The Essentials Mathematics SBA Handbook - Glendon Steele

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O X J I B A J] B L A

C@OAMLA T]OO@O

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.

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JDKAL J DKALS@OMCOIOA S@OMCOIOA] ]

B wlu`m `bko tl thjak Ir. Ttovo Hlpo flr prllfrojmbac tho TEJ prlnodts prosoatom ba thbs ellk jam lfforbac bavjùjeò jmvbdo jam supplrt. B wlu`m j`sl `bko tl thjak jam jdkalwòmco tho wlrk lf Ibss Djambdo Ehjrjt ba prllfrojm prllfrojmbac bac tho ellk jam dlrrodtbac tho Oac`bsh @jacujco. ]hjak ylu! ]hbs ellk dlu`m alt hjvo eooa dlipòtom wbthlut tho supplrt jam mombdjtbla lf Ibss Rvotto Eost whl spoat ijay `lac hlurs rosojrdhbac rosojrdhbac,, dl`òdtbac 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.

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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`òjcuos 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 sbipò `jacujco, ojdh sodtbla bs oxp`jbaom ba motjb`. J sjipò 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 badùmom 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) mbffor mbfforoat oat roj`-wlr`m sdoajrbls jro prosoatom tlcothor wbth succostom prlnodt tbtòs 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.

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CLLM@_DK!

]JE JE@O @O LF DLA DLA]OA]T

Todtbla......................................................................................................Wjco Todtbla ......................................................................................................Wjco Auieor :. Mombdjtbla........... ...................... ....................... ........................ ....................... ....................... ........................ ........................ ....................... ...................: ........: 5. Jdkalwòmcoioat .......................... ...................................... ....................... ....................... ........................ ....................... ....................... ..............5 ..5 4. Wrofjdo............ ........................ ....................... ....................... ........................ ....................... ....................... ........................ ....................... .......................4 ............4 =. ]jeò lf Dlatoats ............ ........................ ........................ ......................... ......................... ........................ ......................... ......................... ...............= ...= ?. Hlw ]l _so ]hbs Ellk ............ ........................ ........................ ......................... ......................... ........................ ......................... .................... .......? ? 6. Ujtblajò ................. ............................ ....................... ........................ ....................... ....................... ........................ ....................... ....................... ................6 ....6 3. Ttrudturo lf j DTOD DTOD Ijthoijtbds TEJ Wrlnodt ............ ........................ ........................ ....................... ...................8 ........8 8. Wrosoatjtbla lf :7 Slrkom Ijthoijtbds Ijthoijtbds TEJ Wrlnodts ............ ........................ ....................... .................57 ......57 • Wrlnodt Lao ........... ...................... ....................... ........................ ....................... ....................... ........................ ....................... .......................5: ............5: • Wrlnodt ]wl .........................................................................................................43 • Wrlnodt ]hroo .......... ...................... ........................ ........................ ....................... ....................... ........................ ....................... .....................?5 ..........?5 • Wrlnodt Flur ........... ...................... ....................... ........................ ....................... ....................... ........................ ....................... .......................68 ............68 • Wrlnodt Fbvo............................... ........................................... ....................... ....................... ........................ ....................... ....................... ................85 ....85 • Wrlnodt Tbx ........... ...................... ....................... ........................ ....................... ....................... ........................ ....................... ....................... ..............24 ..24 • Wrlnodt Tovoa ........... ....................... ........................ ........................ ....................... ....................... ........................ ....................... .................:74 ......:74 • Wrlnodt Obcht ........... ....................... ........................ ........................ ....................... ....................... ........................ ....................... ...................::6 ........::6 • Wrlnodt Abao ........... ...................... ....................... ........................ ....................... ....................... ........................ ....................... .....................:47 ..........:47 • Wrlnodt ]oa ............ ......................... ......................... ........................ ......................... ......................... ........................ ......................... ..................: .....:=3 =3 2. 57 Bmojs flr j Ijthoijtbds Ijthoijtbds TEJ wbth Tdoajrbls jam ]btòs ........... ...................... .....................:66 ..........:66 :7. Uoforoados............ ....................... ....................... ........................ ....................... ....................... ........................ ........................ ....................... .............:36 ..:36

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HLS ]L ]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) plssbeò sdoajrbls jam tbtòs frli whbdh thoy dja dhllso ba lrmor tl movo`lp thobr lwa prlnodts. Ttumoats 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. CLLM@_DK!

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UJ]BLAJ@O 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.’ CJ@B@OL

Shoa Cj`bòl 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, Hlwovor, tho ijauj` bs wrbttoa ba j sdboatb﬊d `jacujco dj`òm Ijthoijtbds whbdh iust eo uamorstllm bf wo wjat tl ua`ldk tho iystorbos lf ajturo. Ijthoijtbds bs tho `jacujco usom tl stumy tho prbadbpòs lf ajturo. Tbado ajturo rovoj`s btso`f tl us thrluch pjttoras, Ijthoijtbds bs j `jacujco thjt stumbos j`` plssbeò 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 prleòis ba tho roj` wlr`m. Hlwovor, trjmbtblaj``y, Ijthoijtb Ijthoijtbds ds 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 ruòs tl eo òjrat 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`òat 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.

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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 vbjeò jrcuioats =. bmoatbfy rbsks ?. ijko `lcbdj` modbsblas 6. tost jaodmltj` ovbmoado flr ro`bjeb` ro`bjeb`bty 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 òjra Ijthoijtbds ba sudh j wjy thjt thoy dja soo bts roòvjado roòvjado ba tho roj` 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> :. Toòdt j prleòi flr rosojrdh rosojrdh frli tho roj` wlr`m. 5. Toòdt tho roòvjat roòvjat Ijthoijtbds Ijthoijtbds tlpbd frli frli jay pjrt lf tho sy``jeus ba lrmor tl rosojrdh jam bavostbcjto tho dhlsoa prleòi. 4. Srbto j dòjr`y dòjr`y oxp`jbaom, oxp`jbaom, `lcbdj` jam soquoadom prlnodt prlnodt thjt sjtbs﬊os sjtbs﬊os dortjba cubmo`baos stbpu`jtom ey tho Djrbeeoja Oxjibajtblas Dluadb` (DXD).

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T]U_D]_UO LF J DTOD IJ IJ]HOI ]HOIJ J]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 prleòi 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 J@DLJ]OM ER D.X.D.

:. ]btò lf Wrlnodt

:

5. Batrlmudtbla

=

4. Iothlm lf Mjtj Dl`òdtbla

5

=. Wrosoatjtbla lf Mjtj

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?. Jaj`ysbs lf Mjtj

5

6. Mbsdussbla lf Fbambacs

5

3. Dladùsbla

5 ]ltj`

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]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`òm sue-sodtblas eodjuso ijrks jro alt jwjrmom flr thoso twl sodtblas.

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]horoflro, j Ijthoijtbds TEJ Wrlnodt hjs abao (2) mbfforoat sodtblas; sovoa (3) sodtblas jro jwjrmom ijrks jam twl (5) sodtblas jro prosoatom flr dlipòtoaoss lf tho prlnodt hlwovor, al ijrks wb`` eo jwjrmom flr thoi. Eoflro wo dl`òdt mjtj flr j prlnodt, wo iust kalw flr whjt purplso wo jro dl`òdtbac tho mjtj; whjt bs tho prleòi thjt wo wbsh tl sl`vo wbth tho mjtj< Hoado, tho ﬊rst stop lf tho prlnodt bs tl bmoatbfy j rosojrdh prleòi thjt wo wlu`m `bko tl jaswor. Ba thbs babtbj` stjco, tho suenodt tojdhor shlu`m p`jy ja batocrj` rlò ba jssbstbac tho stumoat tl bmoatbfy sbipò roj`-wlr`m prleòis prleòis 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 sjipò prlnodt prlnodt bs usom tl oxp`jba ojdh sodtbla lf tho prlnodt.

CO]]BAC T] T]JU]OM JU]OM (@llkbac flr mjtj tl sl`vo j sbipò roj`-wlr`m prleòi) prleòi) TJIW@O WULNOD] EOCBAT> @ot us supplso thjt j stumoat wjats tl motoribao tho òacth lf tbio thjt hbs/hor poors spoam wjbtbac ba `bao flr sorvbdo jt tho sdhll`‒s djfotorbj murbac tho ùadh erojk. ]ho stumoat wb`` hjvo tl dl`òdt qujatbtjtbvo mjtj ba lrmor tl bavostbcjto tho prleòi. ]ho prlnodt dja eo prosoatom js fl``lws>

TOD]BLA :> WULNOD] ]B]@O ]ho prlnodt tbtò bs j dòjr jam dliprohoasbvo stjtoioat thjt stjtos tho roj`-wlr`m prleòi whbdh bs clbac tl eo bavostbcjtom lr oxp`jbaom. Bt to``s tho rojmor whjt tho prlnodt bs jelut. Flr oxjipò, ba thbs sjipò prlnodt tho prlnodt tbtò dja rojm js fl``lws> ‐Ja bavostbcjtbla ba lrmor tl motoribao tho òacth lf tbio stumoats spoam wjbtbac ba `bao flr sorvbdo sorv bdo jt tho sdhll`‒s sd hll`‒s djfotorbj murbac tho ùadh ù adh erojk.’ ’

TOD]BLA 5> BA]ULM_D]BLA Ja batrlmudtbla bs j dòjr`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 dòjr`y stjto tho lenodtbvo lf tho prlnodt. ]ho batrlmudtbla iust j`sl badùmo j ]jeò ]jeò lf Dlatoats flr tho prlnodt. ]ho ]jeò lf Dlatoats to``s tho rojmor whoro tl ﬊am tho mbfforoat sodtblas lf tho prlnodt.

