado thoro jro throo (4) mlcs ba tho yjrm, wo wlu`m `bko tl oad`lso tho cjrmoa wbth j wbro foado. Mjm hjs j pbodo lf wbro ba stlrjco whbdh ho wjats tl uso tl foado tho cjrmoa. So j`sl wjat tl cbvo tho cjrmoa j rodtjacu`jr shjpo, wbth j : iotro flltpjth jrluam. ]hbs wb`` j``lw flr ojsy jddoss, wjtorbac jam fortb`bzbac. Jftor stumybac qujmrjtbd oqujtblas ba sdhll`, B hjvo modbmom tl uso thbs prbadbp`o tl ho`p iy pjroats ijxbibzo tho uso lf tho `jam spjdo flr tho dlastrudtbla lf tho cjrmoa. 2= WULNOD] 6 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA Mjm jam B woat tl tho ejdk lf tho hluso jam usom j iojsurbac tjpo whoro wo iojsurom tho mbioasblas lf tho jvjb`je`o `jam. So j`sl iojsurom tho `oacth lf tho wbro thjt mjm hjm ba stlrjco. ]ho `jam hjm j rluch rodtjacu`jr shjpo, thoroflro, wo iojsurom tho `oacth jam wbmth js jddurjto`y js plssbe`o. 2? WULNOD] 6 TOD]BLA 76 WUOTOA]J]BLA LF MJ]J ]ho mjtj dl``odtom rovoj`om thjt> (b) ]ho `oacth lf tho jvjb`je`o `jam bs jpprlxbijto`y 52.3 iotros. (bb) ]ho wbmth lf tho `jam bs jpprlxbijto`y 5:.2 iotros. (bbb) ]ho jroj lf tho `jam bs 52.3 iotros Ó 5:.2 iotros (b.o. jpprlxbijto`y 6?7 sq. iotros). (bv) ]ho `oacth lf tho wbro tl eo usom bs :77 iotros `lac. y iotros : iotro flltpjth Vocotje`o Cjrmoa x iotros x iotros y iotros ]ho mbjcrji jelvo bs j ilmo` lf tho p`lt lf `jam tl eo foadom wbth :77 iotros lf foadbac wbro. @ot tho `oacth lf tho p`lt lf `jam tl eo foadom eo y iotros. @ot tho wbmth lf tho p`lt lf `jam tl eo foadom eo x iotros. @oacth lf wbro tl oad`lso tho p`lt bs :77 iotros. Hoado, porbiotor (W) lf tho p`lt bs :77 iotros. ∽ 5x + 5y 9 :77 lr x + y y 91 9 ?7 9 ?7 — x (Oqujtbla :) 26 Tbado thoro bs j : iotro fllt pjth jrluam tho cjrmoa; tho Sbmth lf tho cjrmoa 9 (x — 5) iotros 9 ( y — 5) iotros @oacth lf tho cjrmoa Tuestbtuto y 9 ?7 — x frli oqujtbla : batl tho `oacth tl cot> 9 (?7 — x — 5) iotros @oacth lf Cjrmoa 9 (=8 — x) iotros Jroj lf rodtjacu`jr vocotje`o cjrmoa bs `oacth iu`tbp`y ey wbmth ∽ Jroj 9 (=8 — x) (x — 5) 5 9 =8x — 26 — x + 5x 9 ?7x — 26 — x5 Flr tho ro`jtbla J 9 ?7x — 26 — x5, j tje`o lf vj`uos lf plssbe`o wbmths, x, wjs tjeu`jtom, j crjph lf J vs x wjs mrjwa flr tho mlijba vj`uos ? ≭ x ≭ =? x ? :7 :? 57 5? 47 4? =7 =? J :52 47= =52 ?7= ?52 ?7= =52 47= :52 Too Jppoambx flr dj`du`jtbla lf tho rjaco (J) ]ho crjph eo`lw shlws tho ro`jtblashbp eotwooa tho jroj (J) lf tho `jam tl eo oad`lsom jam tho wbmth lf tho `jam (x) 677 ?77 ) (i=77 s o rt o i o r 477 j u q s 5 a b j577 ro J :77 7 7 ? :7 :? 57 5? 47 @oacth ba iotros (i) 4? Fbcuro :> Tdj`o usom> :di ≪ ? iotros la hlrbzlatj` jxbs, :di ≪ :77 squjro iotros la vortbdj` jxbs =7 =? ?7 Alto> ]ho `oacth lf tho jvjb`je`o `jam bs 52.3 i. ]horoflro, dhllsbac mlijba vj`uos (x) thjt jro crojtor thja 52 iotros wb`` sorvo al prjdtbdj` purplso ba tho prlnodt. ]hoso vj`uos woro bad`umom strbdt`y 23 flr tho thorlrotbdj` purplso lf letjbabac j dlip`oto pjrjel`bd shjpo la tho crjph. WULNOD] 6 TOD]BLA 7? [email protected] LF MJ]J Frli tho crjph> :. ]ho ijxbiui vj`uo lf J bs ?52 squjro iotros 5. ]ho ijxbiui jroj lddurs whoa x 9 5? iotros ]ho `oacth lf tho `jam tl eo foadom tl cbvo tho ijxbiui jroj lf tho vocotje`o cjrmoa bs y 9 ?7 — x 9 ?7 — 5? 9 5? iotros. ]ho wbmth lf tho `jam tl eo foadom tl cbvo tho ijxbiui jroj lf tho vocotje`o cjrmoa bs> x 9 5? i (frli crjph) ]ho ijxbiui jroj lf tho vocotje`o cjrmoa bs ?52 iotros5 (frli crjph) Vorbfybac tho crjphbdj` rosu`ts ey dj`du`jtbla wo cot> (b) wbmth lf vocotje`o cjrmoa 9 9 9 54 iotros (bb) `oacth lf vocotje`o cjrmoa 9 9 (y — 5) iotros 9 (5? — 5) iotros 54 iotros Jroj lf vocotje`o cjrmoa 9 9 (x — 5) iotros (5? — 5) iotros 9 `oacth Ó wbmth 9 (y — 5) (x — 5) 5 (54 Ó 54) iotros ?52 iotros 5 ]ho vocotje`o cjrmoa dja eo dlastrudtom usbac tho jelvo mbioasblas sbado tho jroj lf ?52 iotros5 bs wbthba tho jroj lf tho jvjb`je`o `jam, whbdh bs 6?7 iotros 5. J`sl tho jroj lf tho p`lt lf `jam tl eo foadom whbdh wb`` dlatjba tho vocotje`o cjrmoa jam tho lao iotro flltpjth bs (5? Ó 5?) iotros5 9 65? iotros5 ]hbs tll bs wbthba tho jroj lf tho jvjb`je`o `jam tl eo usom flr dlastrudtbla. 28 WULNOD] 6 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT So dja ojsb`y dlastrudt j vocotje`o cjrmoa ey oad`lsbac ja jroj lf `jam jt tho ejdk lf tho hluso wbthlut dlasbmorbac jay rbclrlus jaj`ysbs. Hlwovor, thbs sbip`o j`coerjbd ilmo` puts us ba j plsbtbla tl ijko ilro baflriom dhlbdos ba toris lf tho mbioasblas tl eo usom. Flr oxjip`o, tho ilmo` shlws thjt> :. ]ho ijxbiui jroj thjt dja eo oad`lsom frli tho cbvoa `jam spjdo bs j porfodt squjro lf 65? squjro iotros wbth mbioasblas 5? iotros ey 5? iotros. 5. ]ho jroj lf tho vocotje`o cjrmoa tl eo oad`lsom wbth j lao iotro pjthwjy jrluam bt bs j porfodt squjro lf ?52 squjro iotros wbth mbioasblas 54 iotros ey 54 iotros. 4. ]hbs dlastrudtbla wb`` stb`` `ojvo j rojslaje`o jiluat lf `jam spjdo jrluam tho oad`lsom jroj. =. ]ho `jam spjdo roijbabac jftor dlastrudtbla lf foado bs (6?7 — 65?) squjro iotros 9 5? squjro iotros. ]hbs spjdo wb`` j``lw flr tho mlcs tl p`jy lutmllrs. 22 WULNOD] 6 TOD]BLA 73 [email protected]_TBLA ]ho ﬊ambacs rovoj` thjt tho ijxbiui jroj lf j vocotje`o cjrmoa thjt dja eo sot up frli ja jvjb`je`o pbodo lf `jam lf jroj 6?7 squjro iotros, bs ?52 squjro iotros. ]l j``lw flr tho flltpjth lf lao iotro jrluam tho cjrmoa, ja jroj lf 65? i 5 lf `jam iust eo foadom wbth j :77 iotro `lac foado. 5? iotros :i 5? iotros :i flltpjth lutor foado Vocotje`o Cjrmoa :i 5? iotros :i 5? iotros [email protected] LF [email protected]]OM DLAT]U_D]BLA :77 WULNOD] 6 TOD]BLA 78 UOFOUOADOT D`jrko, @. Hjrwllm, Jmmbtblaj` Wuro Ijthoijtbds, 4rm Ombtbla Hoac, H. H.; ]j`eort, N. F.,Jmmbtblaj` Ijthoijtbds, 6th Ombtbla www.uadw.omu/j`ocerj www.vjrsbtytutlrs.dli :7: WULNOD] 6 TOD]BLA 72 JWWOAMBX [email protected][email protected]]BLA LF UJACO J 9 ?7x — 26 — x5 x ? :7 :? 57 5? 47 4? =7 =? J :52 47= =52 ?7= ?52 ?7= =52 47= :52 Shoa 9 x J Shoa ?7 Ó ? — 26 — ?5 9 5?7 — 26 — 5? 9 :52 i 9 x J Shoa ?7 Ó :7 — 26 — :75 9 ?77 — 26 — :77 9 47= i 9 Shoa ?7 Ó :? — 26 — :?5 9 3?7 — 26 — 55? 9 =52 i 9 Shoa ?7 Ó 57 — 26 — 575 9 :777 — 26 — =77 9 ?7= i 9 Shoa ?7 Ó 5? — 26 — 5?5 9 :5?7 — 26 — 65? 9 ?52 i 9 Shoa ?7 Ó 47 — 26 — 475 9 :?77 — 26 — 277 9 ?7= i 9 5 47i 9 x J 5 5?i 9 x J 5 57i 9 x J 5 :?i 9 x J 5 :7i 9 x J ?i 9 5 4?i 9 ?7 Ó 4? — 26 — 4?5 9 :3?7 — 26 — :55? 9 =52 i 5 :75 WULNOD] 3 TOD]BLA 7: WULNOD] ]B]@O Drojtbac tho ilst dlst offodtbvo eumcot tl dlip`oto j rlli iojsurbac :=‒ x :5‒ x :7‒. :74 WULNOD] 3 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................ Wjco Auieor ?. Jaj`ysbs lf Mjtj ......................................................................Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Iy pjroats hjvo nust dlip`otom tho dlastrudtbla lf j eomrlli iojsurbac :=‒ x :5‒ x :7‒. Sbth j eumcot lf $?,777.77, thoy jro dlasbmorbac tho fl``lwbac> :. bastj``bac dorjibd ſtllr tb`os 5. pjbatbac tho wj``s yo``lw, mllrs e`uo 4. bastj``bac j dob`bac lf obthor cypsui lr W.V.D. pjao`s Sbth iy kalw`omco lf dlasuior jrbthiotbd jam iojsuroioat, B hjvo modbmom tl jssbst thoi wbth thbs voaturo. ]ho purplso lf thbs prlnodt bs tl motoribao tho ilst dlst offodtbvo ostbijto tl dlip`oto tho rlli. :7= WULNOD] 3 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA Flur (=) mbfforoat hjrmwjro stlros J, E, D, jam M woro vbsbtom jam prbdos woro letjbaom la tho ijtorbj` tl eo usom. B j`sl letjbaom prbdos la `jelur dlsts frli twl wlrkioa ajiom : jam 5 ba tho prlnodt. ]ho `jelur dlst qultom frli tho wlrkioa bad`umom tho dlst lf `jelur flr frjibac jam bastj``bac tho cypsui lr WVD dob`bac. :7? WULNOD] 3 TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Ba thbs prlnodt, = ostbijtos woro dlasbmorom flr dlipjrbsla. Jftor tho rjw mjtj wjs dl``odtom frli tho = mbfforoat hjrmwjro stlros jam tho 5 wlrkioa, bt wjs lrcjabzom jam prosoatom ba tje`os js fl``lws> Ostbijto frli Hjrmwjro J Zujatbty Mosdrbptbla :77 :6’x:6’dorjibdſtllrtb`os _abtWrbdo$ 57.77 Jiluat$ 5,777.77 ejcs = thbasot =7.77 :67.77 `es 6 crlut 57.77 :57.77 pk : tb`o spjdos :cj` dladrotoprbior :cj` wjtorejsompjbat cj` ° =?pbodos wllm pjbat 5=’x5=’cypsuidob`bactb`os 67.77 67.77 :87.77 :87.77 5?7.77 5?7.77 37.77 37.77 47.77 :,4?7.77 =,:27.77 ?54.3? VJ] G :5.?