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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 ]jeò ]jeò lf Dlatoats shlu`m eo p`jdom jftor tho hojmbac ‐Batrlmudtbla’ eut eoflro tho jdtuj` Batrlmudtbla bs wrbttoa. Flr oxjipò, tho Batrlmudtbla Batrlmud tbla flr tho sjipò sj ipò TEJ Wrlnodt shlu`m eo prosoatom js fl``lws>

BA]ULM_D]BLA ]JE@O LF DLA]OA]T> Wrlnodt ]btò ........... ....................... ....................... ....................... ........................ ....................... ....................... ........................ ................Wjco ....Wjco auieor Batrlmudtbla ........... ....................... ....................... ....................... ........................ ....................... ....................... ........................ .............. ..Wjco Wjco auieor Iothlm lf Mjtj Dl`òdtbla .......... ...................... ........................ ....................... ....................... ........................ ................Wjco ....Wjco auieor Wrosoatjtbla lf Mjtj ............................ ........................................ ........................ ....................... ....................... ....................Wjco ........Wjco auieor Jaj`ysbs lf Mjtj............ Mjtj........................ ....................... ....................... ........................ ....................... ....................... ....................Wjco ........Wjco auieor Mbsdussbla lf Fbambacs ............................ ........................................ ....................... ....................... ........................ ................Wjco ....Wjco auieor Dladùsbla............ Dladùsbla ........................ ....................... ....................... ........................ ....................... ....................... ........................ ................Wjco ....Wjco auieor Uoforoados ........... ....................... ....................... ....................... ........................ ....................... ....................... ........................ ................Wjco ....Wjco auieor Jppoambx ............ ........................ ....................... ....................... ........................ ........................ ....................... ....................... ..................Wjco ......Wjco auieor ‐Ijay lf iy poors usuj``y jrrbvo `jto flr d`jssos jftor tho ùadh 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 IO]H LM LF MJ]J MJ]J DL@@OD]BLA ]hbs bs j motjbòm mosdrbptbla thjt stjtos oxjdt`y hlw jam whoro tho mjtj flr j prlnodt wjs dl`òdtom. Bt bs biplrtjat tl roioieor thjt tho rosojrdh bs sookbac tl jaswor j prleòi thjt tho stumoat hjs bmoatb﬊om. Hoado, ba lrmor tl ho`p tho stumoat tl jaswor tho rosojrdh prleòi, prleòi, mjtj iust eo djrofu``y dl`òdtom jam stumbom. Mjtj dja eo dl`òdtom ba j auieor lf mbfforo mbfforoat at wjys. ]ho pjrtbdu`jr iothlm dhlsoa flr mjtj dl`òdtbla wb`` vjry jam mopoams la whjt typo lf mjtj tho stumoat bs `llkbac flr. ]ho fl``lwbac jro j fow mbfforoat mbffor oat iothlms thjt dja eo usom tl dl`òdt 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`òdt mjtj frli j `jrco auieor lf porslas. Bt j`sl j``lws flr dl`òdtbac mjtj ojsb`y wbthlut rovoj`bac tho rosplamoat‒s bmoatbty.

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Hlwovor,, slio mbsjmvjatjcos lf usbac quostblaajbros jro> Hlwovor •

Uosplamoats jro sliotbios alt iltbvjtom tl jaswor j`` tho quostblas.

•

Bf slio rosplasos jro dlafusb dlafusbac, ac, thoy jro usuj``y mbf﬊du`t tl d`jrbfy.

•

Tliotbios quostblaajbros jro alt roturaom la tbio.

(e) WOUTLAJ@ 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, 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 truthfu``y suenodtbvo quostblas thjt dlu`m òjm 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`òdtbla, 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`òdt mjtj la j pjrtbdu`jr crlup. Hlwovor, Hlwovor, tho mbsjmvjatjcos lf thbs iothlm jro> • Bt dja tjko j `lac tbio tbio tl slrt jam dl`òdt mjtj mjtj frli frli roplrts roplrts jam rodlrms. • ]ho stumoat ijy alt uamorstjam tho tho mjtj frli tho rodlrms rodlrms jam jrrbvo jt fju`ty dladùsblas. VJUBJE@OT

Uoioieor,, thjt j rosojrdh bavostbcjtos tho ro`jtblashbp eotwooa vjrbjeòs. Uoioieor J vjrbjeò bs jay fjdtlr thjt hjs j qujatbty lr quj`bty thjt dja dhjaco. Flr oxjipò> •

J mopoamjat mopoamjat vjrbjeò vjrbjeò bs bs j vjrbjeò thjt dja dhjaco ejsom la tho bipjdt lf jalthor vjrbjeò.

•

Ja bamopoamoat bamopoamoat vjrbjeò bs j vjrbjeò thjt jffodts jffodts j mopoamjat vjrbjeò whbdh dja djuso bt tl dlatrbeuto tl j prleòi. Flr oxjipò, ba thbs sjipò prlnodt>

Torvbdo jt tho djfotorbj bs ja bamopoamoat vjrbjeò thjt dja bipjdt la tho wjbtbac tbio flr tho sorvbdo. Sjbtbac tbio bs tho mopoamjat vjrbjeò. Shoa dl`òdtbac mjtj flr j prlnodt bt bs cllm prjdtbdo tl bmoatbfy tho mbfforoat typos lf vjrbjeòs.

::

Flr oxjipò, ba thbs sjipò prlnodt tho iothlm lf mjtj dl`òdtbla dlu`m rojm js fl``lws>

]ho iothlm lf mjtj dl`òdtbla dhlsoa wjs porslaj` batorvbows. ‐J flri d`jss wjs soòdtom 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 soòdtom frli ojdh elx. ]hbs drojtom j sjipò 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 ùadh erojk<’ ]ho mjtj wjs dl`òdtom frli Ilamjy tl Frbmjy Frbmjy,, lvor j lao wook porblm. Woribssbla tl survoy tho stumoats murbac tho porblm biiombjto`y jftor tho ùadh 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 prosoats tho mjtj thjt ho/ sho hjs dl`òdtom. Coaorj``y, 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`òdtbac jam lrcjabzbac quj`btjtbvo mjtj, tho stumoat iust prosoat tho mjtj usbac jt òjst twl djrofu``y `jeoòm mbjcrjis. ]hoso dja eo stjtbstbdj` mbjcrjis sudh js> •

Froquoady ]jeòs

•

Ejr Crjphs

•

Wbo Dhjrts

•

Dlipjrjtbvo Ejr Crjphs

•

Hbstlcrjis

•

Froquoady Wl`yclas

•

Duiu`jtbvo Froquoady Durvos.

:5

]ho fl``lwbac bs ja oxjipò lf tho Wrosoatjtbla lf Mjtj flr tho sjipò prlnodt>

]ho froquoady tjeò jam tho duiu`jtbvo froquoady tjeò shlw tho wjbtbac tbio ba ibautos thjt tho lao huamrom (:77) stumoats spoat wjbtbac ba `bao jt tho djfotorbj. Froquoady ]jeò Sjbtbac tbio ba ibautos

Al. lf stumoats (f)

:-?

5

6 - :7

:7

: : - :?

:3

: 6 - 57

:6

5 : - 5?

5?

5 6 - 47

58

4 : - 4?

5

Duiu`jtbvo Froquoady ]jeò Sjbtbac tbio ba ibautos

Al. lf stumoats (f)

Duiiu`jtbvo froquoady (df)

:-?

5

5

6 - :7

:7

:5

:: - :?

:3

52

:6 - 57

:6

=?

5: - 5?

5?

37

56 - 47

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

•

vlùio

•

prl﬊t

•

`lss

•

Hbro Wurdhjso prbdo

Flr oxjipò, j`` dj`du`jtblas flr thbs sjipò 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

4

6

6 - :7

:7

8

87

: : - :?

:3

:4

5 5:

: 6 - 57

:6

:8

5 88

5 : - 5?

5?

54

? 3?

5 6 - 47

58

58

3 8=

4 : - 4?

5

44

66

f Óx

5757

√f 9 :77

√f Ó x

]ho jvorjco lr ioja 9 (tho sui lf f Ó x ) 9 (tho sui lf f) Alto>

(√fx) (√f)

9

5757 :77

Τ bs tho Crook òttor 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 sjipò wjbtom flr ilro 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 Tdjò> 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 ?> JAJ@RTBT LF MJ]J Ba thbs sodtbla, tho iojabac lf tho mjtj prosoatom iust eo mbsdussom ba j dòjr jam `lcbdj` ijaaor. 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 oxjipò, ba thbs sjipò 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 auieor lf stumoats frli tho sjipò wjbtom 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 sjipò, 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 dòjr`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 tbtò jam tho batrlmudtbla lf tho prlnodt. Hoado, ba wrbtbac tho mbsdussbla, tho stumoat shlu`m j`wjys rotura tl tho prlnodt tbtò jam batrlmudtbla flr cubmjado. Flr oxjipò, ba thbs sjipò prlnodt, tho mbsdussbla lf tho ﬊ambacs dja rojm js fl``lws>

‐]ho mjtj rovojòm thjt tho ioja wjbtbac tbio flr sorvbdo jt tho sdhll`‒ sdhll`‒s 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. mjb`y. ]ho ùadh erojk bs lao hlur `lac jam stumoats sjbm thjt, bt tjkos ja jvorjco lf twoaty (57) ibautos tl dlasuio thobr ùadh. ]hbs òjvos stumoats wbth :2.8 ibautos tl propjro thoiso`vos flr d`jssos jftor ùadh. ]hbs shlu`m cbvo stumoats oaluch tbio tl jrrbvo tl d`jss la tbio jftor tho ùadh erojk.’

:6

TOD]BLA 3> DLAD@_TBLA ]ho dladùsbla bs j dòjr`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 dlipòto uamorstjambac lf tho prlnodt‒s lenodtbvos. Shoa wrbtbac tho dladùsbla, tho stumoat shlu`m rotura tl tho batrlmudtbla lf tho prlnodt jam `llk jt tho purplso flr whbdh tho rosojrdh wjs dlamudtom. ]ho dladùsbla shlu`m mbsduss jam jaswor tho purplso lf tho prlnodt. Flr oxjipò, ba thbs sjipò prlnodt tho dladùsbla 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 ùadh erojk bs rojslajeò. Hlwovor, ja jvorjco wjbtbac tbio lf 57.5 ibautos stb`` òjvos thoi wbth oaluch tbio flr ojr`y jrrbvj` tl d`jssos d `jssos flr tho jftoralla sossbla. sossbla.’ ’

Jftor tho sovoa (3) ijba sodtblas lf tho prlnodt jro prosoatom, thoro jro twl lthor sodtblas thjt iust eo prosoatom flr dlipòtoaoss. Hlwovor, 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 oxjipò, tho roforoados flr tho sjipò 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.purpòijth.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 dlipòtoaoss lf tho prlnodt eut ibcht eo dlasbmorom tll `lac jam duieorslio flr tho rojmor tl poruso. Ujw mjtj, tjeòs, dhjrts, crjphs, quostblaajbros jam mo﬊abtblas jro slio lf tho thbacs thjt dja eo badùmom ba tho jppoambx. Bf ylu hjvo ilro thja lao jppoambx, ijko suro thjt ojdh lao eocbas la j aow

:3

pjco jam bs tbtòm; Jppoambx J, Jppoambx E, Jppoambx D otd.

Flr oxjipò, tho Jppoambx flr tho sjipò 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] WUOTOA]J J]BLA LF TJIW@O TJIW@O WULNOD] WULNOD] OAMT OAMT //

UL@O LF ]HO ]OJDHOU> ]ho ejsbd rlò lf tho tojdhor bs tl> • Jssbst stumoats wbth tho soòdtbla soòdtbla lf tlpbds tl tl eo bavostbcjtom flr prlnodts. prlnodts. •

Wrlvbmo iojabacfu` cubmjado thrluchlut tho murjtbla murjtbla lf tho prlnodt. prlnodt. ]ho tojdhor wb`` sot mojm`baos flr stumoats tl dlipòto ojdh pjrt lf tho prlnodt. ]ho tojdhor iust oasuro thjt stumoats jmhoro tl roqubrom mojm`baos.

•

J``lw tho stumoats tl prlmudo prlmudo j auieor auieor lf mrjfts lf tho dhlsoa prlnodt. ]ho tojdhor shlu`m rojm tho mrjfts, lffor foomejdk jam cbvo cubmjado thrluchlut tho dydò lf tho prlnodt. Bt shlu`m eo altom thjt, tho tojdhor‒s rlò bs thjt lf j fjdb`btjtlr jam js sudh ho/sho shlu`m la`y lffor cubmjado rjthor thja cbvo slùtblas tl tho prleòi eobac bavostbcjtom ba tho prlnodt.

•

Mombdjto jt òjst lao porblm por wook ba lrmor lrmor tl fjdb`btjto mbsdussblas la bssuos ro`jtbac tl tho prlnodt.

•

Mbsduss stumoats‒ stumoats‒ prleòis prleòis wbth wbth tho Hojm Hojm lf Mopjrtioat ba lrmor tl jrrbvo jt slùtblas.

:8

UL@O LF ]HO T]_MOA] ]ho ejsbd rlò lf tho stumoat bs tl> • Slrk d`lso`y wbth wbth tho tojdhor ba lrmor tl soòdt ja TEJ Wrlnodt rosojrdh tlpbd. • Jmhoro tl j`` mojm`baos sot ey tho tojdhor. •

Took jmvbdo jmvbdo frli frli tho tojdhor la j`` tho mbffor mbfforoat oat pjrts lf tho prlnodt.

•

Uojm aowspjpors, nluraj`s, ijcjzbaos ijcjzbaos jam ellks ellks ba lrmor tl cot cot baflrijtbla baflrijtbla la tho tlpbd dhlsoa flr bavostbcjtbla. ]ho batoraot bs j`sl ja bavjùjeò tll` ba tho propjrjtbla lf j prlnodt.

•

Wrlmudo mrjfts lf tho prlnodt prlnodt flr tho tojdhor‒ tojdhor‒s s porusj` eoflro eoflro tho ﬊aj` prlnodt prlnodt bs sueibttom. ]hbs wb`` j``lw tho tojdhor tl cbvo iojabacfu` jam tbio`y foomejdk tl stumoats eoflro tho dlipòtbla lf prlnodts jam ﬊aj` sueibssbla.

J SLUM LF DJ_]BLA DJ_]BLA • J Ijthoijtbds Ijthoijtbds TEJ TEJ Wrlnodt Wrlnodt bs iojat tl tost dortjba skb``s 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`òdtbac mjtj flr j prlnodt. Hlwovor, ojdh stumoat bs oxpodtom tl wrbto hbs lr hor lwa jaj`ysbs jam dladùsbla lf mjtj dl`òdtom. •

]ho Ijthoijtbds Ijthoijtbds TEJ Wrlnodt hjs j `bibt lf lao thlusjam (:,777) wlrms wlrms jam ovory offlrt iust eo ijmo tl stjy wbthba tho stbpu`jtom `bibt. Fjbùro 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, tjeòs, rjw mjtj, pbdturos jam mo﬊abtblas ba ja jppoambx.

•

Shoa wrbtbac wrbtbac j prlnodt, prlnodt, ml ml alt uso tho jdtuj` ajios ajios lf eusbaossos, sdhll`s, polpò polpò jam clvoraioat bastbtutblas.

•

Shoa wlrkbac wlrkbac la prlnodts oasuro thjt wlrk 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 jwjrmom flr tho lvorj`` prosoatjtbla lf tho prlnodt. 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 dòjr`y jam `lcbdj``y `lcbdj``y.. ]ho stumoat dja jsk ja Oac`bsh tojdhor tl jssbst hbi lr hor wbth prllfrojm prllfrojmbac bac tho Ijthoijtbds TEJ Wrlnodt eoflro bts ﬊aj` sueibssbla.

:2

WUOTOA]J]BLA LF :7 SLUKOM IJ]H IJ ]HOI OIJ J]BDT TEJ TEJ WULNOD]T

57

WULNOD] :

TOD]BLA 7: WULNOD] WULNOD ] ]B]@O ]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

]JE@O LF DLA]OA]T :. ]btò....... ]btò.................. ....................... ........................ ........................ ....................... ....................... ........................ .............. Wjco Auieor Auieor 5. Batrlmudtbla ........... ....................... ........................ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla ............ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor Auieor =. Wrosoatjtbla lf Mjtj............ ........................ ....................... ....................... ........................ ................. .....Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj Mjtj ............ ........................ ....................... ....................... ........................ .......................Wjco ...........Wjco Auieor 6. Mbsdussbla lf Fbambacs............ ........................ ....................... ....................... ........................ .............. Wjco Auieor 3. Dladùsbla .......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 8. Uoforoados.......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx............. ....................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor Wolpò dlip`jba vbj tho iombj (rjmbl, tj`k shlws, abcht`y aows, aowspjpor jrtbdòs, 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 Sjbtbac j `lac tbio flr sorvbdo dja eo frustrjtbac, badlavoaboat jam ijy djuso ovoa tho ilst tlòrjat porsla tl eodlio jaalyom, jaxblus lr ovoa `lso oiltblaj` dlatrl`. ]hobr jddluat lf `lac wjbtbac tbio ijy, hlwovor, eo rocjrmom js obthor uaro`bjeò lr hojrsjy.

]ho purplso lf thbs prlnodt bs tl uso stjtbstbdj` todhabquos tl bavostbcjto tho d`jbi thjt polpò 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 DL@@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 dòrk bssuom j dlasodutbvo auieor tl ojdh pjtboat js ho lr sho wjs sojtom. J iothlm lf mjtj dl`òdtbla dj`òm ala-pjrtbdbpjat lesorvjtbla wjs usom. ]ho mjtj woro coaorjtom ey mbrodt`y lesorvbac jam rodlrmbac 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 oatorom tho rlli rlli flr sorvbdo

•

jrrbvj` tbios lf ojdh porsla

•

tho tbios jt whbdh thoy woro dj`òm 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`òdtom flr tho ﬊vo mjys, tho rjw mjtj woro thoa lrcjabzom usbac ﬊vo froquoady mbstrbeutbla tjeòs. ]ho tjeòs dlasbst lf sbx d`jss batorvj`s ojdh hjvbac j wbmth lf ?7 ibautos.

ILAMJR

]_OTMJR

SOMAOTMJR

Sjbtbac tbio ba ibautos

Auieor lf pjtboats (f)





: 7 7 - := 2

7

:7 7 - := 2

:

: 7 7 - : =2

7

: ? 7 - :2 2

4

:? 7 - :2 2

2

: ? 7 - : 22

:4

5 7 7 - 5= 2

?

57 7 - 5= 2

:7

5 7 7 - 5 =2

8

5 ? 7 - 52 2

?

5? 7 - 52 2

:7

5 ? 7 - 5 22

=

4 7 7 - 4= 2

:3

47 7 - 4= 2

7

4 7 7 - 4 =2

?

4 ? 7 - 42 2

7

4? 7 - 42 2

7

4 ? 7 - 4 22

7

]L]J@

47

]L]J@

47

]L]J@

47

]H_UTMJR

FUBMJR





: 7 7 - := 2

3

: 77 - := 2

:

: ? 7 - :2 2

2

: ?7 - :2 2

=

5 7 7 - 5= 2

=

5 77 - 5= 2

8

5 ? 7 - 52 2

8

5 ?7 - 52 2

3

4 7 7 - 4= 2

5

4 77 - 4= 2

8

4 ? 7 - 42 2

7

4 ?7 - 42 2

5

]L]J@

47

]L]J@

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 I B ] 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 mjy..

ILAMJR



D`jss ibmplbat (x)

f Óx

:? 7 - : 22

4

:3=.?

?54.?

57 7 - 5 =2

?

55=.?

:: 55 .?

5? 7 - 5 22

?

53=.?

:4 35 .?

47 7 - 4 =2

:3

45=.?

? ?: 6.?

]L]J@

47

]L]J@

8? 4?

]ho jvorjco lr ioja

9

(tho sui lf f Ó x ) 9 (√fx) (tho sui lf f)

5?

9

58=.? ibautos

9

=.3= hlurs

(√f)

9

8?4? 47

]_OTMJR



D`jss ibmplbat (x)

f Óx

: 77 - := 2

:

:5=.?

:5=.?

: ?7 - :2 2

2

:3=.?

:?37.?

5 77 - 5= 2

:7

55=.?

55=?.7

5 ?7 - 52 2

:7

53=.?

53=?.7

]L]J@

47

]L]J@

6 68 ?

]ho jvorjco lr ioja

9


9

555.84 ibautos

9

4.3: hlurs

9

668?

(√f)

47

SOMAOTMJR



D`jss ibmplbat (x)

f Óx

: ?7 - :2 2

:4

:3=.?

5568.?

5 77 - 5= 2

8

55=.?

:3 26

5 ?7 - 52 2

=

53=.?

:7 28

4 77 - 4= 2

?

45=.?

:655.?

]L]J@

47

]L]J@

6 38 ?

]ho jvorjco lr ioja

9


9

556.:3 ibautos

9

4.33 hlurs

(√f)

9

638? 47

56

]H_UTMJR



D`jss ibmplbat (x)

f Óx

:7 7 - : =2

3

:5=.?

83:.?

:? 7 - : 22

2

:3=.?

:? 37 .?

57 7 - 5 =2

=

55=.?

82 8

5? 7 - 5 22

8

53=.?

5 :2 6

47 7 - 4 =2

5

45=.?

6= 2

]L]J@

47

]L]J@

6: 8?

]ho jvorjco lr ioja

9


9

576.5 ibautos

9

4.== hlurs

9

6:8?

(√f)

47

FUBMJR



D`jss ibmplbat (x)

f Óx

:7 7 - : =2

:

:5=.?

:5=.?

:? 7 - : 22

=

:3=.?

62 8

57 7 - 5 =2

8

55=.?

: 32 6

5? 7 - 5 22

3

53=.?

:2 5: .?

47 7 - 4 =2

8

45=.?

5 ?2 6

4? 7 - 4 22

5

43=.?

3= 2

]L]J@

47

]L]J@

38 8?

]ho jvorjco lr ioja

9

(tho sui lf f Ó x ) 9 (√ fx) (tho sui lf f)

53

Alto>

9

565.8 ibautos

9

=.48 hlurs

(√ f)

9

388? 47

Τ bs tho Crook òttor sbcij. Bt bs usom horo tl rop`jdo tho phrjso ‐tho sui lf’

WULNOD] :

TOD]BLA 7? JAJ@R JAJ@ RTBT LF MJ] MJ]J

]ho mjtj dl`òdtom frli thbs rosojrdh rovojòm> :.

]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 òjst 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`òdtom usbac porslaj` lesorvjtbla lvor j lao wook porblm rovojòm 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 DLAD@_TBLA

Ejsom la thbs rosojrdh, tho pue`bd‒s 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, pjrtbdu`jr, porslas wjbtom ja jvorjco lf = hlurs mjb`y flr sorvbdo. ]hbs supplrts tho jaodmltj` d`jbi thjt polpò spoam j `lac tbio wjbtbac flr sorvbdo. ]hbs sbtujtbla bs uatoajeò jam roqubros urcoat jttoatbla ey thlso ba juthlrbty.