% ]ltj` =,3:4.3? Ostbijto frli Hjrmwjro E Zujatbty Mosdrbptbla :77 :6’x:6’dorjibdſtllrtb`os _abtWrbdo$ :8.77 Jiluat$ :,877.77 ejcs = thbasot =?.77 :87.77 `es 6 crlut 56.77 :7=.77 pk : tb`o spjdos :cj` dladrotoprbior :cj` wjtorejsompjbat cj` ° =?pbodos wllm pjbat 5=’x5=’cypsuidob`bactb`os 37.77 37.77 :?7.77 547.77 :?7.77 547.77 27.77 27.77 4?.77 :,?3?.77 =,:22.77 VJ] G :5.?% ]ltj` ?5=.88 =,354.88 :76 Ostbijto frli Hjrmwjro D Zujatbty Mosdrbptbla :77 :6’x:6’dorjibdſtllrtb`os _abtWrbdo$ :3.77 Jiluat$ :,377.77 ejcs = thbasot =7.77 :67.77 `es 6 crlut 47.77 :87.77 pk : tb`o spjdos :cj` dladrotoprbior :cj` ° cj` wjtorejsompjbat wllm pjbat :? `oacths :7’ W.V.D. pjao`s G :2 ¹ ft. 6?.77 6?.77 :57.77 :57.77 577.77 :7?.77 577.77 :7?.77 37.77 :,7?7.77 4,?87.77 VJ] G :5.?% ==3.?7 ]ltj` =,753.?7 Ostbijto frli Hjrmwjro M Zujatbty Mosdrbptbla :77 :6’x:6’dorjibdſtllrtb`os _abtWrbdo$ :3.77 Jiluat$ :,377.77 ejcs = thbasot =?.77 :87.77 `es 6 crlut 57.77 :57.77 pk : tb`o spjdos :cj` dladrotoprbior :cj` wjtorejsopjbat cj` ° :? `oacths wllm pjbat :7’ W.V.D. pjao`s G :2 ¹ ft. 47.77 47.77 :57.77 :?7.77 :57.77 :?7.77 ?7.77 ?7.77 ?7.77 3?7.77 4,:77.77 VJ] G :5.?% ]ltj` :73 483.?7 4,=83.?7 @jelur Dlst> ]wl wlrkioa whl woro so`odtom tl ml tho wlrk cjvo tho fl``lwbac `jelur dlst> @jelur dlst frli Slrkija : 9 $5,777.77 @jelur dlst frli Slrkija 5 9 $:,?77.77 Tuiijry lf Ostbijtos jam @jelur Dlsts Ostbijto Ostbijto Ostbijto Ostbijto HjrmwjroJ $=,3:4.3? HjrmwjroJ $=,3:4.3? @jelur Slrkija #: ]ltj` $5,777.77 $6,3:4.3? @jelur Slrkija #5 $:,?77.77 $6,5:4.3? HjrmwjroE $=,354.88 HjrmwjroE $=,354.88 @jelur Slrkija #: $5,777.77 @jelur Slrkija #5 $:,?77.77 ]ltj` $6,354.88 $6,554.88 HjrmwjroD $=,753.?7 HjrmwjroD $=,753.?7 @jelur Slrkija #: $5,777.77 @jelur Slrkija #5 $:,?77.77 ]ltj` $6,753.?7 $?,?54.?7 HjrmwjroM $4,43?.77 HjrmwjroM $4,=83.?7 @jelur Slrkija #: $5,777.77 @jelur Slrkija #5 $:,?77.77 ]ltj` $?,43?.7 7 $=,283.?7 W`ojso alto thjt Hjrmwjro J jam Hjrmwjro E hjm al WVD dob`bac la sj`o. ]horoflro, WVD dob`bac wjs alt sooa ba tho eumcots flr Hjrmwjro J jam Hjrmwjro E. Hjrmwjro D jam Hjrmwjro M hjm al cypsui la sj`o. ]horoflro, cypsui tb`os woro alt sooa ba tho eumcots flr Hjrmwjro D jam Hjrmwjro M. Ba lrmor tl drojto tho = ostbijtos, tho fl``lwbac dj`du`jtblas woro porflriom. Ba porflribac tho dj`du`jtblas tho fl``lwbac dlavorsblas woro ijmo; (b) badhos tl foot — : foot 9 :5 badhos ∽ tl dlavort badhos tl foot wo mbvbmo ey :5 (bb) luados tl pluams — : pluam 9 :6 luados ∽ tl dlavort luados tl pluams wo mbvbmo ey :6 :78 ]ho F`llr Btoi aoomom tl tb`o tho ſtllr jro> (b) tb`os (bb) thbasot (bbb) crlut (bv) tb`o spjdors (b) ]b`os Lao ſtllr tb`o iojsuros :6’ x :6’ whbdh bs :.444 foot x :.444 foot. Tbado tho tb`os hjvo j squjro shjpo jam tho jroj lf j squjro bs sbmo x sbmo, bt fl``lws thjt tho jroj lf : tb`o bs :.444 foot x :.444 foot 9 :.8 squjro foot. Tbado tho ſtllr hjs j rodtjacu`jr shjpo lf := foot x :5 foot jam tho jroj lf j rodtjac`o bs `oacth x wbmth, bt fl``lws thjt tho jroj lf tho ſtllr tl eo tb`om bs := foot x :5 foot 9 :68 squjro foot. ]l tb`o ja jroj lf :68 squjro foot usbac :.8 squjro foot tb`os, tho auieor lf tb`os aoomom bs :68 squjro foot 9 2= tb`os jpprlxbijto`y. :.8 squjro foot Ja oxtrj 6 tb`os jro tl eo elucht ba lrmor tl ijko prlvbsbla flr erojkjco. ∽ ]ltj` auieor lf tb`os tl eo elucht bs :77. ]hbasot ]hbasot bs tho ijtorbj` usom tl p`jstor tho ſtllr eoflro `jybac tho tb`os. ]ho baflrijtbla la tho pjdkjco stjtos thjt : ejc dlvors j surfjdo jroj lf =7 sq. ft. ∽ ]ho tltj` auieor lf ejcs thjt dlvors :68 sq. ft. lf ſtllr surfjdo bs :68 9 = ejcs ∽ ]ho tltj` auieor lf ejcs lf thbasot tl eo elucht bs = ejcs =7 Crlut Crlut bs tho ijtorbj` usom tl soj` tho spjdos eotwooa ojdh tb`o. ]ho baflrijtbla la tho pjdkjco stjtos thjt : luado lf crlut soj`s jpprlxbijto`y lao :6’ x :6’ tb`o. ∽ ]ho jiluat lf crlut aoomom bs : luado ey 2= tb`os 9 2= luados 9 ?.2 `es ∽ ]ho jiluat lf crlut tl eo elucht bs 6 pluams ]b`o Tpjdors ]b`o spjdors jro usom tl drojto tho ovoa spjdo eotwooa ojdh tb`o. ]b`o spjdors jro sl`m ba pjdkjcos lf :77 por pjdk. ∽ ]ho jiluat lf spjdors aoomom flr 2= tb`os bs : pjdk Tuiijry lf btois aoomom flr tb`bac tho ſtllr jro js fl``lws> = ejcs lf thbasot 6 `es lf crlut :72 : pjdk lf spjdors Dob`bac ]ho spjdo tl eo soj`om bs ſtjt jam rodtjacu`jr ba shjpo. @oacth lf dob`bac Sbmth lf dob`bac ∽ 9 := ft. 9 :5 ft. Jroj lf Dob`bac 9 := ft. x :5 ft. 9 :68 sq. ft. ]ho spjdo bs soj`om wbth obthor cypsui dob`bac tb`os lr WVD dob`bac pjao`s. (b) Cypsui Dob`bac ]b`os Jroj lf : tb`o 9 5=’ x 5=’ squjro badhos 9 5‒ x 5‒ sq. ft. 9 = sq. ft. ∽ Al. lf dob`bac tb`os roqubrom 9 :68 9 =5 tb`os = 4 oxtrj tb`os jro elucht ∽ ]ltj` auieor lf dob`bac tb`os tl eo elucht 9 =5 + 4 9 =? (bb) WVD Dob`bac ]b`os : 5 @oacth lf : WVD pjao` 9 :2 Sbmth lf : WVD pjao` 9 :7 badhos 9 :5 ft. Sbmth lf rlli 9 :5 ft. ∽ ft. :7 Al. lf WVD pjao` roqubrom 9 :5 9 :5 Ó :5 9 :== 9 :=.= :7 :7 :7 :5 ]horoflro, tltj` auieor lf pjao`s tl eo elucht 9 :? ::7 Wjbat ]ho wj``s jro tl eo pjbatom yo``lw jam tho mllr e`uo. ]ho rlli hjs flur wj``s, j`` lf whbdh jro rodtjacu`jr ba shjpo. ]wl sbmos iojsuro :=‒ x :7‒ ojdh ]ltj` jroj lf tho twl sbmos ∽ 9 (:=‒ x :7‒) x 5 9 587 sq. ft. ]ho lthor 5 sbmos iojsuro :5‒ x :7‒ ojdh ∽ ]ltj` jroj lf tho lthor 5 sbmos 9 (:5‒ x :7‒) x 5 ]horoflro, tho tltj` jroj lf wj`` spjdo tl eo pjbatom 9 5=7 sq. ft. 9 587 + 5=7 9 ?57 sq. ft. Mllr sbzo 9 ?=’ x 5=’ sq. ft. 9 =.?‒ x 5‒ sq. ft. 9 2 sq. ft. Sbamlw sbzo 9 5=’ x 5=’ sq. badhos 9 5‒ x 5‒ sq. ft. 9 = sq. ft. 9 (2 + =) sq. ft. 9 :4 sq. ft. ∽ ]ltj` jroj lf wbamlw jam mllr ]horoflro, tho tltj` jroj lf wj`` spjdo tl eo pjbatom 9 (?57 - :4) sq. ft. 9 ?73 sq. ft. ]ho baflrijtbla la tho pjbat tba stjtos thjt lao cj``la lf prbior jam lao cj``la lf pjbat ojdh hjs j dlvorjco lf =57 tl ?57 sq. ft. ∽ Jiluat lf pjbat jam prbior aoomom flr wj``s jro> : cj``la lf prbior : cj``la lf yo``lw pjbat Mllr jroj 9 2 sq. ft. ∽ ::: : = cj``la lf e`uo lb` pjbat bs aoomom tl pjbat mllr. WULNOD] 3 TOD]BLA 7? [email protected] LF MJ]J ]ho mjtj rovoj`om tho fl``lwbac; :. ostbijto frli Hjrmwjro E wbth `jelur dlst frli Slrkija : djio ba wbth tho hbchost eumcot lf $6,354.88 5. ostbijto frli Hjrmwjro J wbth `jelur dlst frli Slrkija : cjvo tho 5am hbchor ostbijto lf $6,3:4.3? 4. ostbijto frli Hjrmwjro E wbth `jelur dlst frli Slrkija 5 cjvo tho 4rm hbchost ostbijto lf $6,554.88 =. ostbijto frli Hjrmwjro J wbth `jelur dlst frli Slrkija 5 cjvo tho =th hbchost ostbijto lf $6,5:4.3? ?. ostbijto frli Hjrmwjro D wbth `jelur dlst frli Slrkija : cjvo tho ?th hbchost ostbijto lf $6,753.?7 6. ostbijto frli Hjrmwjro D wbth `jelur dlst frli Slrkija : cjvo tho 6th hbchost ostbijto lf $?,?54.?7 3. ostbijto frli Hjrmwjro M wbth `jelur dlst frli Slrkija : cjvo tho 3th hbchost ostbijto lf $?,43?.77 8. ostbijto frli Hjrmwjro M wbth `jelur dlst frli Slrkija 5 cjvo tho dhojpost ostbijto lf $=,283.?7 ]l motoribao whothor furthor sjvbac wjs plssbe`o jam whbdh ostbijto bs ilst dlst offodtbvo, j`` 8 ostbijtos woro porusom jam tho `lwost prbdo lf ojdh btoi wjs oxtrjdtom frli tho mbfforoat hjrmwjros. Hjrmwjro D & M lfforom tho dhojpost tb`o Hjrmwjro D lfforom tho dhojpost thbasot Hjrmwjro J & M lfforom tho dhojpost crlut Hjrmwjro M lfforom tho dhojpost spjdos Hjrmwjro D & M lfforom tho dhojpost prbior Hjrmwjro M lfforom tho dhojpost wjtor ejsom pjbat, wllm pjbat jam WVD pjao`s Frli tho jelvo lesorvjtbla, tho ostbijto whbdh lfforom tho ilst dlst offodtbvo eumcot wjs coaorjtom. Lvorj``, Hjrmwjro M, lfforom tho dhojpost prbdos wbth tho oxdoptbla lf Hjrmwjro D whbdh lfforom tho dhojpost thbasot. ]horoflro j`` ijtorbj`s jro tl eo purdhjsom frli Hjrmwjro M, wbth tho oxdoptbla lf thbasot wb`` eo purdhjsom frli Hjrmwjro D. ::5 Frli tho jelvo dlasbmorjtbla tho dhojpost ostbijto bs js fl``lws> Hjrmwjro Btoi _abtWrbdo$ M Dorjibdtb`os :3.77 D ]hbasot =7.77 ejcs = M Crlut 57.77 M Tpjdors 47.77 M Wrbior :57.77 M Sjtor Wjbat M Lb` Wjbat M WVDWjao`s :?7.77 ?7.77 ?7.77 Zujatbty :77 - - :67.77 `es 6 :57.77 - pk : 47.77 - cj` : :57.77 :cj` ∽ dlst lf ostbijto ]ltj` ::4 - :?7.77 ° cj` ?7.77 :?