47

WULNOD] :

TOD]BLA 78 UOFOUOADOT

]ll`sbo, U.; Ijthoijtbds> J Dlipòto Dlurso wbth DXD Zuostblas . Vl`. 5 www.dlipjss.plrt.jd.uk www.ylurjrtbdò`berjry.dli

4:

WULNOD] :

TOD]BLA 72 JWWOAMBX

ILAMJR Wjtb Wj tboa oatt Al. Al.

Jrrb Jr rbvj vj`` ]bi ]bio o flr flr To Torv rvbd bdo o

]bio ]b io Dj Dj`` `òm om fl flrr To Torv rvbd bdo o

]bio ]b io Sjb jbto tom m fl flrr To Torv rvbd bdo o

:

3 >7 7 j .i .

2 > 4 7 j .i .

5 hlurs 47 ibautos

5

3 >7 7 j .i .

2 > = : j .i .

5 hlurs =: ibautos

4

3 >7 4 j .i .

:7>77 j.i.

5 hlurs ?3 ibautos

=

3 >7 ? j .i .

:7>57 j.i.

4 hlurs 5= ibautos

?

3 >: 7 j .i .

:7>=7 j.i.

4 hlurs 47 ibautos

6

3 >: ? j .i .

:7>?7 j.i.

4 hlurs 4? ibautos

3

3 >: 8 j .i .

::>75 j.i.

4 hlurs == ibautos

8

3 >5 7 j .i .

::>57 j.i.

= hlurs 7 ibautos

2

3 >5 4 j .i .

::>4? j.i.

= hlurs :5 ibautos

:7

3 >5 8 j .i .

::>== j.i.

= hlurs :6 ibautos

::

3 >4 7 j .i .

::>?8 j.i.

= hlurs 58 ibautos

:5

3 >4 8 j .i .

:5>:? p.i.

= hlurs 43 ibautos

:4

3 >= 5 j .i .

:5>48 p.i.

= hlurs ?6 ibautos

:=

8 >7 7 j .i .

:>77 p.i.

? hlurs 7 ibautos

:?

8 >: 7 j .i .

:>:? p.i.

? hlurs ? ibautos

:6

8 >: 5 j .i .

:>47 p.i.

? hlurs :8 ibautos

:3

8 >4 7 j .i .

:>48 p.i.

? hlurs 8 ibautos

:8

8 >4 4 j .i .

:>=? p.i.

? hlurs :5 ibautos

:2

8 >4 8 j .i .

:>?7 p.i.

? hlurs :5 ibautos

57

8 >= 7 j .i .

5>77 p.i.

? hlurs 57 ibautos

5:

8 >= ? j .i .

5>:5 p.i.

? hlurs 53 ibautos

55

8 >? 6 j .i .

5>57 p.i.

? hlurs 5= ibautos

54

2 >7 : j .i .

5>5? p.i.

? hlurs 5= ibautos

5=

2 >: ? j .i .

5>4? p.i.

? hlurs :7 ibautos

5?

2 >5 8 j .i .

5>48 p.i.

? hlurs :5 ibautos

56

2 >4 7 j .i .

5>=? p.i.

? hlurs :? ibautos

53

2 >4 6 j .i .

5>=8 p.i.

? hlurs :5 ibautos

58

2 >4 2 j .i .

5>?7 p.i.

? hlurs :: ibautos

52

2 >= = j .i .

5>?? p.i.

? hlurs :: ibautos

47

2 >= ? j .i .

4>77 p.i.

? hlurs :? ibautos

45

]_OTMJR Wjtb Wj tboa oatt Al. Al.

44

Jrrb Jr rbvj vj`` ]b ]bio io fl flrr To Torv rvbd bdo o

]bio ]b io Dj Dj`` `òm om fl flrr Tor Torvb vbdo do

]bio ]b io Sjb jbto tom m fl flrr Tor Torvb vbdo do

:

3>77 j.i.

2>57 j.i.

5 hlurs 57 ibautos

5

3>:7 j.i.

2>=7 j.i.

5 hlurs 47 ibautos

4

3>:: j.i.

2>=8 j.i.

5 hlurs 43 ibautos

=

3>:8 j.i.

:7>7: j.i.

5 hlurs =4 ibautos

?

3>5? j.i.

:7>:? j.i.

5 hlurs ?7 ibautos

6

3>52 j.i.

:7>5: j.i.

5 hlurs ?: ibautos

3

3>47 j.i.

:7>47 j.i.

4 hlurs 7 ibautos

8

3>4? j.i.

:7>42 j.i.

4 hlurs = ibautos

2

3>42 j.i.

:7>?7 j.i.

4 hlurs : ibautos

:7

3>=4 j.i.

::>7: j.i.

4 hlurs :8 ibautos

::

3>=2 j.i.

::>:? j.i.

4 hlurs 56 ibautos

:5

3>?4 j.i.

::>57 p.i.

4 hlurs 53 ibautos

:4

3>?2 j.i.

::>58 j.i.

4 hlurs 52 ibautos

:=

8>7? j.i.

::>4? j.i.

4 hlurs 47 ibautos

:?

8>78 j.i.

::>=4 j.i.

4 hlurs 4? ibautos

:6

8>:? j.i.

::>=2 j.i.

4 hlurs 4= ibautos

:3

8>:8 j.i.

::>?4 j.i.

4 hlurs 4? ibautos

:8

8>54 j.i.

:5>57 p.i.

4 hlurs ?3 ibautos

:2

8>52 j.i.

:5>4? p.i.

= hlurs 6 ibautos

57

8>47 j.i.

:5>=7 p.i.

= hlurs ? ibautos

5:

8>42 j.i.

:5>=2 p.i.

= hlurs :7 ibautos

55

8>=5 j.i.

:5>?4 p.i.

= hlurs :: ibautos

54

8>?7 j.i.

: >: 7 p . i .

= hlurs 57 ibautos

5=

8>?? j.i.

: >: ? p . i .

= hlurs 57 ibautos

5?

2>7: j.i.

: >4 7 p . i .

= hlurs 52 ibautos

56

2>78 j.i.

: >4 8 p . i .

= hlurs 57 ibautos

53

2>:: j.i.

: >= = p . i .

= hlurs 44 ibautos

58

2>:? j.i.

: >? ? p . i .

= hlurs =7 ibautos

52

2>:8 j.i.

5 >: 7 p . i .

= hlurs ?5 ibautos

47

2>44 j.i.

5 >: ? p . i .

= hlurs =5 ibautos

SOMAOTMJR Wjtb Wj tboa oatt Al. Al.


]bio ]b io Dj Dj`` `òm om fl flrr To Torv rvbd bdo o

]bio ]b io Sjb jbto tom m fl flrr To Torv rvbd bdo o

:

3>77 j.i.

2>7? j.i.

5 hlurs ? ibautos

5

3>77 j.i.

2>5? j.i.

5 hlurs 5? ibautos

4

3>77 j.i.

2>58 j.i.

5 hlurs 58 ibautos

=

3>7? j.i.

2>42 j.i.

5 hlurs 4= ibautos

?

3>:5 j.i.

2>=? j.i.

5 hlurs 44 ibautos

6

3>:= j.i.

2>?? j.i.

5 hlurs =: ibautos

3

3>:? j.i.

:7>7? j.i.

5 hlurs ?7 ibautos

8

3>:8 j.i.

:7>:? j.i.

5 hlurs ?3 ibautos

2

3>54 j.i.

:7>4: j.i.

4 hlurs 8 ibautos

:7

3>47 j.i.

:7>42 j.i.

4 hlurs 2 ibautos

::

3>44 j.i.

:7>?7 j.i.

4 hlurs :3 ibautos

:5

3>42 j.i.

:7>?? j.i.

4 hlurs :6 ibautos

:4

3>=: j.i.

::>77 j.i.

4 hlurs :2 ibautos

:=

3>?7 j.i.

::>:: j.i.

4 hlurs 5: ibautos

:?

3>?= j.i.

::>57 j.i.

4 hlurs 56 ibautos

:6

8>77 j.i.

::>52 j.i.

4 hlurs 52 ibautos

:3

8>7? j.i.

::>=7 j.i.

4 hlurs 4? ibautos

:8

8>78 j.i.

::>=2 j.i.

4 hlurs =: ibautos

:2

8>:5 j.i.

::>?? j.i.

4 hlurs =4 ibautos

57

8>:8 j.i.

:5>57 p.i.

= hlurs 5 ibautos

5:

8>54 j.i.

:5>47 p.i.

= hlurs 3 ibautos

55

8>52 j.i.

:5>=? p.i.

= hlurs :6 ibautos

54

8>44 j.i.

:>:7 p.i.

= hlurs 43 ibautos

5=

8>42 j.i.

:>47 p.i.

= hlurs ?: ibautos

5?

8>== j.i.

:>42 p.i.

= hlurs ?? ibautos

56

8>=8 j.i.

:>=8 p.i.

? hlurs 7 ibautos

53

8>?? j.i.

5>77 p.i.

? hlurs ? ibautos

58

8>?8 j.i.

5>:? p.i.

? hlurs :3 ibautos

52

2>7: j.i.

5>5? p.i.

? hlurs := ibautos

47

2>7? j.i.

5>47 p.i.

? hlurs 5? ibautos

4=

]H_UTMJR

4?

Wjt jtbboa oatt Al. Al.


]bio ]b io dj` j`ò òm m flr flr To Torv rvbd bdo o

]bio ]b io wj wjbt btom om fl flrr Tor Torvb vbdo do

:

3 > 7 7 j .i .

2>74 j.i.

5 hlurs 4 ibautos

5

3 > 7 7 j .i .

2>:7 j.i.

5 hlurs :7 ibautos

4

3 > 7 ? j .i .

2>57 j.i.

5 hlurs :? ibautos

=

3 > : 7 j .i .

2>47 j.i.

5 hlurs 57 ibautos

?

3 > : 5 j .i .

2>48 j.i.

5 hlurs 56 ibautos

6

3 > : ? j .i .

2>?7 j.i.

5 hlurs 4? ibautos

3

3 > 4 7 j .i .

2>?? j.i.

5 hlurs 5? ibautos

8

3 > 4 ? j .i .

:7>:? j.i.

5 hlurs 4? ibautos

2

3 > 4 2 j .i .

:7>57 j.i.

5 hlurs =: ibautos

:7

8 > 7 7 j .i .

:7>58 j.i.

5 hlurs 58 ibautos

::

8 > 7 ? j .i .

:7>4? j.i.

5 hlurs 47 ibautos

:5

8 > 7 8 j .i .

:7>=2 j.i.

5 hlurs =: ibautos

:4

8 > : : j .i .

::>?? j.i.

5 hlurs == ibautos

:=

8 > : 4 j .i .

::>:: j.i.

5 hlurs ?8 ibautos

:?

8 > 5 ? j .i .

::>57 j.i.

5 hlurs ?? ibautos

:6

8 > 4 2 j .i .

::>47 j.i.

5 hlurs ?: ibautos

:3

8 > ? 7 j .i .

:5>:7 j.i.

4 hlurs 57 ibautos

:8

8 > ? ? j .i .

:5>5? j.i.

4 hlurs 47 ibautos

:2

2 > 7 7 j .i .

:>77 p.i.

= hlurs 7 ibautos

57

2 > 7 8 j .i .

:>:7 p.i.

= hlurs 5 ibautos

5:

2 > : 7 j .i .

:>52 p.i.

= hlurs :2 ibautos

55

2 > : ? j .i .

:>47 p.i.

= hlurs := ibautos

54

2 > 5 : j .i .

:>42 p.i.

= hlurs :8 ibautos

5=

2 > 5 4 j .i .

5>77 p.i.

= hlurs 43 ibautos

5?

2 > 5 ? j .i .

5>:: p.i.

= hlurs =6 ibautos

56

2 > 5 8 j .i .

5>57 p.i.

? hlurs ?5 ibautos

53

2 > 4 7 j .i .

5>5? p.i.

? hlurs ?? ibautos

58

2 > 4 : j .i .

5>52 p.i.

? hlurs ?8 ibautos

52

2 > 4 = j .i .

5>4? p.i.

? hlurs : ibautos

47

2 > 4 ? j .i .

5>=: p.i.

? hlurs 6 ibautos

FUBMJR Wjt jtbo boat at Al Al..

Jrrb Jr rbvj vj`` ]bi ]bio o flr flr To Torv rvbbdo

]bio ]b io dj dj`` `ò om flr flr To Torv rvbd bdo o

]bio ]b io wj wjbbto tom m flr flr To Torv rvbd bdo o

:

3>77 j.i.

2>:? j.i.

5 hlurs :? ibautos

5

3>77 j.i.

2>47 j.i.

5 hlurs 47 ibautos

4

3>77 j.i.

2>4? j.i.

5 hlurs 4? ibautos

=

3>7? j.i.

:7>77 j.i.

5 hlurs ?? ibautos

?

3>78 j.i.

:7>4? j.i.

4 hlurs :3 ibautos

6

3>:5 j.i.

:7>== j.i.

4 hlurs 45 ibautos

3

3>:2 j.i.

:7>?? j.i.

4 hlurs 46 ibautos

8

3>5? j.i.

::>47 j.i.

= hlurs ? ibautos

2

3>47 j.i.

::>4? j.i.

= hlurs ? ibautos

:7

3>4? j.i.

::>48 j.i.

= hlurs 4 ibautos

::

3>42 j.i.

::>== j.i.

= hlurs ? ibautos

:5

3>== j.i.

::>=2 j.i.

= hlurs ? ibautos

:4

3>=8 j.i.

::>?? j.i.

= hlurs 6 ibautos

:=

3>?? j.i.

:5>78 p.i.

= hlurs :4 ibautos

:?

8>77 j.i.

:5>57 p.i.

= hlurs 57 ibautos

:6

8>7? j.i.

:5>4? p.i.

= hlurs 57 ibautos

:3

8>:7 j.i.

:5>=2 p.i.

= hlurs 42 ibautos

:8

8>:8 j.i.

:>77 p.i.

= hlurs =5 ibautos

:2

8>5? j.i.

:>57 p.i.

= hlurs ?? ibautos

57

8>47 j.i.

:>58 p.i.

= hlurs ?8 ibautos

5:

8>44 j.i.

:>42 p.i.

? hlurs 6 ibautos

55

8>=7 j.i.

:>=? p.i.

? hlurs ? ibautos

54

8>=? j.i.

5>77 p.i.

? hlurs :? ibautos

5=

8>=2 j.i.

5>57 p.i.

? hlurs 4: ibautos

5?

8>?5 j.i.

5>52 p.i.

? hlurs 43 ibautos

56

8>?? j.i.

5>48 p.i.

? hlurs =4 ibautos

53

8>?2 j.i.

5>=? p.i.

? hlurs =6 ibautos

58

2>7: j.i.

5>?7 p.i.

? hlurs =2 ibautos

52

2>74 j.i.

4>77 p.i.

? hlurs ?3 ibautos

47

2>7? j.i.

4>:7 p.i.

6 hlurs 6 ibautos

46

WULNOD] 5


Ja bavostbcjtbla batl vjrblus Hbro Wurdhjso p`jas frli flur mbfforoat stlros ba ]rbabmjm ]rbabmjm jam ]lejcl. ]lejcl.

43

WULNOD] 5

TOD]BLA 7: BA]ULM_D]BLA

]JE@O LF DLA]OA]T :. ]btò....... ]btò.................. ....................... ........................ ........................ ....................... ....................... ........................ .............. Wjco Auieor Auieor 5. Batrlmudtbla ........... ....................... ........................ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla ............ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor Auieor =. Wrosoatjtbla lf Mjtj............ ........................ ....................... ....................... ........................ ................. .....Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj Mjtj ............ ........................ ....................... ....................... ........................ .......................Wjco ...........Wjco Auieor 6. Mbsdussbla lf Fbambacs............ ........................ ....................... ....................... ........................ .............. Wjco Auieor 3. Dladùsbla .......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 8. Uoforoados.......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx............. ....................... ........................ ....................... ....................... ........................ .....................Wjco .........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 bastjìoats. ]hbs jrrjacoioat jam bts prldoss bs roforrom tl js Hbro Wurdhjso. Flr oxjipò> 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 kalwòmco lf Hbro Wurdhjso tl jssbst thoi ba bavostbcjtbac vjrblus Hbro Wurdhjso p`jas.

]ho purplso lf thbs prlnodt bs tl 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 DL@@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`òdtom 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 bastjìoats (m) al mlwa pjyioat jam 5= ilath`y bastjìoats

42

WULNOD] 5

TOD]BLA 7= WUOTOA]J]BLA LF MJ]J T]LUO J ]ypo lf W`ja

Iothlm lf Wjyioat W`ja

Djsh

lao-lff fu`` pjyioat

]ypo lf W`ja


Dlst lf `bvbac rlli sot ($) : 5 , 4 7 2 .6 7

Uocu`jr Wrbdo ($)

Dlst lf `bvbac rlli sot ($)

Hbro Wurdhjso W`ja j

4 ilaths flr djsh

:?,483.77

: 6 ,: ? 6 .4 ?

Hbro Wurdhjso W`ja e

: yojr jt rocu`jr prbdo

:?,483.77

: 8 ,= 6 = .= 7

Hbro Wurdhjso W`ja d

Mlwa pjyioat jam 5= oquj` ilath`y bastjìoats

:?,483.77

5 : ,? = : .8 7

Hbro Wurdhjso W`ja m

Al mlwa pjyioat jam 5= ilath`y bastjìoats

:?,483.77

5 : ,? = : .8 7

T]LUO E ]ypo lf W`ja


Djsh


]ypo lf W`ja


Dlst lf `bvbac rlli sot ($) : 5 , 8 7 7 .7 7

Uocu`jr Wrbdo ($)



4 ilaths flr djsh

:6,777.77

: 6 ,8 7 7 .7 7



:6,777.77

: 2 ,5 7 7 .7 7



:6,777.77

5 5 ,= 7 7 .7 7



:6,777.77

5 5 ,= 7 7 .7 7

=7

T]LUO D ]ypo lf W`ja


Djsh


]ypo lf W`ja


Dlst lf `bvbac rlli sot ($) : 5 ,4 7 2 .6 7

Uocu`jr Wrbdo ($)



4 ilaths flr djsh

: = ,8 7 7 .7 7

: ? ,? = 7 .7 7



: = ,8 7 7 .7 7

: 3 ,3 6 7 .7 7



: = ,8 7 7 .7 7

5 7 ,3 5 7 .7 7



: = ,8 7 7 .7 7

5 7 ,3 5 7 .7 7

T]LUO M ]ypo lf W`ja


Djsh


]ypo lf W`ja

=:


Dlst lf `bvbac rlli sot ($) : : ,5 7 7 .7 7

Uocu`jr Wrbdo ($)



4 ilaths flr djsh

: = ,7 7 7 .7 7

: = ,3 7 7 .7 7



: = ,7 7 7 .7 7

: 6 ,8 7 7 .7 7



: = ,7 7 7 .7 7

: 2 ,6 7 7 .7 7



: = ,7 7 7 .7 7

: 2 ,6 7 7 .7 7

]ho crjph shlws hlw tho djsh prbdo dlipjros tl tho mbfforoat Hbro Wurdhjso p`jas jt stlro J.

57 :8 7 7 7 , : Ó $ A B O D B U W

:6 := :5 :7 78 76 7= 75 j

e

d

m

]RWO LF HBUO W_UDHJTO W@JA

DW

HW WUBDO

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` prbadbpò lf Hbro Wurdhjso p`jas. Wòjso 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>

?% batorost bs jmmom tl tho rocu`jr prbdo.

6 ilaths flr djsh>

: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 $: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 pùs ?% batorost lf tho rocu`jr prbdo. ]hbs jiluat iust eo pjbm ba 4 ilaths. Uocu`jr prbdo 9 $:?,483.77 Batorost

9 9

?% lf rocu`jr prbdo ?

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 bastjìoats 9 4 ∽

Jiluat lf ojdh ilath`y bastjìoat

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 bastjìoats lf $?,48?.=?.

=4

W`ja e> Lao Rojr jt Uocu`jr Wrbdo ]hbs dlasbsts lf tho rocu`jr prbdo pùs 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

$:?,483 + $4,733.=7 9 $:8,=6=.=7

Auieor lf ilath`y bastjìoats 9 :5 ∽


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 bastjìoats lf $:,?48.37.

W`ja d> Mlwa Wjyioat jam 5= Ilath`y Bastjìoats Uocu`jr prbdo

9

$:?,483.77

Batorost

9

=7% lf rocu`jr prbdo

9

=7

Ó

$:?,483

9 $6,:?=.87

:77 ∽


9


9

$:?,483 + $6,:?=.87 9 $5:,?=:.87

Mlwa pjyioat 9 5?% lf dlst lf sot

9

5?

Ó 5:,?=:.8 5:,?=:.8 7

:77 Ej`jado tl eo pjbm ba ilath`y bastjìoat

9

$?,48?.=?

9

dlst lf sot — mlwa pjyioat

9

$5:,?=:.87 — $?,48?.=?

9

$:6,:?6.4?

Auieor lf ilath`y bastjìoats 9 5= ∽


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 bastjìoats lf $634.57 jam ja babtbj` mlwa pjyioat lf $?,48?.=?.

==

W`ja m> Al Mlwa Wjyioat jam 5= Ilath`y Bastjìoats Uocu`jr prbdo

9

$:?,483.77

Batorost

9

=7% lf rocu`jr prbdo

9

=7

Ó

$:?,483

9

$6,:?=.87

:77 ∽


9


9

$:?,483 + $6,:?=.87 9 $5:,?=:.87

Auieor lf ilath`y bastjìoats 9 5= ∽


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 bastjìoats lf $823.67.

=?