`oacths 3?7.77 5,257.77 :67.77 VJ]G:5.?% 46?.77 57.77 ]ltj` wbth VJ] 4,58?.77 :87.77 9 ]ltj` dlst frli Hjrmwjro M + ]ltj` dlst frli Hjrmwjro D 9 $4,58?.77 + $:87.77 @jelur frli Slrkija 5 Dlst$ :,377.77 ]ltj` wbthlut VJ] ]ltj` dlst lf ijtorbj` Dlst$ 9 $4,=6?.77 9 $:,?77.77 9 $=,26?.77 WULNOD] 3 TOD]BLA 76 [email protected]_TBLA ]ho ilst dlst offodtbvo ostbijto thoroflro bs tho dliebajtbla lf prbdos frli Hjrmwjro D jam M jam `jelur dlst frli Slrkija 5 whbdh tltj`s $=,26?.77 jam fj``s wbthba tho eumcot lf $?,777.77. ::= WULNOD] 3 TOD]BLA 73 UOFOUOADOT www.wbkbhlw.dli www.so`feub`maowhlios.dli ::? WULNOD] 8 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla batl ﬊xom rjto ilrtcjcos. ::6 WULNOD] 8 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................Wjco Auieor ?. Jaj`ysbs lf Mjtj ...................................................................... Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Iy pjroats jro dlasbmorbac tjkbac j `lja frli j ejak tl purdhjso j hluso. ]hoy jro oip`lyom js D`orks ba tho clvoraioat sorvbdo jam hjvo sjvbacs whbdh wb`` eo usom js j mlwa-pjyioat tlwjrms tho purdhjso lf tho hluso. ]ho purplso lf thbs prlnodt bs tl shlw hlw ilath`y ilrtcjco pjyioats jro dj`du`jtom la ﬊xom rjto ilrtcjcos cbvoa mbfforoat toris lf ropjyioat. ::3 WULNOD] 8 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA B sjt wbth iy pjroats jam dl``odtom thobr porslaj` mjtj sudh js jco, nlbat badlio, sjvbacs, dlst lf tho hluso jam lthor baflrijtbla whbdh wlu`m jbmo ba thobr ilrtcjco dj`du`jtbla. B j`sl vbsbtom j `ldj` ejak jam batorvbowom j ilrtcjco @ljas Lf﬊dor whl prlvbmom baflrijtbla la ilrtcjcos sudh js> typo lf ilrtcjco, prbadbpj`, batorost rjto, toris lf ropjyioat jam lthor fjdts whbdh woro portbaoat tl dj`du`jtbac ilrtcjcos. ::8 WULNOD] 8 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA ]ho mjtj dl``odtom frli iy pjroats jro js fl``lws> Jco lf elth pjroats — 47 yojrs Nlbat badlio — $54,777 por ilath Tjvbacs (mlwa pjyioat) — $?7,777.77 Dlst lf tho hluso — $?77,777.77 Iy batorvbow wbth tho ilrtcjco @ljas Lf﬊dor batrlmudom io tl tho fl``lwbac fjdts jelut ilrtcjco whbdh iust eo kalwa eoflro j ilrtcjco bs dj`du`jtom. :. Ilrtcjcos jro usuj``y dj`du`jtom jt rjtos whbdh stjy tho sjio flr tho `bfotbio lf tho ilrtcjco, thoroflro, thoy jro dj``om ﬊xom rjto ilrtcjcos. ]hoso djrry j `lw batorost rjto rjacbac eotwooa 4% jam :7% eodjuso tho `lja bs sodurom, cbvbac tho `oamor tho romross tl sobzo tho prlporty bf tho `lja bs alt eobac ropjbm. 5. ]ho jco lf tho elrrlwor bs j ijnlr fjdtlr. ]ho yluacor tho elrrlwor, tho sij``or tho ilrtcjco rjto jam tho `lacor tho `bfospja lf tho `lja. 4. ]ho l`mor tho elrrlwor, tho `jrcor tho ilath`y pjyioat lvor j shlrtor `lja `bfospja. =. J mlwa pjyioat lf jt `ojst :7% iust eo ijmo ?. ]ho ilath`y pjyioat iust oam la lr eoflro, 47 yojrs. ]hbs iojas thjt iy pjroats hjvo j ijxbiui lf 47 yojrs ba whbdh tl ropjy thobr ilrtcjco. ]horoflro, B hjvo modbmom tl dj`du`jto 4 ilrtcjco p`ja lptblas wbth 4 mbfforoat toris lf ropjyioat lf 57 yojrs, 5? yojrs jam tho ijxbiui 47 yojrs. ]ho fl``lwbac prosoatjtbla cbvos j motjb`om lut`bao lf hlw tho throo mbfforoat ilrtcjco p`jas wb`` eo sotup jam dj`du`jtom> ]ho vj`uo lf ojdh ilath`y pjyioat wb`` eo dj`du`jtom usbac j stjamjrm dlipluam batorost flriu`j. ]hbs flriu`j hjs flur vjrbje`os. ]hoso vjrbje`os jro> :. ]ho Wrbadbpj` jiluat lf ilaoy thjt iy pjroats wjat tl elrrlw. ]hbs bs roprosoatom ey tho `ottor W ba tho flriu`j. 5. ]ho batorost rjto por ilath thjt tho ejak bs dhjrcbac iy pjroats tl elrrlw tho Wrbadbpj` sui. ]hbs bs roprosoatom ey tho `ottor r ba tho flriu`j. 4. ]ho auieor lf ilaths thjt iy pjroats wb`` tjko ::2 tl ropjy tho Wrbadbpj` sui. ]hbs bs roprosoatom ey tho `ottor a ba tho flriu`j. =. ]ho jiluat lf ojdh ilath`y pjyioat thjt iy pjroats wb`` hjvo tl ropjy. ]hbs roprosoatom ey tho `ottor I ba tho flriu`j. Vj`uos flr tho throo vjrbje`os; prbadbpj` (W), tbio (a) jam rjto (r) wb`` eo dl``odtom frli tho ejak jam suestbtutom batl tho flriu`j tl letjba tho flurth vjrbje`o, tho ilath`y pjyioat (I). ]ho dlipluam batorost flriu`j thjt wb`` eo usom ba thbs prlnodt bs> { I9W r (:+r)a (:+r)a - : } J`` dj`du`jtblas wbthba tho dur`y erjdkots iust eo mlao ﬊rst tl letjba j vj`uo. ]hbs vj`uo bs thoa iu`tbp`bom ey W tl letjba tho vj`uo lf I. ]ho mlwa pjyioat lf :7% lf $?77,777.77 wb`` eo dj`du`jtom. ]hbs mlwa pjyioat wb`` eo suetrjdtom frli $?77,777.77 tl letjba tho prbadbpj` (W) thjt wb`` eo usom tl dj`du`jto tho ilath`y pjyioat (I) Mlwa pjyioat tl eo ijmo ey iy pjroats bs :7% lf $?77,777.77 Mlwa pjyioat ∽ 9 :7% lf ?77,777 9 :7 :77 Ó ?77,777 9 $?7,777.77 ]ho ilrtcjco dja eo letjbaom uamor throo mbfforoat toris. (:) ]ori J> (5) ]ori E> (4) ]ori D> Wrbadbpj` (W) 9 $=?7,777 ]bio (a) 9 47 yojrs 9 (47 Ó :5) ilaths 9 467 ilaths Ujto (r) 9 =.?% por yojr 9 =.? %9 7.43?% por ilath :5 Wrbadbpj` (W) 9 $=?7,777 ]bio (a) 9 5? yojrs 9 (5? Ó :5) ilaths 9 477 ilaths Ujto (r) 9 3% por yojr 9 3 % 9 7.?84% por ilath :5 Wrbadbpj` (W) 9 $=?7,777 ]bio (a) 9 57 yojrs 9 (57 Ó :5) ilaths 9 5=7 ilaths Ujto (r) 9 2.?% por yojr 9 2.?:5% 9 7.325% por ilath :57 ]ho fl``lwbac dj`du`jtblas woro porflriom tl motoribao tho vj`uo lf ojdh ilath`y pjyioat thjt iy pjroats wb`` hjvo tl ijko uamor tho throo mbfforoat ilrtcjco p`jas. Dj`du`jtbla lf ilath`y pjyioat uamor ]ori J W 9 $=?7,777 a 9 467 ilaths r 9 7.43?% 9 7.43? 9 7.7743? :77 I 9W 9 =?7777 { r (:+r)a (:+r)a - : { } (7.7743? (: + 7.7743?)467 (: + 7.7743?)467 - : 9 =?7777 { (7.7743? Ó (4.8=36287?) 9 =?7777 { 7.7:==58863 4.8=36287? - : 5.8=36287? } } } 9 =?7777 Ó 7.77?7668?5 9 $5,587.78 ]horoflro, uamor ]ori J> 9 tho tltj` dlst lf tho hluso bs> mlwa pjyioat + ilath`y pjyioat Ó 467 9 $?7,777.77 + $5,587.78 Ó 467 9 $?7,777.77 + $857,858.87 9 $837,858.87 Dlst lf `lja 9 ilath`y pjyioat x 467 — $=?7,777 9 $5,587.78 Ó 467 — $=?7,777 9 $857,858.87 — $=?7,777 9 $437,858.87 :5: Dj`du`jtbla lf ilath`y pjyioat uamor ]ori E W 9 $=?7,777 a 9 477 ilaths r 9 7.?84% 9 7.?84 9 7.77?84 :77 I 9W { r (:+r)a (:+r)a - : } { 7.77?84 (: + 7.77?84) 477 9 =?7777 { 7.77?84 Ó (?.3:23588:?) 9 =?7777 { 9 =?7777 (: + 7.77?84)477 - : ?.3:23588?: - : 7.744=67:8 =.3:23588:? } } } 9 =?7777 Ó 7.77376?5= 9 $4,:32.46 ]horoflro, uamor ]ori J> 9 tho tltj` dlst lf tho hluso bs> mlwa pjyioat + ilath`y pjyioat Ó 477 9 $?7,777.77 + $4,:32.46 Ó 477 9 $?7,777.77 + $2?4,878.77 9 $:,774,878.77 Dlst lf `lja 9 ilath`y pjyioat x 467 — $=?7,777 9 $5,587.78 Ó 477 — $=?7,777 9 $2?4,878 — $=?7,777 9 $?74,878 :55 Dj`du`jtbla lf ilath`y pjyioat uamor ]ori D W 9 $=?7,777 a 9 5=7 ilaths r 9 7.325% 9 7.325 9 7.77325 :77 I 9W 9 =?7777 9 =?7777 9 =?7777 { r (:+r)a (:+r)a - : } { 7.77325 (: + 7.77325)5=7 { 7.77325 Ó(6.6=:447642) { 7.7?5?22448 (: + 7.77325)5=7 - : 6.6=:447642 - : ?.6=:447642 } } } 9 =?7777 Ó 7.772454254 9 $=,:2?.33 ]horoflro, uamor ]ori J> 9 tho tltj` dlst lf tho hluso bs> mlwa pjyioat + ilath`y pjyioat Ó 5=7 9 $?7,777.77 + $=,:2?.33 Ó 5=7 9 $?7,777.77 + $:,776,28=.87 9 $:,7?6,28=.87 Dlst lf `lja 9 ilath`y pjyioat x 467 — $=?7,777 9 $=,:2?.33 Ó 5=7 — $=?7,777 9 $:,776,28=.87 — $=?7,777 9 $??6,28=.87 :54 Ejr crjph shlwbac tho ﬊aj` dlst lf tho hluso uamor tho throo mbfforoat ilrtcjco ]oris. Tdj`o> :di ≪ $:77,777 la tho vortbdj` jxbs :5 :7 ) 7 7 ,7 7 7 : $ x ( o s u l h f l t s l d ` j ba F 8 6 = 5 7 ]ori J ]ori E ]ori D Ilrtcjco ]oris :5= WULNOD] 8 TOD]BLA 7? [email protected] LF MJ]J _sbac ]ori J, bt wjs fluam thjt iy pjroats wb`` hjvo tl pjy $5,587.78 por ilath flr 467 ilaths (47 yojrs). ]ho ﬊aj` dlst lf tho hluso wb`` eo $837,858.87 _sbac ]ori E, thoy wb`` hjvo tl pjy $4,:32.46 por ilath flr 477 ilaths (5? yojrs). ]ho ﬊aj` dlst lf tho hluso wb`` eo $:,774,878.77 _sbac ]ori D, thoy wb`` hjvo tl pjy $=,:2?.33 por ilath flr 5=7 ilaths (57 yojrs). ]ho ﬊aj` dlst lf tho hluso wb`` eo $:,7?6,28=.87 ]ho ejr crjph la tho provblus pjco dlipjros tho ﬊aj` dlst lf tho hluso uamor tho throo ilrtcjco ]oris J, E jam D. :5? WULNOD] 8 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT Bt bs biplssbe`o flr iy pjroats tl purdhjso j hluso thjt bs vj`uom jt $?77,777.77 wbthlut j ilrtcjco jam euybac thbs hluso bs `bko`y tl eo tho ebccost bavostioat thoy wb`` ovor ijko. ]jkbac j ilrtcjco cbvos thoi tho ſtoxbeb`bty lf sprojmbac tho ropjyioat lf tho hluso lvor porblms lf 57, 5?, lr 47 yojrs. ]horoflro, ilath`y ropjyioats wb`` eo ilro ijajcoje`o flr thoi. Bf thoy jro mosbrlus lf pjybac tho sij``ost ilath`y ropjyioat wbth tho sij``ost batorost dhjrco, thoy dja tjko tho lptbla thjt lffors tho ilrtcjco flr 47 yojrs. Horo, tho ropjyioat wb`` eo $5,887.78 por ilath wbth ja batorost lf =.?% por jaaui. Sbth thbs lptbla tho dlst lf tho ilrtcjco wb`` eo $437,858.87. J`thluch tho lthor twl lptblas lffor j shlrtor ropjyioat tbio, tho dlst lf tho ilrtcjco bs sbcab﬊djat`y crojtor. :56 WULNOD] 8 TOD]BLA 73 [email protected]_TBLA ]ho ilrtcjco dj`du`jtblas rovoj`om thjt> :. ]ho ﬊aj` dlst lf tho hluso usbac W`ja J wb`` eo $837,858.87. ]ho ilath`y ropjyioat wb`` eo $5,887.78. ]ho batorost dhjrco flr tho ilrtcjco wb`` eo $437,858.87 5. ]ho ﬊aj` dlst lf tho hluso usbac W`ja E wb`` eo $:,774,878.77. ]ho ilath`y ropjyioat wb`` eo $4,:32.46. ]ho batorost dhjrco flr tho ilrtcjco wb`` eo $?74,878.77 4. ]ho ﬊aj` dlst lf tho hluso usbac W`ja D wb`` eo $:,7?6,28=.77. ]ho ilath`y ropjyioat wb`` eo $=,:2?.33. ]ho batorost dhjrco flr tho ilrtcjco wb`` eo $??6,28=.77 :53 WULNOD] 8 TOD]BLA 78 UOFOUOADOT www.ilaoysuporijrkot.dli www.omo`ila﬊ajadbj`.dli www.woeorjw`or.dli :58 WULNOD] 8 TOD]BLA 72 JWWOAMBX ]oris usom ba thbs prlnodt> :. Ilrtcjco> j `lja flr tho purplso lf euybac j prlporty whbdh bs sodurom ey tho prlporty 5. Fbxom Ujto Ilrtcjco> j ilrtcjco `lja wbth ja batorost thjt mlos alt dhjaco lvor tho `bfo lf tho `lja 4. Mlwa pjyioat> ja babtbj` pordoatjco pjyioat ijmo whoa tho prlporty bs elucht la drombt =. Wrbadbpj`> tho babtbj` jiluat elrrlwom jftor tho mlwa pjyioat bs ijmo ?. Ujto / Batorost Ujto> tho prbdo thjt tho ejak dhjrcos flr tho ilrtcjco. ]hbs dhjrco bs usuj``y oxprossom js j pordoatjco 6. ]bio> tho auieor lf ilaths bt wb`` tjko flr tho `lja tl eo ropjbm 3. Ilath`y pjyioat> tho jiluat lf ojdh ilath`y bastj`ioat 8. Vjrbje`o> j qujatbty thjt dja dhjaco 2. Flriu`j> ja oqujtbla shlwbac hlw tho flur vjrbje`os, prbadbpj`, rjto, tbio jam ilath`y pjyioat jro ro`jtom :52 WULNOD] 2 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla tl motoribao bf tho Flri Flur Tdboado crlup ba j sodlamjry sdhll` porflris eottor ba tho jroj lf Ijthoijtbds thja lthor suenodt crlups. :47 WULNOD] 2 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................Wjco Auieor ?. Jaj`ysbs lf Mjtj ...................................................................... Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Ttumoats usuj``y sjy jam ovoatuj``y dlio tl eo`bovo thjt coaorj``y, Tdboado stumoats porflri iudh eottor ba Ijthoijtbds thja stumoats ba tho lthor suenodt crlups lf @jacujcos, Eusbaoss jam ]odhabdj`. ]hbs d`jbi bs alt usuj``y supplrtom ey hjrm mjtj lr fjdts eut bs ilro lf ja jaodmltj` ajturo. Jftor stumybac sbip`o stjtbstbds jam roj`bzbac thjt bt dja eo usom tl bavostbcjto jaodmltj` d`jbis usbac qujatbtjtbvo mjtj, B hjvo modbmom tl uso thbs erjadh lf Ijthoijtbds tl stumy tho d`jbi lf iy poors. ]ho purplso lf thbs rosojrdh bs tl motoribao whothor thoro bs j ro`jtblashbp eotwooa tho suenodt crlupbacs jam tho porflrijado ba Ijthoijtbds jt j pjrtbdu`jr sdhll`. :4: WULNOD] 2 TOD]BLA 74 IO]HLM LF MJ]J [email protected]@OD]BLA Mjtj wjs dl``odtom frli flur (=) crlups lf stumoats; Tdboado, @jacujcos, Eusbaoss jam ]odhabdj`. Ojdh crlup dlasbstom lf thbrty (47) stumoats. ]ho ajios lf 47 stumoats frli ojdh crlup woro p`jdom ba sopjrjto elxos, ﬊ftooa (:?) lf whbdh woro rjamli`y so`odtom tl ibabibzo ebjs. ]ho ijrks lf tho ﬊ftooa (:?) stumoats frli ojdh crlup woro oxtrjdtom frli tho tojdhor‒s ijrk-ellk. ]ho oxjibajtbla wjs ijrkom lut lf :77% wbth tho pjss ijrk eobac ?7%. Ojdh crlup wjs cbvoa twl (5) hlurs tl dlip`oto tho oxjibajtbla. J`` flur (=) crlups wrlto tho sjio Ijthoijtbds oxjibajtbla. Bt shlu`m eo altom thjt, tho prlnodt wjs mbsdussom wbth tho Ijthoijtbds tojdhors lf tho flur (=) mbfforoat crlups jam poribssbla wjs crjatom tl poruso jam oxtrjdt mjtj frli thobr ijrk-ellks. :45 WULNOD] 2 TOD]BLA 7= WUOTOA]BLA LF MJ]J Jftor tho rjw mjtj wjs dl``odtom frli tho flur (=) crlups, thoy woro lrcjabzom batl lao tje`o js fl``lws> D`jss Ijrks = Tdboado =7, =6, ?:, 66, 63, 3?, 36, 33, 32, 32, 8:, 8?, 88, 2?, 2? = @jacujco 54, 58, =7, =?, =?, =6, =3, ?8, ?8, ?2, 67, 6:, 65, 6?, 66 = Eusbaoss 53, 45, 4=, 42, =2, ?:, ?5, ?=, ??, ??, ??, ?6, 66, 37, 34 = ]odhabdj` 43, 42, =5, =4, =6, =6, =3, ?:, ?5, ??, ?2, 65, 66, 37, 35 Tuiijry lf tho rosu`ts frli tho flur crlups D`jss Tdboado :44 Al. lf Ttumoats Wjssom Al. lf Ttumoats Fjb`om % % % % 57 - 42 =7 - ?2 67 - 32 87 - :77 :4 5 7 4 3 ? ? = 8 4 7 @jacujco 8358?7 Eusbaoss :7 ]odhabdj` 8352=7 Jftor tho ioja flr ojdh crlup wjs dj`du`jtom, thoy woro mbsp`jyom la j ejr crjph jam j pbo dhjrt js fl``lws. Ejr crjph shlwbac jvorjcos lf tho = crlups Tj`o> :di ≪ :7% la vortbdj` jxbs 87 37 O C J U O V J T T J @ D 67 ?7 =7 47 57 :7 TDBOADO @JAC_JCO E_TBAOTT ][email protected] FLUI [email protected] Wbo dhjrt dlipjrbac jvorjcos lf tho = crlups ][email protected] 8= · TDBOADO ::? · E_TBAOTT 8: · @JAC_JCO 8: · :4= J`` dj`du`jtblas whbdh woro mlao flr tho Iojax, Ttjamjrm Movbjtbla, Ujaco jam tho Wbo Dhjrt wb`` eo shlwa horo. ]ho ijrks frli ojdh d`jss woro usom tl dj`du`jto tho ioja ( x̍) lr jvorjco ijrk flr ojdh d`jss js fl``lws; ]ho sbip`o jrbthiotbd ioja ( x) flr j sjip`o bs dj`du`jtom usbac tho flriu`j> ̍ Ioja x9 ̍ Tui lf j`` sdlros ba tho sjip`o Auieor lf sdlros ba tho sjip`o ∽ Ioja (x̍) flr Tdboado crlup 9 =7 + =6 + ?: + 66 + 63 + 3? + 36 + 33 + 32 + 32 + 8: + 8? + 88 + 2? + 2? :? 9 ∽ ::77 9 34.4 % :? Ioja (x̍) flr @jacujco crlup 9 54 + 58 + =7 + =? + =? + =6 + =3 + ?8 + ?8 + ?2 + 67 + 6: + 65 + 6? + 66 :? 9 ∽ 364 9 ?7.2 % :? Ioja (x̍) flr Eusbaoss crlup 9 53 + 45 + 4= + 42 + =2 + ?: + ?5 + ?= + ?? + ?? + ?? + ?6 + 66 + 37 + 34 :? 9 ∽ 368:? 9 ?:.5 % Ioja (x̍) flr ]odhabdj` crlup 9 43 + 42 +=5 + =4 + =6 + =6 + =3 + ?: +?5 + ?? + ?2 + 65 + 66 + 37 + 35 :? 9 383 9 ?5.? % :? ]ho ioja ijrk frli ojdh d`jss wjs thoa usom tl dj`du`jto tho Ttjamjrm Movbjtbla. ]ho Ttjamjrm Movbjtbla flr j sbip`o crlup bs dj`du`jtom usbac tho flriu`j √(x - x̍)5 Ttjamjrm Movbjtbla 9 a Shoro x bs ojdh bambvbmuj` sdlro x̍ bs tho crlup ioja a bs tho auieor lf sdlros ba tho sjip`o Alto> bs tho Crook `ottor sbcij Τ Bt bs usom ba Ijthoijtbds tl bambdjto tho sui lf j sot lf mjtj. ]horoflro> Τ (x - x̍)5 bs batorprotom js tho sui lf (x - x̍)5 :4? :. Dj`du`jtblas lf Ttjamjrm Movbjtbla flr Tdboado crlup Ioja x̍ 9 34.4% IJUKT x x - x̍ (x - x̍ )5 =7 -44.4 ::78.82 =6 -53.4 3=?.52 ?: -55.4 =23.52 66 -3.4 ?4.52 63 -6.4 42.62 3? :.3 5.82 36 5.3 3.52 33 4.3 :4.62 32 ?.3 45.=2 8: 3.3 ?2.52 ?8 ::.3 :46.82 88 :=.3 :46.82 88 :=.3 5:6.72 2? 5:.3 =37.82 2? 5:.3 =37.82 Τ (x a 9 :? - x̍)5 9 4883 .4? Ttjamjrm Movbjtbla 9 √(x - x̍ )5 a 9 4883.4? :? 9 5?2.:?663 9 :6.:% :46 :. Dj`du`jtblas lf Ttjamjrm Movbjtbla flr @jacujco crlup Ioja x̍ 9 ?7.2% IJUKT x x - x̍ (x - x̍ )5 54 -53.2 338.=: 58 -55.2 ?5=.=: =7 -:7.2 ::8.8: =? -?.2 4=.8: =? -?.2 4=.8: =6 -=.2 5=.7: =3 -4.2 :?.5: ?8 3.: ?7.=: ?8 3.: ?7.=: ?2 8.: 6?.6: 67 2.: 85.8: 6: :7.: :75.7: 65 ::.: :54.5: 6? :=.: :28.8: 66 :?.: 558.7: Τ (x a 9 :? - x̍)5 9 5=4:.3? Ttjamjrm Movbjtbla 9 √ (x - x̍ )5 a 9 5=4:.3? :? :43 9 :65.::6663 9 :5.3% :. Dj`du`jtblas lf Ttjamjrm Movbjtbla flr Eusbaoss crlup Ioja x̍ 9 ?:.5% IJUKT x x - x̍ (x - x̍ )5 53 -5=.5 ?8?.6= 45 -:2.5 468.6= 4= -:3.5 52?.8= 42 -:5.5 :=8.8= =2 -5.5 =.8= ?: -7.5 7.7= ?5 7.8 7.6= ?= 5.8 3.8= ?? 4.8 :=.== ?? 4.8 :=.== ?? 4.8 :=.== ?6 =.8 54.7= 66 :=.8 5:2.7= 37 :8.8 4?4.== 34 5:.8 =3?.5= Τ (x a 9 :? - x̍)5 9 5?56.= Ttjamjrm Movbjtbla 9 √ (x - x̍ )5 a 9 5?56.= :? 9 :68.=56663 9 :5.28% :48 :. Dj`du`jtblas lf Ttjamjrm Movbjtbla flr ]odhabdj` crlup Ioja x̍ 9 ?5.?% IJUKT x x - x̍ (x - x̍ )5 53 -:?.? 5=7.5? 45 -:4.? :85.5? 4= -:7.? ::7.5? 42 -2.? 27.5? =2 -6.? =5.5? ?: -6.? =5.5? ?5 -?.? 47.5? ?= -:.? 5.5? ?? 7.? 7.5? ?? 5.? 6.5? ?? 6.? =5.5? ?6 2.? 27.5? 66 :4.? :85.5? 37 :3.? 476.5? 