WULNOD] 5


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 Djsh prbdo

9 $:5,472.67

Mbfforoado Mbfforoad o ba prbdo

9 ($:6,:?6.4? — $:5,472.67)

9 $:6,:?6.4?

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 Djsh prbdo Mbfforoado Mbfforoad o ba prbdo

9 $:8,=6=.=7 9 $:5,472.67 9 ($: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 Djsh prbdo Mbfforoado Mbfforoad o ba prbdo

9 $ 5:,?=:.=7 9 $:5,472.67 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 Djsh prbdo Mbfforoado Mbffor oado ba prbdo

9 $5:,?=:.87 9 $:5,472.67 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`òdtom, bt bs sooa thjt> :. j`` stlros hjvo tho sjio pjyioat strudturo strudturo js stjtom stjtom ba tho prosoatjtbla lf mjtj. 5. j`` Hbro Hbro Wurdhjso Wurdhjso prbdos lrbcbajtom frli tho tho djsh prbdo. prbdo. 4. purdhjsbac tho `bvbac rlli sot uamor tho djsh p`ja bs tho tho dhojpost lptbla. lptbla. =. flr ojdh iothlm lf Hbro Wurdhjso tho badrojso ba batorost batorost vjrbos badroioatj``y frli 4:% up tl 3?%. ?. thoro bs j dlrro`jtbla dlrro`jtbla eotwooa tho òacth lf tbio lf ropjyioat, tho tho jiluat lf ilath`y bastjìoats, jam tho batorost dhjrcom uamor ojdh p`ja. (o.c. tho `lacor iy pjroats tjko tl ropjy, ropjy, tho sij`òr tho ilath`y bastjìoats jam tho hbchor tho batorost) 6. ]ho la`y truo djsh prbdo bs j lao-lff fu`` pjyioat ijmo jt tho tbio lf purdhjsbac 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 ibsòjm dlasuiors batl eo`bovbac thjt thoy jro pjybac djsh flr tho btoi). ]horo jro ijay pjyioat p`jas jvjb`jeò tl iy pjroats ba purdhjsbac tho `bvbac rlli sot vbj Hbro Wurdhjso. Hlwovor, 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 jeò 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. 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 jìlst mlueò tho djsh prbdo.

=8

WULNOD] 5


]ho bavostbcjtbla lf tho mbfforoat Hbro Wurdhjso pjyioat p`jas rovoj` tho fl``lwbac dj`du`jtblas> :. Dlst lf tho `bvbac rlli 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 rlli sot uamor W`ja e> : yojr jt rocu`jr rocu`jr prbdo 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 W`ja d> mlwa mlwa pjyioat jam 5= ilath`y ilath`y bastjìoats bastjìoats bs $5:,?=:.=7 whbdh roprosoats j 37% badrojso ba batorost la tho djsh prbdo. =. Dlst lf tho `bvbac rlli rlli sot uamor W`ja W`ja m> 5= ilath`y bastjìoats bastjìoats 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


Croor, J. & @jyao, D. O. (:22:) Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja.

]ll`sbo, U, (:222). J Dlipòto 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 Wurdhjso/Uocu`jr prbdo >

Lao fu`` pjyioat jt tho tbio lf purdhjso tho Hbro Hbro Wurdhjso Wurdhjso prbdo bs j`sl roforrom tl js tho Uocu`jr 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 tho Hbro Wurdhjso prldoss.

Bastjìoats

>

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 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 òttor 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


Ja bavostbcjtbla batl tojdhors‒ puadtuj`bty jam rocu`jrbty jt j clvoraioat sdhll`.

?5

WULNOD] 4


]JE@O LF DLA]OA]T :. ]btò....... ]btò................... ........................ ........................ ....................... ....................... ........................ ....................... ............. Wjco Auieor Auieor 5. Batrlmudtbla ............ ........................ ....................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla .......... ...................... ........................ ....................... ....................Wjco .........Wjco Auieor =. Wrosoatjtbla lf Mjtj........... ...................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj ........... ....................... ....................... ....................... ........................ ....................... ............. Wjco Auieor 6. Mbsdussbla lf Fbambacs........... ...................... ....................... ........................ ....................... .............. ... Wjco Auieor 3. Dladùsbla ........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 8. Uoforoados........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx.............. ........................ ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor Ttjkohl`mors sudh js W]J, òjmors 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 durrbduùi 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 DL@@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 sjipò sbzo dlasbstom lf =? tojdhors.

?=

WULNOD] 4

TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Jftor tho mjtj woro dl`òdtom, thoy woro lrcjabzom usbac j tjeò, dlipjrjtbvo ejr dhjrts jam froquoady tjeòs js fl``lws> ]ho tjeò shlws tho auieor lf tojdhors whl woro `jto jam jesoat flr tho pjrtbdu`jr ilath

Sook Mjy Ilamjy

@jto

Jesoat

Wrosoat

:7

::

4=

:5

:=

4:

: ]uosmjy k o Somaosmjy o S

:=

78

43

]hursmjy

:3

:=

4:

Frbmjy

:=

:=

4:

Ilamjy

::

74

=5

:4

73

48

5 ]uosmjy k o Somaosmjy o S

:6

72

46

]hursmjy

:6

76

42

Frbmjy

:5

:3

58

Ilamjy

72

:5

44

:6

::

4=

4 ]uosmjy k o Somaosmjy o S

:7

72

46

]hursmjy

:5

74

=5

Frbmjy

::

:=

4:

Ilamjy

:5

:5

44

:5

78

43

= ]uosmjy k o Somaosmjy o S

72

72

46

]hursmjy

78

75

=4

Frbmjy

:7

57

5?

]jeò Lao

??

Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook Lao

] 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

JETOA]

Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook ]wl


57 :8 :6 := :5 :7 78 76 7= 75

ILA

]_OT

SOM

]H_U

FUB


JETOA]

?6

Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook ]hroo


57 :8 :6 := :5 :7 78 76 7= 75

ILA

]_OT

SOM

]H_U

FUB


JETOA]

Ejr crjph shlwbac auieor lf tbios `jto jam jesoat ba Sook Flur


57 :8 :6 := :5 :7 78 76 7= 75

ILA

]_OT

SOM

]H_U

FUB


?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 ]jeò ]wl> Froquoady tjeò shlwbac hlw tho rjw mjtj woro lrcjabsom ]bio ]bi o ba ba ibaut ibautos os Aui Auieor eor lf ]ojd ]ojdhor hors s : — :7

:4

:: — 57

76

5: — 47

:7

4: — =7

7?

=: — ?7

73

?: — 67

7=

]jeò ]hroo> ]jeò shlwbac tho dj`du`jtbla lf tho ioja auieor lf ibautos `jto ey tojdhors ba j ilath ]bio ba Ibautos

Auieor lf ]ojdhors (f)

Ibmplbat x

fÓx

: — :7

:4

?.?

3:.?

:: — 57

76

:?.?

24

5: — 47

:7

5?.?

5??

4: — =7

7?

4?.?

: 33 .?

=: — ?7

73

=?.?

4 :8 .?

?: — 67

=

??.?

5 55

√ f 9 =?

]ho sui lf f 9 ]ho sui lf fx 9

=?

]ho ioja x̍̍

√fx 9 ::43.? 9 5?.4 ibautos

9

√fx 9 :,:43.?

:,:43.7 √f

=?

?8

Tdjò> :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

]jeò Flur> ]ho tjeò 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,

y

mjy.

`jto la mjy y Ó:77% J

x Ó:77% J

x Ilamjy

=?

::

:7

5=

55

]uosmjy

=?

:=

:5

4:

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

=?

4

::

3

5=

]uosmjy

=?

3

:4

:6

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


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.


x Ó:77% J

Ilamjy

=?

:5

:5

53

53

]uosmjy

=?

8

:5

:8

53

Somaosmjy

=?

2

2

57

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

>

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%


53+52+57+3+4:

9 55.8%

?

Sook Flur Jvorjco pordoatjco lf tojdhors `jto

>

53+53+57+:8+55

9 55.8%


53+:8+57+=+==

9 55.6%

?

65

WULNOD] 4


]jeò Flur shlws thjt frli j stjff lf =? tojdhors> :. Ba Sook Lao, jpprlxbijto`y jpprlxbijto`y 53% lf tho tojdhbac stjff wjs jesoat mjb`y mjb`y jam 47% lf tojdhors woro `jto mjb`y 5. Ba Sook ]wl, ]wl, jpprlxbijto`y jpprlxbijto`y :2% lf tho tojdhbac stjff stjff wjs jesoat mjb`y mjb`y jam 4:% lf tojdhors woro `jto mjb`y 4. Ba Sook ]hroo, ]hroo, jpprlxbijto`y jpprlxbijto`y 54% lf tho tho tojdhbac stjff stjff wjs jesoat mjb`y jam 56% lf tojdhors woro `jto mjb`y =. Ba Sook Flur, Flur, jpprlxbijto`y jpprlxbijto`y 54% lf tho tojdhbac tojdhbac stjff wjs 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 rovojòm thjt flr tho ilath uamor dlasbmorjtbla> :. 54% lf tojdhor woro woro jesoat la j mjb`y ejsbs 5. 58% lf tojdhor woro woro `jto la j mjb`y ejsbs ]jeò ]wl ]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 rovojòm 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 jam la lao mjy tho sjio auieor wjs `jto js 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 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. mjy. ]hbs bs ovbmoat ba tho fjdt thjt la tho Frbmjy lf> (j) Sook Lao

—

:= tojdhors woro jesoat

(e) Sook ]wl

—

:3 tojdhor tojdhors s woro jesoat

(d) Sook ]hroo

—

:= tojdhors woro jesoat

(m) Sook Flur

—

57 tojdhors woro jesoat

]jeò ]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


]ho ﬊ambacs rovojòm 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 mjy ba cottbac tl sdhll` jam tho jesoatoobsi rjto bs hbch.

66

WULNOD] 4


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] =


Ja bavostbcjtbla ba lrmor tl motoribao bf tho Tdhll` Foombac Wrlcrjiio badrojsos puadtuj`bty jam rocu`jrbty jt j pjrtbdu`jr sdhll`.

68

WULNOD] =


]JE@O LF DLA]OA]T :. ]btò....... ]btò................... ........................ ........................ ....................... ....................... ........................ ....................... ............. Wjco Auieor Auieor 5. Batrlmudtbla ............ ........................ ....................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla .......... ...................... ........................ ....................... ....................Wjco .........Wjco Auieor =. Wrosoatjtbla lf Mjtj........... ...................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj ........... ....................... ....................... ....................... ........................ ....................... ............. Wjco Auieor 6. Mbsdussbla lf Fbambacs........... ...................... ....................... ........................ ....................... .............. ... Wjco Auieor 3. Dladùsbla ........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 8. Uoforoados........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx.............. ........................ ....................... ....................... ........................ ....................... ....................Wjco .........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 oarlìoat

•

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 DL@@OD]BLA ]ho mjtj wjs dl`òdtom vbj j quostblaajbro. ]ho quostblaajbro dlasbstom lf obcht (8) pro-sot stjamjrmbzom stjamjrmbzom quostblas, ba lrmor tl j``lw tho sjio baflrijtbla tl eo coaorjtom frli ojdh stumoat. ]ho quostblas woro jskom ba tho sjio lrmor. lrmor. ]ho sjipò dlasbstom lf :77 stumoats, 57 lf whli woro dhlsoa frli ojdh flri òvo`. ]horo jro = d`jssos jt ojdh flri òvo` 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 ùadh erojk jftor stumoats wlu`m hjvo dlasuiom tho erojkfjst jam ùadh. (Too jppoambx flr

quostblaajbro usom ba survoy) Bt tllk flur (=) wooks tl dl`òdt tho mjtj frli tho sjipò sbzo.