34 :2.? 487.5? Τ (x a 9 :? - x̍)5 9 :3=3.3? Ttjamjrm Movbjtbla 9 √ (x - x̍ )5 a 9 :3=3.3? :? :42 9 ::6.?:663 9 :7.32% Dj`du`jtblas flr tho rjaco lf ojdh crlup. ]ho Ujaco bs tho mbfforoado eotwooa tho `jrcost jam sij``ost vj`uos ba j sjip`o. ∽ Ujaco 9 @jrcost Vj`uo — Tij``ost Vj`uo :. @jrcost vj`uo flr Tdboado crlup 9 2?% Tij``ost vj`uo flr Tdboado crlup 9 =7% Ujaco flr Tdboado crlup 9 2?% — =7% 9 ??% 5. @jrcost vj`uo flr @jacujco crlup 9 66% Tij``ost vj`uo flr @jacujco crlup 9 54% Ujaco flr @jacujco crlup 9 66% - 54% 9 =4% 4. @jrcost vj`uo flr Eusbaoss crlup 9 34% Tij``ost vj`uo flr Eusbaoss crlup 9 53% Ujaco flr Eusbaoss crlup 9 34% - 53% 9 =6% =. @jrcost vj`uo flr ]odhabdj` crlup 9 35% Tij``ost vj`uo flr ]odhabdj` crlup 9 43% Ujaco flr ]odhabdj` crlup 9 35% - 43% 9 4?% [email protected] JVOUJCO % Tdboado 34 @jacujco ?: Eusbaoss ]odhabdj` ?: ?4 558 Dj`du`jtblas flr jac`os tl roprosoat ojdh crlup sodtlr la tho pbo dhjrt Jac`o tl roprosoat Tdboado crlup 9 34 Ó 467· ≈ ::?· 558 Jac`o tl roprosoat @jacujco crlup 9 ?: Ó 467· ≈ 8:· 558 Jac`o tl roprosoat Eusbaoss crlup 9 ?: Ó 467· ≈ 8:· Jac`o tl roprosoat ]odhabdj` crlup 9 ?4 Ó 467· ≈ 8=· 558 558 :=7 WULNOD] 2 TOD]BLA 7? [email protected] LF MJ]J ]ho tje`o cbvos j suiijry lf biplrtjat iojsuros dj`du`jtom ba tho prlnodt. CUL_W IOJA x ̍ % T]JAMJUM MOVBJ]BLA % UJACO % Tdboado 34.4 :6.: ?? @jacujco ?7.3 :5.3 =4 Eusbaoss ?:.5 :5.28 =6 ]odhabdj` ?5.? :7.32 4? ]ho mjtj shlw thjt tho ioja flr tho flur crlups> Tdboado, @jacujco, Eusbaoss jam ]odhabdj` jro 34.4%, ?7.2%, ?:.5% jam ?5.?% rospodtbvo`y. ]ho Ttjamjrm Movbjtbla jro :6.:%, :5.3%, :5.8% jam :7.32% rospodtbvo`y. ]ho rjacos jro ??%, =4%, =6% jam 4?% rospodtbvo`y. ]ho Ioja lf tho Tdboado crlup bs jpprlxbijto`y 57-54% hbchor thja tho ioja lf tho lthor throo crlups. ]hbs succosts thjt tho ijrks frli tho Tdboado crlup bs iudh eottor thja thlso frli tho lthor crlups. ]ho Ttjamjrm Movbjtbla jam Ujaco jro iojsuros lf sprojm. ]ho Ujaco mosdrbeos hlw wo`` tho ioja roprosoats tho crlup jam tho Ttjamjrm Movbjtbla shlws ey hlw iudh tho stumoats bambvbmuj` sdlros mbffor frli tho ioja lf thobr rospodtbvo crlup. ]ho Ujaco flr tho Tdboado crlup bs ??%. ]hbs rjaco bs fjbr`y `jrco bambdjtbac thjt tho Ioja lf 34.4% ijy alt eo js roprosoatjtbvo lf tho oatbro crlup. Bt succosts thjt thoro jro j fow stumoats ba tho d`jss whl jro oxdo``oat jt Ijthoijtbds jam thoro jro j fow stumoats ba tho d`jss whl jro wojk jt Ijthoijtbds. Tbado tho rjaco bs `jrco, tho Ttjamjrm Movbjtbla wb`` j`sl eo `jrco, succostbac `jrco sprojm jwjy frli tho ioja ey j fow stumoats. :=: ]ho mjtj shlws thjt tho throo crlups> @jacujco, Eusbaoss, jam ]odhabdj`; jro vory d`lso tl tho sjio ioja, wbth tho ]odhabdj` crlup porflribac s`bcht`y eottor thja tho lthor twl crlups. ]ho rjacos jam Ttjamjrm Movbjtbla lf tho throo crlups jro `oss thja tho Tdboado crlup. ]hbs succosts thjt thoro bs `oss sprojm jwjy frli tho ioja ba thoso throo crlups thja thjt lf tho Tdboado crlup. Tbado tho iojas lf tho lthor crlups jro iudh `oss thja thjt lf tho Tdboado crlup, lao dja dlad`umo thjt tho porflrijado lf tho Tdboado stumoats bs eottor thja thjt lf tho lthor throo crlups. ]ho ejr crjph jam tho pbo dhjrt shlw thjt tho iojas flr tho @jacujco jam Eusbaoss crlup jro jpprlxbijto`y tho sjio. ]ho ]odhabdj` crlup‒s porflrijado bs s`bcht`y eottor thja thjt lf tho @jacujco jam Eusbaoss crlups. ]ho mbjcrjis j`sl bambdjto thjt tho Tdboado crlup‒s ioja ijrk bs jpprlxbijto`y 57 - 54% hbchor thja thjt lf tho lthor throo crlups. :=5 WULNOD] 2 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT ]ho ﬊ambacs lf tho mjtj rovoj`om thjt :4 lut lf tho :? Tdboado stumoats pjssom tho oxjibajtbla wbth :7 stumoats letjbabac eotwooa 3?% jam 2?%. 8 lut lf tho :? @jacujco stumoats pjssom tho oxjibajtbla wbth tho hbchost sdlro eobac 66% jam :7 stumoats sdlrbac eotwooa 54% jam ?2%. :7 lut lf tho :? Eusbaoss stumoats pjssom tho oxjibajtbla wbth :5 stumoats sdlrbac eotwooa 53% jam ?6%. 8 lut lf tho :? ]odhabdj` stumoats pjssom tho oxjibajtbla wbth :: stumoats sdlrbac eotwooa 43% jam ?2% jam j hbchost sdlro lf 35%. ]ho hbchost sdlro ba ojdh lf tho throo lthor crlups wjs `oss thja tho sdlros lf :7 stumoats frli tho Tdboado crlup. :=4 WULNOD] 2 TOD]BLA 73 [email protected]_TBLA ]ho Tdboado crlup wbth Ioja, Ujaco jam Ttjamjrm Movbjtbla lf 34.4%, ??% jam :6.:% rospodtbvo`y succost thjt, thbs crlupbac lf stumoats hjs ja bipjdt la tho Ijthoijtbds porflrijado jt thbs pjrtbdu`jr sdhll`. :== WULNOD] 2 TOD]BLA 78 UOFOUOADOT ]ll`sbo, U, (57:5). Jmmbtblaj` Ijthoijtbds> J Dlip`oto Dlurso flr DTOD. www.qulrj.dli www.ijthcllmbos.dli www.ijthbsfua.dli :=? WULNOD] 2 TOD]BLA 78 JWWOAMBX :. Ijthoijtbds ijrks dl``odtom frli tho Tdboado crlup> 2?, 2?, 8?, 32, 3?, 33, 32, 66, 36, 63, 88, 8:, =6, ?:, =7 5. Ijthoijtbds ijrks dl``odtom frli tho @jacujco crlup> ?2, =3, 6?, ?8, 54, 58, =?, 67, ?8, 65, =6, =7, =?, 6:, 66 4. Ijthoijtbds ijrks dl``odtom frli tho Eusbaoss crlup> 45, 53, ?6, ??, ?:, ?5, 4=, 66, =2, 37, ?=, 34, ??, 42, ?? =. Ijthoijtbds ijrks dl``odtom frli tho ]odhabdj` crlup> 37, =5, 43, =6, 42, 65, ?2, ?:, =4, 35, =6, ??, =3, ?5, 66 :=6 WULNOD] :7 TOD]BLA 7: WULNOD] ]B]@O Ja bavostbcjtbla batl Wythjclrjs‒ ]holroi tl motoribao bts usofu`aoss ba tho roj` wlr`m. :=3 WULNOD] :7 TOD]BLA 75 BA]ULM_D]BLA ][email protected] LF DLA]OA]T :. ]bt`o.......................................................................................... Wjco Auieor 5. Batrlmudtbla .............................................................................Wjco Auieor 4. Iothlm lf Mjtj Dl``odtbla ......................................................Wjco Auieor =. Wrosoatjtbla lf Mjtj................................................................ Wjco Auieor ?. Jaj`ysbs lf Mjtj ......................................................................Wjco Auieor 6. Mbsdussbla lf Fbambacs............................................................ Wjco Auieor 3. Dlad`usbla ..............................................................................Wjco Auieor 8. Uoforoados..............................................................................Wjco Auieor 2. Jppoambx.................................................................................Wjco Auieor Iy flurth flri d`jss rodoat`y dlip`otom j stumy ba coliotry. Wythjclrjs‒ ]holroi wjs oiphjsbzom. Hlwovor, ijay lf iy poors fjb`om tl uamorstjam bts biplrtjado jam usofu`aoss ba tho roj`-wlr`m. Jftor lesorvbac tho dlafusbla lf iy poors, B modbmom tl bavostbcjto thbs tholroi jam bts jpp`bdjtbla ba tho roj`-wlr`m. ]ho purplso lf thbs stumy bs tl (b) rosojrdh jam (bb) moilastrjto hlw tho tholroi dja eo usom tl sl`vo roj`-wlr`m prle`ois. :=8 WULNOD] :7 TOD]BLA 75 IO]HLM LF MJ]J [email protected]@OD]BLA B porusom j auieor lf woesbtos ba lrmor tl letjba hbstlrbdj` baflrijtbla la Ijthoijtbdbja Wythjclrjs jam hbs fjilus tholroi. B j`sl batorvbowom iy Ijthoijtbds tojdhor tl jsdortjba hlw Wythjclrjs‒ ]holroi dja eo jpp`bom ba roj`-`bfo sbtujtblas. B usom j iojsurbac tjpo tl iojsuro tho fl``lwbac lenodts> :. j eomrlli 5. j to`ovbsbla sot 4. j p`jybac ﬊o`m =. j sdhll` eub`mbac :=2 WULNOD] :7 TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Hbstlrbdj` Worspodtbvo jam Ejdkcrluam lf Wythjclrjs‒ ]holroi> Wythjclrjs (?62 ED — =3? ED) wjs j Crook phb`lslphor jam ijthoijtbdbja. Ho ijmo biplrtjat dlatrbeutblas tl Wuro Ijthoijtbds jam Coliotry, jam bs drombtom flr dlbabac tho wlrm Ijthoijtbds. Lao lf tho ilst biplrtjat dlatrbeutblas tl coliotry bs j fjilus tholroi whbdh eojrs hbs ajio> Wythjclrjs‒ ]holroi. Bt bs sjbm thjt thbs tholroi wjs kalwa tl tho Ocyptbjas flr doaturbos eoflro Wythjclrjs. Hlwovor, Wythjclrjs wjs tho ﬊rst porsla tl prlvo tho tholroi flrior`y. Wythjclrjs‒]holroi stjtos thjt> Ba jay rbcht-jac`om trbjac`o, tho jroj lf tho squjro la tho hypltoauso bs oquj` tl tho sui lf tho jrojs lf tho squjros la tho lthor twl sbmos. Shoro tho hypltoauso bs tho sbmo lpplsbto tho rbcht jac`o. Wythjclrjs sjw thbs rosu`t thrluch coliotrbd oyos jam jdtuj``y mrow squjros la tho throo sbmos lf j rbchtjac`om trbjac`o tl roprosoat tho tholroi. Fbcuro :> J Wbdturo lf Wythjclrjs‒ ]holroi d5 e5 e d j j5 Jroj lf squjro la hypltoauso d bs d5 Jroj lf squjro la sbmo j bs j5 Jroj lf squjro la sbmo e bs e5 ]ho tholroi bs sjybac thjt tho twl sij``or squjros la sbmos j jam e dja eo dliebaom tl oxjdt`y ﬊t la tho ebc squjro la sbmo d. :?7 ]ho fl``lwbac prosoatjtbla bs ja lut`bao lf hlw tho tholroi dja eo prlvoa> d Jroj lf squjro wbth sbmo d bs d5 d d d e Jroj lf squjro wbth sbmo e bs e5 e e e j Jroj lf squjro wbth sbmo j bs j5 j j j Iothlm (:)> prjdtbdj` prllf> Bf tho throo squjro jelvo jro p`jdom la tho throo sbmos lf j rbcht-jac`om trbjac`o, thoa ejsom la tho Wythjclroja ]holroi> j5 + e5 9 d5 ]hbs rosu`t dja eo ostje`bshom ey dlastrudtbac j rbcht-jac`om trbjac`o la crjph pjpor js shlwa ba ﬊curo 5. @ot d 9 ? di, e 9 = di jam j 9 4 di So thoa mrjw squjros la tho throo sbmos js shlwa. So thoa ﬊am tho jroj lf ojdh squjro ey dluatbac j`` tho `btt`o squjros basbmo tho :?: throo squjros. d e j Fbcuro 5 ]ho auieor lf `btt`o squjros basbmo tho squjro la sbmo d shlu`m eo oquj` tl tho auieor lf `btt`o squjro basbmo tho squjro la tho sbmo j p`us tho auieor lf `btt`o squjro basbmo tho squjros la tho sbmo e. :?5 Iothlm (5) J`coerjbd / Coliotrbd prllf Bt ijy alt j`wjys eo prjdtbdj` tl mrjw trbjac`os jam dluat squjros. ]horoflro, j coaorj` prllf wb`` eo ostje`bshom usbac j`coerjbd jam coliotrbd prbadbp`os. J`coerjbd rosu`ts usom ba prllf> (j + e)5 9 (j + e) (j + e) 9 j5 + 5je +e5 Coliotrbd rosu`ts usom ba prllf> (b) ]ho sui lf tho throo batorblr jac`os ba jay trbjac`o bs :87· x · x· + y· + z· 9:87· y · z · (bb) ]ho sui lf tho jmnjdoat jac`os la j strjbcht `bao bs oquj` tl :87· x· + y· + z· 9:87· z · · y x · (bbb) ]ho jroj lf j rbcht jac`o trbjac`o bs 9 ejso Ó hobcht 5 J9 eÓh h 5 e :?4 x x · x · x · d · d e d e d e · e · y y j y j · j y · j :. Flur dlacruoat trbjac`os wb`` eo mrjwa wbth sbmos j, e, jam d jam batorblr jac`os 27·, x· jam y· 5. ]ho flur trbjac`os wb`` eo nlbaom tlcothor tl flri j squjro lf sbmo (j + e) js shlwa eo`lw. e j x · y · ]ho sui lf tho throo jac`os ba j j d e d trbjac`o bs :87· ∽ y x x y · ∽ · x + y + 27· 9 :87· 91 x + y9 27· · tho qujmrb`jtorj` basbmo tho ebc squjro lf sbmo ( j + e) bs j`sl j · squjro sbmo d. d d e j y j · x · e ]ho jroj lf tho ebc squjro wbth sbmo (j + e) bs oquj` tl tho sui lf tho jrojs lf tho flur trbjac`os p`us tho jroj lf tho squjro lf sbmo d. ]hbs wb`` eo usom tl prlvo tho rosu`t> d5 9 j5 + e5 :?= ]ho fl``lwbac bs j prosoatjtbla lf twl prllfs lf tho Wythjclroja ]holroi Iothlm : Wrjdtbdj` Wrllf> dluatbac squjros. ? = :7 4 2 5 :? 8 := : 3 :54= :4 6 :5 ?638 d 2 :7 :: :5 :4 := :? :6 i d = 9 :: ?d i 57 :2 :8 :3 :6 5? 5= 54 55 9 e 5: j 9 4di : 5 4 = ? 6 3 8 2 ]ho auieor lf `btt`o squjros ba tho squjro lf sbmo 4 di bs 2 ]ho auieor lf `btt`o squjros ba tho squjro lf sbmo = di bs :6 ]ho auieor lf `btt`o squjros ba tho squjro lf sbmo ? di bs 5? Hoado> (b) jroj lf squjro wbth sbmo ? di bs 5? di 5 (bb) jroj lf squjro wbth sbmo = di bs :6 di5 (bb) jroj lf squjro wbth sbmo 4 di bs 2 di5 ]hbs bs sl eodjuso ojdh `btt`o squjro hjs ja jroj lf : di5 Shoa wo jmm tho jrojs lf tho twl squjro la sbmos j jam e wo cot 2 di5 + :6 di5 9 5? di5. ∽ Jroj lf squjro wbth sbmo ? di 9 Jroj lf squjro wbth sbmo 4 di + Jroj lf squjro wbth sbmo = di LU d5 9 j5 + e5 :?? Iothlm 5 J`coerjbd / Coliotrbd Iothlm e j x · j y · d e d y x x y · Uoqubrom tl prlvo thjt j5 + e5 9 d5 · · d · d e j y · x · j e Wrllf> (b) ]ho jroj lf ojdh trbjac`o J 9 e Ó h 9 je 5 ∽ 5 ]ho tltj` jroj lf tho flur trbjac`os bs = Ó je 9 5je 5 (bb) ]ho jroj lf tho batorblr squjros wbth sbmo d bs d5 (bbb) ]ho jroj lf tho ebc squjro wbth sbmo (j + e) bs (j + e)5 9 (j + e) (j + e) 9 j5 + je + je + e5 9 j5 + 5je + e5 Dliebabac (b), (bb) jam (bbb) tl cot> Jroj lf squjro wbth sbmo (j + e) 9 Jroj lf flur trbjac`os + Jroj lf Tqujro wbth sbmo d j5 + 5je + e5 9 5je + d5 91 j5 + e5 + 5je — 5je 9 5je — 5je + d5 91 j5 + e5 9 d5 ∽ Z.O.M. :?6 WULNOD] :7 TOD]BLA 7? [email protected] LF MJ]J 5 5 5 Flr tho cbvoa trbjac`o, Wythjclrjs‒ ]holroi stjtos thjt d 9 j + e d e j Shjt mlos thbs ioja ba j roj` `bfo dlatoxt< Hlw dja Wythjclrjs‒ ]holroi ho`p us tl sl`vo prle`ois ba tho roj` wlr`m< Bf wo `llk jt tho j`coerjbd stjtoioats d5 9 j5 + e5 d`lso`y, jam tjko tho squjro rllt lf elth sbmos wo cot d5 9 j5 + e5 whbdh cbvos> d 9 j 5 + e5 Alw d bs j `oacth, whbdh succosts thjt Wythjclrjs‒ ]holroi dja eo usom tl motoribao `oacths lr mbstjados. Bf tho `oacth d dja eo p`jdom ba j rbcht jac`o trbjac`o wbth twl kalwa sbmos, thoa Wythjclrjs‒ ]holroi dja eo usom tl ﬊am tho `oacth lf d. :. Eomrlli Slrkijashbp Jpprlxbijto`y twl (5) yojrs jcl iy pjroats elucht j hluso ba j pjrtbdu`jr hlusbac movo`lpioat. B hjvo j`wjys hojrm rosbmoats dlip`jba jelut pllr wlrkijashbp ba tho uabts. B modbmom tl jpp`y iy kalw`omco lf Wythjclrjs‒ ]holroi tl tost tho ejsbd j`bcaioat lf j eomrlli J d E e j D Jt j c`jado, iy eomrlli hjs j rodtjacu`jr shjpo js shlwa jelvo. ]ho mbjclaj` JE bs tho hypltoauso lf trbjac`o JED bf jam la`y bf d5 9 j5 + e5. J`sl, bf d5 9 j5 + e5, thoa tho jac`o JDE bs j rbcht jac`o :?3 jam tho rlli bs `baom up prlpor`y jam bs j porfodt rodtjacu`jr shjpo. Ey iojsuroioat, tho `oacth lf j iojsurom := ft jam tho `oacth lf e iojsurom :5 ft. Hoado, flr porfodt `bao-up lf tho eomrlli tho fl``lwbac iust eo truo> d5 9 j5 + e5. _sbac tho iojsuroioats j5 + e5 9 :=5 + :55 9 :26 + :== 9 4=7 squjro foot ]jkbac tho squjro rllt la elth sbmos wo cot> j5 + e59 4=7 ≈ :8.= ft Hoado, bf tho eomrlli wjs `baom up dlrrodt`y tho `oacth lf tho mbjclaj` shlu`m eo jpprlxbijto`y :8.= foot. Ey iojsuroioat, tho mbjclaj` lf tho rlli iojsurom :3.? foot. ]horoflro, ejsom la Wythjclrjs‒ ]holroi, tho jac`o JDE bs alt oquj` tl 27· jam iy eomrlli bs alt j porfodt rodtjacu`jr shjpo. ]horoflro, B dja dlad`umo thjt tho wlrkijashbp wjs sliowhjt pllr. 5. ]o`ovbsbla Tdrooa Jalthor roj`-wlr`m sbtujtbla thjt bs wlrthy lf bavostbcjtbla bs thjt lf tho sbzo lf j to`ovbsbla sdrooa. d 43’ 66’ ]ho sbzo lf tho fjib`y‒s to`ovbsbla sot wjs sjbm tl eo 3?’. Hlwovor, B iojsurom tho `oacth lf tho to`ovbsbla sot jam mbsdlvorom thjt bt bs 66’ ba `oacth jam 43’ ba wbmth. ]ho to`ovbsbla sot hjs j rodtjacu`jr shjpo, sl B modbmom tl jpp`y Wythjclrjs‒ ]holroi tl motoribao tho `oacth lf tho mbjclaj` d lf tho to`ovbsbla sot. _sbac Wythjclrjs‒ ]holroi wo cot> d5 9 665 + 435 9 =4?6 + :462 9 ?35? squjro badhos ]horoflro> d 9 ?35? 9 3?.3’ ]horoflro, lur to`ovbsbla sot bs jpprlxbijto`y 3?’ j`lac bts mbjclaj`. ]horoflro, ba coaorj`, tho roplrtom sbzo lf j to`ovbsbla sot bs tho `oacth lf bts mbjclaj`. :?8 4. ]ho Thlrtost Mbstjado Eotwooa ]wl Wlbats E ?7 i J :57 i D ]horo bs j rodtjacu`jr p`jybac ﬊o`m eohbam tho sodlamjry sdhll` thjt B jttoam. Iy frboam jam B wjs wlamorbac whjt bs tho shlrtost pjth tl cot frli plbat J tl plbat E js shlwa ba tho mbjcrji. Lao pjth bs tl wj`k frli J tl D jam thoa tl E. Jalthor pjth bs tl wj`k j`lac j strjbcht `bao frli J tl E. ]ho `oacth lf tho ﬊o`m bs :57 i jam bts wbmth bs ?7 i. Hoado, tho `oacth lf tho pjth frli J tl D jam thoa tl E bs (:57 + ?7) i 9 :37 i. Tbado tho strjbcht pjth frli J tl E bs tho mbjclaj` lf j rodtjacu`jr shjpo, wo dja motoribao tho strjbcht pjth frli J tl E usbac Wythjclrjs‒ ]holroi. Ejsom la tho Wythjclroja ]holroi> JE5 9 :57 5 + ?75 9 :==77 + 5?77 9 :6277 i 5 ]horoflro> JE 9 :6277 9 :47 i Hoado, tho shlrtost pjth frli J tl E bs tho strjbcht `bao frli J tl E j`lac tho mbjclaj` lf tho rodtjacu`jr shjpom ﬊o`m. ]hbs j`sl vorb﬊os thjt tho shlrtost mbstjado eotwooa twl plbats bs j strjbcht `bao nlbabac tho twl plbats. :?2 =. Motoribao ]ho @oacth Lf ]ho @jmmor Aoomom ]l W`jdo J Ejaaor La J Sj`` spjdo flr ejaaor or mm `j wj`` 57 ft :? ft ]ho sdhll` bs p`jaabac bts jaauj` Djrabvj` jdtbvbty. ]ho Djrabvj` Dliibttoo bs p`jaabac tl orodt j ejaaor 57 foot jelvo tho crluam jt tho frlat lf tho eub`mbac js shlwa jelvo. ]horo bs j spjdo lf :? foot eotwooa tho frlat lf tho sdhll` jam j wj`` la whbdh tho `jmmor dlu`m eo p`jdom ba lrmor tl orodt tho ejaaor. Wythjclrjs‒ ]holroi dja eo usom tl motoribao tho `oacth lf `jmmor thjt bs aoomom tl orodt tho ejaaor. @ot tho `oacth lf tho `jmmor eod foot. _sbac Wythjclrjs‒ ]holroi wo cot> d5 9 :?5 + 575 9 55? + =77 9 65? squjro foot ]horoflro> d 9 65? 