37

WULNOD] =

TOD]BLA 7= WUOTOA]J]BLA LF MJ]J Jftor tho mjtj wjs dl`òdtom, bt wjs lrcjabzom jam prosoatom usbac tjeòs, dlipjrjtbvo dlipjrjtbv o ejr dhjrts jam pbo dhjrts js fl``l fl``lws. ws. :. ]ho tjeò eo`lw shlws tho auieor auieor lf stumoats pjrtbdbpjtom pjrtbdbpjtom ba tho sdhll` foombac prlcrjiio Flr lri i

Auie Au ieor or Wjrt rtj jkb kba ac

Auie Au ieor or Al Altt Wjr jrtj tjkb kba ac

:

:8

5

5

:?

?

4

:=

6

=

:5

8

?

:7

:7

62

4: ]jeò :

]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 :

3:

5

4 FLUI D@JTT

=

?

Fbcuro : ROT

AL

5. ]ho tjeò eo`lw shlws tho auieor lf stumoats ey flri flr i 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:

:7 7

Flri

]ltj`

]jeò 5 4. ]ho tjeò 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

:7 7

Flri

]ltj`

]jeò 4 =. ]ho tjeò 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

:

:

5

Tdhll` Foombac

Djfotorbj

]ltj`

:8

:

57

4

:?

5

57

4

5

:=

=

57

=

5

:5

6

57

?

4

:7

3

57

::

62

57

: 77

Wrlcrjiio

]jeò =

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 tjeò eo`lw shlws tho auieor lf stumoats whl jttoamom sdhll` rocu`jr`y flr ùadh frli tho Tdhll` Foombac Wrlcrjiio Jttoam Tdhll`

Ml Alt Jttoam

flr @uadh

Tdhll` flr @uadh

:

:8

5

5

:?

?

4

:=

6

=

:5

8

?

:7

:7

62

4:

Flri

]jeò ?

34

6. ]ho tjeò eo`lw shlws tho auieor lf stumoats whl hjm ùadh ovory mjy ey flri. Auieor Hjvbac

Auieor Alt Hjvbac

@uadh Ovory Mjy

@uadh Ovory Mjy

:

57

7

5

57

7

4

57

7

=

57

7

?

57

7

:7 7

7

Flri

]jeò 6 3. ]ho tjeò shlws tho auieor lf stumoats whl letjba ùadh frli tho Tdhll` Foombac Wrlcrjiio

Shoro ùadh bs letjbaom

Flri

Hlio

:

:

5

Tdhll` Foombac

Djfotorbj

]ltj`

:8

:

57

4

:?

5

57

4

5

:=

=

57

=

5

:5

6

57

?

4

:7

3

57

::

62

57

:7 7

Wrlcrjiio

3=

]ho pbo dhjrt shlws tho prlplrtbla lf stumoats whl letjbaom ùadh frli tho Tdhll` Foombac Wrlcrjiio, hlio jam djfotorbj.

Hlio

Djfotorbj

Tdhll` Foombac Wrlcrjiio

3?

WULNOD] =


]jeò : shlws thjt lut lf tho :77 stumoats whl woro survoyom, 62 woro pjrtbdbpjats lf tho Tdhll` Foombac Wrlcrjiio, whbdh iojas thjt 62% lf tho sjipò woro rodbpboats lf ioj`s frli tho Tdhll` Foombac Wrlcrjiio. ]jeò : 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 ]jeò 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 Foombac Wrlcrjiio 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 ]jeò 4 jam 6 shlw thjt :77% lf tho stumoats survoyom hjm erojkfjst jam ùadh ovory mjy. Hlwovor, tjeòs 5 jam = shlw thjt 62% clt erojkfjst jam ùadh frli tho Tdhll` Foombac Wrlcrjiio; whb`st ::% clt frli hlio jam 57% frli tho djfotorbj. ]hbs bs b`ùstrjtom ba Fbcuro 5 jam 4. Ba dlastrudtbac tho pbo dhjrts, jacòs woro dj`du`jtom tl roprosoat tho sodtlrs>

- Tdhll` Foombac Wrlcrjii Wrlcrjiio o - hlio - djfotorbj

]hbs wjs mlao js fl``lws> Tdhll` Foombac Wrlcrjiio

62

Hlio

::

Djfotorbj

57 :77

36

Jacò roprosoatb roprosoatbac ac Tdhll` Foombac Wrlcrjiio 9

62

Ó 467· 9 5=8.=·

:77 Jacò roprosoatb roprosoatbac ac Hlio

9

::

Ó 467· 9 42.6·

:77 Jacò roprosoatb roprosoatbac ac 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 ùadh frli tho sdhll` foombac prlcrjiio. ]horoflro, bf j stumoat bs dhlsoa jt rjamli frli tho sjipò, tho prlejeb`bty lf thjt dhb`m jrrbvbac ojr`y flr erojkfjst jam rocu`jr`y flr ùadh bs 62% lr 7.62

33

WULNOD] =

TOD]BLA 76 MBTD_TTBLA MBT D_TTBLA LF FBAMBACT J`thluch j`` lf tho stumoats survoyom hjm erojkfjst jam ùadh 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 prlcrjii prlcrjiio. o. ]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] =


Cbvoa tho hbch prlplrtbla lf stumoats whl jrrbvo ojr`y jam rocu`jr`y flr tho Tdhll` Foombac Wrlcrjiio, lao dja dladùmo 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] =


www.wbkbhlw.dli www.ttdlaaodt.clv.tt www.cujrmbja.dl.tt

87

WULNOD] =

TOD]BLA 72 JWWOAMBX

Z_OT]BLAAJBUO FLU T_UVOR

:. Wòjso 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 ùadh<

 Ros

 Al

3. Ml ylu hjvo ùadh ovory mjy<

 Ros

 Al

8. Bf tho jaswor tl quostbla 3 bs yos, thoa whoro ml ylu cot ùadh<

 Hlio

8:

 Tdhll`

 Djfotorbj

WULNOD] ?


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] ?


]JE@O LF DLA]OA]T :. ]btò....... ]btò................... ........................ ........................ ....................... ....................... ........................ ....................... ............. Wjco Auieor Auieor 5. Batrlmudtbla ............ ........................ ....................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla .......... ...................... ........................ ....................... ....................Wjco .........Wjco Auieor =. Wrosoatjtbla lf Mjtj........... ...................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj ........... ....................... ....................... ....................... ........................ ....................... ............. Wjco Auieor 6. Mbsdussbla lf Fbambacs........... ...................... ....................... ........................ ....................... .............. ... Wjco Auieor 3. Dladùsbla ........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 8. Uoforoados........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx.............. ........................ ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor Iy mjm hjs modbmom tl stjrt j sij`` eusbaoss tl suppòioat 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`òm `baojr prlcrjiibac tl ho`p hbi ilmo` hbs eusbaoss p`ja. @baojr prlcrjii prlcrjiibac bac 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.

Shbò trybac tl ostje`bsh tho eusbaoss, mjm ijy oadluator `bibtjtblas jam rostrbdtblas. ]hoso `bibtjtblas jam rostrbdtblas jro dj`òm dlastrjbats.

84

WULNOD] ?

TOD]BLA 74 IO]HLM LF MJ]J DL@@OD]BLA :. B vbsbtom j plu`try fjri jam dl`òdtom mjtj js fl``lws> (b) whlòsjò prbdos la dhbdkoas jam mudks (bb) tho ibabiui auieor lf ebrms thjt iust eo purdhjsom ba lrmor tl letjba tho whlòsjò prbdo. (bbb) tho succostom prbdos jt whbdh tho ebrms dja eo rotjbòm. (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`òdtom shlws, thjt ba lrmor tl letjba whlòsjò jam rotjb` prbdos, mjm iust sjtbsfy tho fl``lwbac flur dlastrjbats> :. Ho iust euy euy jt òjst :7 mudks; thbs thbs iojas thjt tho ibabiui jiluat lf mudks mudks thjt ho dja purdhjso bs :7 5. Ho iust euy euy jt òjst 57 dhbdkoas; thbs thbs iojas thjt ho iust euy euy 57 lr ilro ilro dhbdkoas 4. Ho hjs stlrjco stlrjco spjdo flr la`y 34 ebrms; ebrms; thbs iojas thjt ho djaalt euy ilro ilro thja 34 ebrms. =. Ho la`y hjs $4,777.77 tl spoam la ebrms. 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‒ mjm‒s s eusbaoss ilmo`, ojdh dlastrjbat wb`` cbvo rbso tl ja baoquj`bty. baoquj`bty. Ba lrmor tl wrbto baoquj`btbos, wo iust batrlmudo vjrbjeòs. Flr thbs ilmo`, B wb`` uso twl vjrbjeòs, x jam y. B wb`` òt x roprosoat tho auieor lf mudks jam y roprosoat tho auieor lf dhbdkoas thjt mjm wjats tl purdhjso. :. Mjm iust euy jt òjst òjst :7 mudks ]hoa x iust eo crojtor thja lr oquj` tl :7 ]hbs bs wrbttoa js x ≯ :7 5. Ho iust euy euy jt òjst 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 ebrms ]hoa tho tltj` auieor lf ebrms iust eo òss 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 òss thja lr oquj` tl $4777.77 ]hbs bs wrbttoa js 87x + 47y ≭ $4,777.77 Ojdh lf tho jelvo baoquj`btbos wb`` roprosoat roprosoat j rocbla la j crjph shoot. ]l bmoatbfy 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 87x + 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

7

34

y

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

Tdjò> 5di ≪:7 mudks la hlrbzlatj`, 5di ≪:7 dhbdkoas la vortbdj`

:77

x 9 :7

27

87 ) T A O K 37 D B 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] ?


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 stjtos stj tos thjt lao lf tho flur vortbdos wb`` cbvo vjùos lf x jam y thjt wb`` ijxbibzo tho oqujtbla W 9 37 37x x + 47y 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 iojas thjt bf mjm purdhjsos :6 mudks mudks jam ?3 dhbdkoas, ho wb`` 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 MBT D_TTBLA LF FBAMBACT ]hbs sbipò `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 oxjipò, ejsom la hbs mocroo lf froomli, mjm kalws thjt> :. bf ho purdhjsos purdhjsos :7 mudks jam 57 dhbdkoas, dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $:,477.77 por wook. 5. bf ho purdhjsos purdhjsos :7 mudks jam 64 dhbdkoas, dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,?27.77 por wook. 4. bf ho purdhjsos purdhjsos :6 mudks jam ?3 dhbdkoas, dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,847.77 por wook. =. bf ho purdhjsos purdhjsos 47 mudks jam 57 dhbdkoas, dhbdkoas, ho wb`` roj`bzo j prl﬊t lf $5,377.77 por wook.