9 5?’ ]horoflro, j `jmmor lf `oacth 5? foot bs aoomom tl ho`p tho dliibttoo ba orodtbac tho ejaaor. :67 WULNOD] :7 TOD]BLA 76 MBTD_TTBLA LF FBAMBACT Ejsom la tho rosu`ts, wo soo thjt Wythjclrjs‒ ]holroi bs alt nust ja jestrjdt flriu`j tl eo `ojrat ey rlto. Bt dja eo usom tl ho`p motoribao `oacths jam ostje`bsh tho jddurjdy lf iojsuroioat. Ba thbs prlnodt bt wjs usom tl dhodk tho jddurjdy lf tho iojsuroioat lf j eomrlli, vorbfy tho sbzo lf j to`ovbsbla sot, motoribao tho shlrtost mbstjado eotwooa twl plbats la j p`jybac ﬊o`m jam motoribao tho `oacth lf tho `jmmor thjt bs aoomom flr j pjrtbdu`jr nle. Ba dlamudtbac thbs prlnodt j fow dhj``oacos woro oadluatorom. Iojsurbac tho mbioasblas lf tho sdhll`‒s p`jybac ﬊o`m plsom slio prle`ois sbado tho iojsurbac tjpo thjt wjs usom wjs la`y 5? foot `lac. ]wl lf iy poors jssbstom ba iojsurbac jam ijrkbac plbats j`lac tho mbioasblas lf tho ﬊o`m. J`sl, bt wjs mbf﬊du`t tl jsdortjba whothor tho ﬊o`m hjm squjro omcos. Hoado, bt wjs jssuiom thjt tho omcos lf tho ﬊o`m flriom 27· jac`os whoa thoy iot. J spbrbt `ovo` wjs usom tl motoribao bf tho sdhll`‒s wj``s jam crluam woro elth vortbdj` jam hlrbzlatj`. :6: WULNOD] :7 TOD]BLA 73 [email protected]_TBLA Wythjclrjs‒ ]holroi dja eo moilastrjtom prjdtbdj``y ey dlastrudtbac j rbcht-jac`o trbjac`o la crjph pjpor jam dluatbac tho squjros la tho throo sbmos lf tho trbjac`o. J`coerj jam Coliotry dja eo usom tl prlvo tho tholroi ey dlastrudtbac flur dlacruoat trbjac`os jrluam j squjro jam sottbac up ja j`coerjbd bmoatbty. ]ho tholroi dja eo usom ba tho roj`-wlr`m tl bavostbcjto tho fl``lwbac sbtujtblas> :. tho jddurjto dlastrudtbla lf j rodtjacu`jr rlli, 5. tho sbzo lf j to`ovbsbla sot, 4. tho shlrtost mbstjado eotwooa twl plbats, =. tho `oacth lf tho `jmmor aoomom tl orodt j ejaaor la j vortbdj` wj`` :65 WULNOD] :7 TOD]BLA 78 UOFOUOADOT www.erbchthueomudjtbla.dli www.thofjiluspolp`o.dli www.col.ubud.omu www.stlrylfijthoijtbds.dli :64 WULNOD] :7 TOD]BLA 72 JWWOAMBX (:) Uosu`ts usom ba thbs prlnodt J squjro bs j qujmrb`jtorj` wbth = oquj` sbmos. Ojdh batoraj` jac`o oquj` tl 27·. Jroj lf j squjro 9 sbmo Ó sbmo 9 sbmo5 h Jroj lf j rbcht jac`o trbjac`o 9 ejso Ó hobcht 5 e j ]ho sui lf tho 4 batorblr jac`os ba j trbjac`o bs oquj` tl :87· ∽ j· + e· + d· 9 :87· d e ]ho sui lf tho jmnjdoat jac`os la j strjbcht `bao ∽ j e j· + e· + d· 9 :87· d :6= (5) ]oris usom ba prlnodt> (b) Hypltoauso> ]ho sbmo lpplsbto tho rbcht jac`o ba j rbcht-jac`o trbjac`o J Hypltoauso E D (bb) Mbjclaj`> J `bao nlbabac twl vortbdos lf j pl`ycla whoa thlso vortbdos jro alt la tho sjio omco. JE bs j mbjclaj` E vortox vortox J (bbb) ]holroi> J ijthoijtbdj` stjtoioat thjt wjs prlvoa tl eo truo wbthba j cbvoa systoi. (bv) Z.O.M.> Jeerovbjtbla flr tho @jtba phrjso ‐qulm orjt moilastrjamui’ trjas`jtom batl Oac`bsh iojas ‐thjt whbdh wjs tl eo moilastrjtom’ usuj``y usom jt tho oam lf j prllf. (v) Hlrbzlatj` W`jao> ſtjt sillth surfjdo wbth al brrocu`jrbtbos. :6? 57 BMOJT FLU J IJ]HOIJ]BDT TEJ SB]H TDOAJUBLT JAM ]B]@OT :66 Ijthoijtbdj` ro`jtblas poriojto tho wlr`m, thoroflro, stumoats hjvo j woj`th lf lptblas frli whbdh thoy dja dhllso. Ttumoats shlu`m ﬊rst `llk wbthba thobr biiombjto oavbrlaioat jam lesorvo sbtujtblas thjt ijy roqubro bavostbcjtbla. Flr oxjip`o> :. ]ho hlio bs ja oxdo``oat p`jdo tl stjrt `llkbac flr TEJ Wrlnodt bmojs> j. Drojtbac j eumcot lr ostbijto flr hlio roalvjtblas dja cbvo rbso tl ja TEJ Wrlnodt. e. Wurdhjsbac ijnlr btois flr tho hlio dja j`sl spjrk bmojs flr ja TEJ Wrlnodt. 5. ]ho sdhll` bs jalthor p`jdo whoro TEJ Wrlnodt bmojs dja eo movo`lpom. ]ho fl``lwbac jro j`` crojt dladopts flr TEJ Wrlnodts> j. jesoatoobsi e. `jto dlibac d. biprlpor uabflri m. pllr djfotorbj sorvbdo o. stumoats‒ jdjmoibd porflrijado f. d`jssrlli> Ttumoats shlu`m pjy pjrtbdu`jr jttoatbla tl tojdhors whoa thoy jro prosoatbac thobr `osslas. ]lpbds sudh js> iojsuroioats, stjtbstbds, coliotry, ro`jtblas jam fuadtblas jam dlasuior jrbthiotbd jro j`` oxdo``oat tlpbds thjt dja eo usom ba lrmor tl bavostbcjto roj`-wlr`m prle`ois. Shoa j tojdhor bs prosoatbac j pjrtbdu`jr tlpbd, stumoats shlu`m jsk tho tojdhor tl oxp`jba hlw tho cbvoa tlpbd dja jssbst thoi wbth tho TEJ Wrlnodts. 4. ]ho dliiuabty bs j`sl j crojt p`jdo tl cot TEJ Wrlnodt bmojs. Ttumoats shlu`m `bstoa tl dlip`jbats lf pllr sorvbdo ey dustliors. ]hoso dlip`jbats dja thoa eo bavostbcjtom ey usbac sbip`o Ijthoijtbdj` todhabquos. Coaorj``y, stumoats dja `llk jt jay dlip`jbat lr roj`-wlr`m prle`oi whbdh ijy eo jaodmltj` ba ajturo jam dja eo bavostbcjtom ey usbac j sbip`o Ijthoijtbdj` todhabquo. ]ho fl``lwbac bs j `bst lf twoaty (57) sdoajrbls jam tbt`os thjt dja eo usom js rosojrdh prlnodts uamor mbfforoat tlpbds ba Ijthoijtbds. ]hoso tlpbds jro stjtbstbds, dlasuior jrbthiotbd, j`coerj, coliotry jam ijtrbdos. :63 T]J]BT]BDT TDOAJUBL : Ttumoats jt tho Flri throo (4) `ovo` wrbto tho Ajtblaj` Dortb﬊djto lf Todlamjry Omudjtbla (ADTO) Oxjibajtbla ovory yojr. Hlwovor, tho rosu`ts lf thoso oxjibajtblas ijy alt eo sorblus`y jaj`yzom ey sdhll` ijajcoioat tl baflri tojdhbac strjtocbos. J stumoat dja thoroflro ml j rosojrdh prlnodt ejsom la tho ADTO rosu`ts jam tho tbt`o dja rojm js fl``lws> ‐ Ja bavostbcjtbla lf tho `jst flur (=) yojrs lf ATOD rosu`ts jt j pjrtbdu`jr sdhll`.’ TDOAJUBL 5 J stumoat ijy wjat tl kalw hlw hbs lr hor sdhll` porflris ba j pjrtbdu`jr suenodt jroj jt tho Djrbeeoja Todlamjry Omudjtbla Dortb﬊djto (DTOD) Oxjibajtbla. ]ho fl``lwbac tbt`o dja eo usom tl pursuo j prlnodt> ‐J stumy lf tho `jst ﬊vo (?) yojrs lf tho DTOD Oac`bsh @jacujco oxjibajtbla rosu`ts jt j pjrtbdu`jr sdhll`.’ TDOAJUBL 4 J crlup ijy wjat tl stumy tho porflrijado lf `lwor flri stumoats jt j sdhll` ba j pjrtbdu`jr suenodt jroj. ]ho fl``lwbac tbt`o dja eo usom flr j rosojrdh prlnodt> ‐J stumoat ijy wjat tl stumy tho porflrijado lf tho `lwor sdhll` stumoats lf hbs lr hor sdhll` ba j pjrtbdu`jr suenodt jroj. ]ho fl``lwbac tbt`o dja eo usom flr j rosojrdh prlnodt.’ TDOAJUBL = ]ojdhors lftoa dlip`jba lf Flri ? stumoats eobac tjrmy jam jesoat frli sdhll`. ]hbs d`jbi dja eo bavostbcjtom ba j prlnodt. ]ho fl``lwbac tbt`o dja sot tho coaorj` rosojrdh thoio flr tho prlnodt> ‐Ja bavostbcjtbla batl tho puadtuj`bty jam rocu`jrbty lf Flri ? stumoats jt j sodlamjry sdhll`.’ :68 TDOAJUBL ? ]ho jelvo sbtujtbla dja j`sl eo bavostbcjtom j`lac tho fl``lwbac `bao> ‐Ja bavostbcjtbla ba lrmor tl motoribao bf tho mbstjado thjt stumoats `bvo frli tho sdhll` hjs ja bipjdt la thobr puadtuj`bty’. TDOAJUBL 6 Wjroats usuj``y sjy thjt oxtrjdurrbdu`jr jdtbvbtbos jffodt tho dhb`mroa‒s jdjmoibd porflrijado. ]hbs d`jbi dja eo bavostbcjtom ey usbac tho fl``lwbac tbt`o js j coaorj` thoio flr tho prlnodt> ‐Ja bavostbcjtbla lf stumoats‒ jdjmoibd porflrijado jt j pjrtbdu`jr sdhll` ba lrmor tl motoribao bf thoy jro jffodtom ey oxtrjdurrbdu`jr jdtbvbtbos..‒‒ TDOAJUBL 3 ]ho sdhll`‒s ijajcoioat hjs sorblus prle`ois wbth stumoats j`torbac tho sdhll` uabflri. J prlnodt dja eo mlao la tho sovorbty lf tho prle`oi. ]ho fl``lwbac tbt`o dja eo usom js j cubmo flr j prlnodt> ‐Ja bavostbcjtbla batl tho auieor lf uppor sdhll` stumoats jt j pjrtbdu`jr sdhll` whl j`tor thobr sdhll` uabflri.’ TDOAJUBL 8 Ttumoats ijy dhllso tl bavostbcjto tho jdjmoibd porflrijado lf tho Flri lao stumoats ba j pjrtbdu`jr suenodt jroj jt j sdhll`. ]ho fl``lwbac tbt`o dja eo usom tl cubmo tho prlnodt> ‐Ja bavostbcjtbla batl tho porflrijado lf Flri : stumoats ba tho jroj lf Ijthoijtbds jt j sodlamjry sdhll`.’ TDOAJUBL 2 ]horo jro j`wjys dlip`jbats lf stumoats alt sueibttbac hliowlrk jssbcaioats. ]hbs d`jbi dja eo bavostbcjtom ey usbac tho fl``lwbac tbt`o js j cubmo> ‐Ja bavostbcjtbla lf tho hliowlrk hjebts lf tho uppor jam `lwor flris ba lrmor tl motoribao whbdh crlup bs ilro `bko`y tl sueibt hliowlrk jssbcaioats.’ :62 DLAT_IOU JUB]HIO]BD TDOAJUBL :7 J stumoat dja dhllso tl jssbst hbs lr hor pjroat wbth tho fjib`y‒s eumcot. J eumcot dja eo drojtom ey tjkbac batl jddluat sj`jrbos jam oxpoambturo. ]ho fl``lwbac tbt`o dja eo j crojt thoio flr tho prlnodt> ‐Drojtbac j fjib`y eumcot usbac dlasuior jrbthiotbd todhabquos.’ TDOAJUBL :: ]ho Hluso Tystois jt sdhll`s usuj``y uso fuamrjbsors tl ho`p wbth tho purdhjso lf uabflris jam lthor btois flr Tplrts Mjy. J crlup lf stumoats dja drojto j eusbaoss p`ja flr j pjrtbdu`jr hluso ba lrmor tl jssbst wbth fuamrjbsbac. ]hoy dja `bst tho btois tl eo sl`m jam tho prbdo jt ojdh btois iust rotjb`om ba lrmor tl coaorjto j sbcab﬊djat prl﬊t. ]ho fl``lwbac tbt`o dja eo usom tl cubmo tho prlnodt movo`lpioat> ‐Movo`lpbac j eusbaoss p`ja tl rjbso fuams flr lao lf tho hlusos thjt eo`lac tl j pjrtbdu`jr sdhll`‒s hluso systoi.’ TDOAJUBL :5 Tupplso j stumoat‒s fjthor wjats tl so`` hbs iltlr vohbd`o jftor obcht (8) yojrs. ]ho vohbd`o hjs moprodbjtom ey j cbvoa pordoatjco ovory yojr flr tho `jst obcht (8) yojrs. ]ho stumoat dja movo`lp j prlnodt ba lrmor tl motoribao tho prosoat vj`uo lf tho vohbd`o jam lthor fjdtlrs thjt ijy jffodt tho ﬊aj` so``bac prbdo. ]ho tbt`o lf tho prlnodt dja eo stjtom js fl``lws> ‐Ja bavostbcjtbla batl tho vj`uo lf iy fjthor‒s iltlr vohbd`o jftor obcht (8) yojrs.’ :37 F_AD]BLAT JAM [email protected]]BLAT CUJWHT & @BAOJU WULCUJIIBAC TDOAJUBL :4 Mjm bs j p`uieor. Ho dhjrcos j ﬊xom foo lf $577 por sbto vbsbt. Ho j`sl dhjrcos j rjto lf $:77 por hlur. J `baojr ro`jtbla dja eo sot up jam usom ba lrmor tl prombdt tho tltj` foo thjt Mjm dja dhjrco flr spoambac x hlurs la j nle sbto. ]ho fl``lwbac tbt`o dja cubmo tho prlnodt> ‐_sbac j `baojr ro`jtbla ba lrmor tl motoribao tho tltj` jiluat lf ilaoy thjt iy fjthor dja dhjrco flr hbs p`uiebac sorvbdos.’ TDOAJUBL := : ]ho dbrduiforoado (D) lf jay dbrd`o bs 4 3 tbios bts mbjiotor (m). ]hbs bs stjtom js : D9 m, whoro 9 34 . ]hbs bip`bos thjt D bs mbrodt`y prlplrtblaj` tl m. Hoado, j crjph lf D vs m bs j strjbcht `bao. ]hbs dladopt dja eo usom tl motoribao tho jpprlxbijto vj`uo lf ey usbac prjdtbdj` iojsuroioats. ]ho tbt`o lf tho prlnodt dja rojm js fl``lws> ‐Ja bavostbcjtbla batl tho ro`jtblashbp eotwooa tho dbrduiforoado lf j dbrd`o jam bts mbjiotor ba lrmor tl motoribao tho vj`uo lf pb ( )’. TDOAJUBL :? Ttumoats usuj``y ﬊am bt mbf﬊du`t tl ijajco thobr tbio flr stumbos jam lthor jdtbvbtbos. ]hbs bs sl eodjuso, thoro jro usuj``y j auieor lf dlastrjbats la thobr `bvos. @baojr prlcrjiibac dja jssbst stumoats tl motoribao hlw ijay hlurs lf stumy thjt thoy aoom la j wook`y ejsbs ba lrmor tl jdhbovo ijxbiui eoao﬊t cbvoa j`` tho dlastrjbats la thobr `bvos. J tbt`o flr thbs prlnodt dja rojm js fl``lws> ‐_sbac `baojr prlcrjiibac todhabquos tl motoribao tho ijxbiui auieor lf hlurs thjt j stumoat shlu`m stumy ojdh wook ba lrmor tl jdhbovo ijxbiui eoao﬊ts, cbvoa j`` tho dlastrjbats la hbs lr hor `bfo.’ :3: [email protected] TDOAJUBL :6 ]horo bs j pbodo lf `jam jt tho ejdk lf tho sdhll` thjt dja eo usom ey tho Rluac @ojmors Crlup tl drojto j rodtjacu`jr vocotje`o cjrmoa. ]ho cjrmoa iust eo foadom jam j flltpjth iust eo p`jdom jrluam bt flr jddoss. J qujmrjtbd fuadtbla dja eo drojtom tl ilmo` tho cjrmoa jam tho iothlm lf dlip`otbac tho squjro dja eo usom tl motoribao tho ijxbiui jroj lf `jam thjt dja eo usom. ]ho prlnodt tbt`o dlu`m rojm> ‐_sbac tho iothlm lf dlip`otbac tho squjro tl motoribao tho ijxbiui jroj lf j vocotje`o cjrmoa.’ TDOAJUBL :3 Ttumoats jro lftoa jskom tl fjdtlrbzo tho j`coerjbd oxprossbla j5 - e5. ]holrotbdj``y, tho rosu`t lf thbs fjdtlrbzjtbla bs j 5 - e5 9 (j + e) (j - e). J crlup lf stumoats dja jrrjaco wbth tho Sllmwlrk Mopjrtioat lr j trjmosija tl dut j pbodo lf wllm batl j porfodt squjro lf j pjrtbdu`jr jroj. J sij``or squjro dja thoa eo dut frli tho ebccor squjro jam tho stumoats dja moilastrjto tho rosu`ts j5 - e59 (j + e) (j - e) ba j prjdtbdj` wjy. ]ho tbt`o lf j prlnodt dja rojm js fl``lws> ‐J stumy batl tho j`coerjbd bmoatbty j5 - e5 9 (j + e) (j - e) ba lrmor tl physbdj``y moilastrjto tho rosu`t.’ :35 COLIO]UR TDOAJUBL :8 J coaorj` flriu`j (5a - =) Ó 277 bs usuj``y cbvoa tl stumoats tl motoribao tho sui lf tho batorblr jac`os ba j pl`ycla. ]hbs flriu`j bs usuj``y cbvoa wbthlut prllf. J crlup lf stumoats dja physbdj``y prlvo thbs rosu`t ey duttbac mbfforoat pl`yclas lut lf Erbstl` Eljrm jam ro`jtbac ojdh pl`ycla tl j trbjac`o js shlwa eo`lw. Thjpo Thjpo mbvbmom batl trbjac`os Auieor Dj`du`j- Tui lf lf sbmos tbla jac`os 4 :x:87· :87· = 5x:87· 467· ? 4x:87· ?=7· 8 6x:87· :787· Ttumoats shlu`m eo je`o tl `llk jt tho pjttora jam flriu`jto j coaorj` flriu`j flr tho sui lf tho batorblr jac`os lf jay pl`ycla. ]ho tbt`o lf tho prlnodt dja rojm> ‐Ja bavostbcjtbla batl mbfforoat pl`yclas ba lrmor tl motoribao j coaorj` flriu`j flr tho sui lf tho batorblr jac`os lf jay :34 pl`ycla wbth tho uso lf j prjdtbdj` iothlm.’ IJ]UBDOT TDOAJUBL :2 Iy pjroats usuj``y cbvo jwjy hjipors ovory Dhrbstijs. ]hbs yojr thoy wjat tl cbvo lut toa (:7) hjipors dlasbstbac lf : `btro ib`k djrtlas, ? kb`lcrji pjdks lf rbdo jam 5 `btro eltt`os lf dllkbac lb`. Ojdh hjipor hjs toa (:7) btois. Ib`k dlsts $:5.?7, rbdo dlsts $47.77 jam lb` dlsts $=?.77. Hjipor Ib`k Ubdo Lb` 4 = 4 Btoi Dlst $ :?45 5=?: 46:4 =53: ?4=4 6:64 3=5= 844= 2:35 :7 Ib`k :5.?7 Ubdo 47.77 Lb` =?.77 Ttumoats dja drojto twl ijtrbdos ba lrmor tl motoribao> :. tho tltj` vj`uo lf ojdh hjipor 5. tho tltj` dlst tl drojto j`` :7 hjipors ]ho tbt`o lf tho prlnodt dja eo wrbttoa js> ‐_sbac ijtrbdos ba lrmor tl motoribao tho tltj` dlst lf prlmudtbla flr toa (:7) Dhrbstijs hjipors.’ :3= [email protected]]BLA LF IJ]HOIJ]BDT TDOAJUBL 57 Ttumoats j`wjys dlip`jba thjt Ijthoijtbds hjs al roj` wlr`m iojabac tl thoi. ]hoy j`wjys jsk tho quostblas; ‐Shy ji B mlbac thbs tlpbd<’ jam ‐Shoa wb`` B uso Ijthoijtbds ba `bfo<’ ]hbs prlnodt cbvos stumoats j dhjado tl jaswor thobr lwa quostblas. Ttumoats dja dhllso throo djroors jam shlw hlw Ijthoijtbds dja p`jy j koy rl`o ba thoso ﬊o`ms. ]ho fl``lwbac tbt`o dja eo usom js j cubmo flr thbs prlnodt> ‐Ja bavostbcjtbla ba lrmor tl moilastrjto tho biplrtjado lf Ijthoijtbds ba mbfforoat djroors.’ :3? UOFOUOADOT D`jrko, @. Hjrwllm, Jmmbtblaj` Wuro Ijthoijtbds, 4rm Ombtbla Croor, J. & @jyao, D. O. (:22:)Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja. Hoac, H. H.; ]j`eort, N. F., Jmmbtblaj` Ijthoijtbds, 6th Ombtbla ]ll`sbo, U, (:222). J Dlip`oto Dlurso wbth DXD Zuostblas. www.erbchthueomudjtbla.dli www.omo`ila﬊ajadbj`.dli www.omuſtlw.wlrmpross.dli/tjrmbaoss www.ovorythbacijths.dl.zj www.froopbk.dli www.col.ubud.omu www.cujrmbja.dl.tt www.ijth.ud`j.omu www.ijthcllmbos.dli www.ijthbsfua.dli www.ijthswlrk.dli www.ilaoysuporijrkot.dli www.qulrj.dli www.so`feub`maowhlios.dli www.stlrylfijthoijtbds.dli www.thojstlfom.dli www.thofjiluspolp`o.dli www.ttdlaaodt.clv.tt www.uadw.omu/j`ocerj www.vjrsbtytutlrs.dli www.woeorjw`or.dli www.wbkbOmudjtlr.lrc www.wbkbhlw.dli :36 JEL_] ]HO J_]HLU C`oamla Ttoo`o hjs eooa tojdhbac Ijthoijtbds flr tho pjst t woaty (57) yojrs. Ho durroat`y sorvos js Hojm lf tho Ijthoijtbds Mopjrtioat jt Tt. Njios Todlamjry Tdhll`, ]rbabmjm jam ]lejcl. Ho bs j crjmujto lf ]ho _abvorsbty lf tho Sost Bambos jam hl`ms j E.Td. Ijthoijtbds (Hlas) jam j Wlst Crjmujto Mbp`lij ba Omudjtbla]ojdhbac lf Ijthoijtbds. Ho hjs j`sl eooa j Djrbeeoja Oxjibajtblas Dluadb` Jssbstjat Oxjibaor flr tho pjst ﬊ftooa (:?) yojrs. Lvor tho yojrs ho hjs eooa dlasdboatblus`y propjrbac stumoats flr tho jaauj` Justrj`bja Ijthoijtbds L`yipbjm Dlipotbtbla. C`oamla Ttoo`o bs j dlasuiijto tojdhor ba ijay rocjrms jam hl`ms tho mbstbacubshom jddlip`bshioat lf offodtbvo`y prosoatbac tho to`ovbsbla sorbos, ‘J Dladoptuj` Jpprljdh tl @ojrabac Ijthoijtbds‒, la ]ho Baflrijtbla Dhjaao` = flr jpprlxbijto`y ﬊vo yojrs murbac whbdh, oiphjsbs wjs p`jdom la `ojrabac Ijthoijtbds ey eub`mbac la j sot lf fuamjioatj` prbadbp`os. Horo, ho oiphjsbzom thjt Ijthoijtbds shlu`m alt eo tjucht ey prosoatbac j sot lf todhabquos thjt stumoats shlu`m ioilrbzo ey rlto eut bastojm bt shlu`m eo tjucht ey ho`pbac stumoats tl rodlcabzo thjt Ijthoijtbds bs ejsom la j sot lf fuamjioatj` dladopts thjt flri tho ejsbs lf `ojrabac jay tlpbd ba Ijthoijtbds. Ir. Ttoo`o‒s phb`lslphy bs thjt Ijthoijtbds shlu`m eo prosoatom ba j ijaaor ba whbdh stumoats dja soo, jdkalw`omco jam jpprodbjto bts ro`ovjado ba tho roj` wlr`m jam ovoatuj``y dlio tl fj`` ba `lvo wbth tho suenodt.