Hoado, mjm alw kalws tho oxjdt auieor lf mudks jam j am dhbdkoas ho iust purdhjso wook`y wbthba tho cbvoa dlastrjbats ba lrmor tl ijxbibzo prl﬊t la hbs bavostioat.

27

WULNOD] ?


Ejsom la tho ﬊ambacs, bt dja eo dladùmom 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] ?


Croor, J. & @jyao, D. O., (:287); Dortb﬊djto Ijthoijtbds> J Uovbsbla Dlurso flr tho Djrbeeoja.

]ll`sbo, U.; Ijthoijtbds> J Dlipòto Dlurso wbth DXD Zuostblas. Vl`. 5 www.ijth.ud`j.omu www.ijthswlrk.dli

25

WULNOD] 6


Ja bavostbcjtbla tl motoribao tho ijxbiui jroj lf j vocotjeò cjrmoa thjt dja eo dlastrudtom frli frli j cbvoa p`lt lf `jam.

24

WULNOD] 6


]JE@O LF DLA]OA]T :. ]btò....... ]btò.................. ....................... ........................ ........................ ....................... ....................... ........................ .............. Wjco Auieor Auieor 5. Batrlmudtbla ........... ....................... ........................ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla ............ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor Auieor =. Wrosoatjtbla lf Mjtj............ ........................ ....................... ....................... ........................ ................. .....Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj Mjtj ............ ........................ ....................... ....................... ........................ .......................Wjco ...........Wjco Auieor 6. Mbsdussbla lf Fbambacs............ ........................ ....................... ....................... ........................ .............. Wjco Auieor 3. Dladùsbla .......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 8. Uoforoados.......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx............. ....................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor ]l moj` wbth rbsbac prbdos, iy pjroats jam B hjvo modbmom tl drojto j vocotjeò 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 prbadbpò 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 DL@@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`jeò `jam. So j`sl iojsurom tho òacth lf tho wbro thjt mjm hjm ba stlrjco. ]ho `jam hjm j rluch rodtjacu`jr shjpo, thoroflro, wo iojsurom tho òacth jam wbmth js jddurjto`y js plssbeò.

2?

WULNOD] 6

TOD]BLA 76 WUOTOA]J]BLA LF MJ]J ]ho mjtj dl`òdtom rovojòm thjt> (b) ]ho òacth lf tho jvjb`jeò `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 jpprlxbijto`y 6?7 sq. iotros). (bv) ]ho òacth lf tho wbro tl eo usom bs :77 iotros `lac.

y iotros : iotro flltpjth

Vocotjeò 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 òacth 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

9 ?7

91

9 ?7 — x (Oqujtbla :)

y

26

Tbado thoro bs j : iotro fllt pjth jrluam tho cjrmoa; tho Sbmth lf tho cjrmoa

9 (x — 5) iotros

@oacth lf tho cjrmoa

9 ( y — 5) iotros

Tuestbtuto y

9 ?7 — x frli oqujtbla : batl tho òacth tl cot>

@oacth lf Cjrmoa

9 (?7 — x — 5) iotros 9 (=8 — x) iotros

Jroj lf rodtjacu`jr vocotjeò cjrmoa bs òacth iu`tbp`y ey wbmth ∽

Jroj 9 (=8 — x) (x — 5) 9 =8x — 26 — x5 + 5x 9 ?7x — 26 — x5

Flr tho ro`jtbla J 9 ?7x — 26 — x5, j tjeò lf vjùos lf plssbeò wbmths, x, wjs tjeu`jtom, j crjph lf J vs x wjs mrjwa flr tho mlijba vjùos ? ≭ x ≭ =?

x

?

:7

:?

57

5?

47

4?

=7

=?

J

:52

47 =

=5 2

? 7=

? 52

?7=

=5 2

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 )

5

i=77 ( s o r t o i o477 r j u q s a b j577 o r J

:77

7 7

?

:7

:?

Fbcuro :> Tdjò usom> :di

≪

:di

≪

57 5? 47 @oacth ba iotros (i)

4?

=7

=?

?7

? iotros la hlrbzlatj` jxbs, :77 squjro iotros la vortbdj` jxbs

Alto> ]ho òacth lf tho jvjb`jeò `jam bs 52.3 i. ]horoflro, dhllsbac mlijba vjùos (x) thjt jro crojtor thja 52 iotros wb`` sorvo al

23

prjdtbdj` purplso ba tho prlnodt. ]hoso vjùos woro badùmom strbdt`y flr tho thorlrotbdj` purplso lf letjbabac j dlipòto pjrjel`bd shjpo la tho crjph.

WULNOD] 6


Frli tho crjph> :. ]ho ijxbiui vjùo lf J bs ?52 squjro iotros 5. ]ho ijxbiui jroj lddurs whoa x 9 5? iotros ]ho òacth lf tho `jam tl eo foadom tl cbvo tho ijxbiui jroj lf tho vocotjeò 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 vocotjeò cjrmoa bs>

x 9 5? i (frli crjph) ]ho ijxbiui jroj lf tho vocotjeò cjrmoa bs ?52 iotros5 (frli crjph) Vorbfybac Vorb fybac tho crjphbdj` rosu`ts ey dj`du`jtbla wo cot> (b) wbmth lf vocotjeò cjrmoa

9

(x — 5) iotros

9

(5? — 5) iotros

9

54 iotros (y — 5) iotros

(bb) òacth lf vocotjeò cjrmoa 9

Jroj lf vocotjeò cjrmoa

9

(5? — 5) iotros

9

54 iotros

9

òacth Ó wbmth

9

(y — 5) (x — 5)

9

(54 Ó 54) iotros5

9

?52 iotros5

]ho vocotjeò cjrmoa dja eo dlastrudtom usbac tho jelvo mbioasblas sbado tho jroj lf ?52 iotros5 bs wbthba tho jroj lf tho jvjb`jeò `jam, whbdh bs 6?7 iotros 5. J`sl tho jroj lf tho p`lt lf `jam tl eo foadom whbdh wb`` dlatjba tho vocotjeò cjrmoa jam tho lao iotro flltpjth bs (5? Ó 5?) iotros5 9 65? iotros5 ]hbs tll bs wbthba tho jroj lf tho jvjb`jeò `jam tl eo usom flr dlastrudtbla.

28

WULNOD] 6

TOD]BLA 76 MBTD_TTBLA MBT D_TTBLA LF FBAMBACT So dja ojsb`y dlastrudt j vocotjeò cjrmoa ey oad`lsbac ja jroj lf `jam jt tho ejdk lf tho hluso wbthlut dlasbmorbac jay rbclrlus jaj`ysbs. Hlwovor, thbs sbipò j`coerjbd ilmo` puts us ba j plsbtbla tl ijko ilro baflriom dhlbdos ba toris lf tho mbioasblas tl eo usom. Flr oxjipò, 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 vocotjeò cjrmoa tl tl eo oad`lsom wbth j lao iotro pjthwjy pjthwjy jrluam bt bs j porfodt squjro lf ?52 squjro iotros wbth mbioasblas 54 iotros ey 54 iotros. 4. ]hbs dlastrudtbla wb`` wb`` stb`` òjvo j rojslajeò jiluat lf `jam spjdo jrluam jrluam tho oad`lsom jroj. =. ]ho `jam spjdo spjdo roijbabac jftor dlastrudtbla lf foado bs (6?7 — 65?) squjro squjro iotros iotros 9 5? squjro iotros. ]hbs spjdo wb`` j``lw flr tho mlcs tl p`jy lutmllrs.

22

WULNOD] 6


]ho ﬊ambacs rovoj` thjt tho ijxbiui jroj lf j vocotjeò cjrmoa thjt dja eo sot up frli ja jvjb`jeò 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

Vocotjeò Cjrmoa

lutor foado

:i

5? iotros

:i 5? iotros ILMO@ LF DLIW@O]OM DLAT]U_D]BLA

:77

WULNOD] 6


D`jrko, @. Hjrwllm, Jmmbtblaj` Wuro Ijthoijtbds , 4rm Ombtbla Hoac, H. H.; ]jèort, N. F., Jmmbtblaj` Ijthoijtbds, 6th Ombtbla www.uadw.omu/jòcerj www.vjrsbtytutlrs.dli

:7:

WULNOD] 6

TOD]BLA 72 JWWOAMBX

DJ@D_@J]BLA LF UJACO J 9 ?7x — 26 — x5

x

?

:7

:?

57

5?

47

4?

=7

=?

J

: 52

47 =

=5 2

?7 =

? 52

? 7=

= 52

47 =

:52

Shoa

Shoa

Shoa

Shoa

Shoa

Shoa

Shoa

9

?i

9

?7 Ó ? — 26 — ?5

9

5?7 — 26 — 5? 9 :52 i5

x

9

:7i

J

9

?7 Ó :7 — 26 — :75

9

?77 — 26 — :77 9 47= i5

x

9

:?i

J

9

?7 Ó :? — 26 — :?5

9

3?7 — 26 — 55? 9 =52 i5

x

9

57i

J

9

?7 Ó 57 — 26 — 575

9

:777 — 26 — =77 9 ?7= i5

9

5?i

9

?7 Ó 5? — 26 — 5?5

9

:5?7 — 26 — 65? 9 ?52 i5

9

47i

9

?7 Ó 47 — 26 — 475

9

:?77 — 26 — 277 9 ?7= i5

9

4?i

9

?7 Ó 4? — 26 — 4?5

9

:3?7 — 26 — :55? 9 =52 i5

x J

x J

x J

x J

:75

WULNOD] 3


Drojtbac tho ilst dlst offodtbvo offodtbvo eumcot tl dlipòto j rlli iojsurbac :=‒ x :5‒ x :7‒.

:74

WULNOD] 3


]JE@O LF DLA]OA]T :. ]btò....... ]btò.................. ....................... ........................ ........................ ....................... ....................... ........................ .............. Wjco Auieor Auieor 5. Batrlmudtbla ........... ....................... ........................ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla ............ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor Auieor =. Wrosoatjtbla lf Mjtj............ ........................ ....................... ....................... ........................ ................. .....Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj Mjtj ............ ........................ ....................... ....................... ........................ .......................Wjco ...........Wjco Auieor 6. Mbsdussbla lf Fbambacs............ ........................ ....................... ....................... ........................ .............. Wjco Auieor 3. Dladùsbla .......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 8. Uoforoados.......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx............. ....................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor Iy pjroats hjvo nust dlipòtom 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 tbòs 5. pjbatbac tho wj``s yo``lw yo``lw,, mllrs eùo 4. bastj``bac j dob`bac lf obthor cypsui lr W.V .V.D. .D. pjao`s

Sbth iy kalwòmco 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 dlipòto tho rlli.

:7=

WULNOD] 3

TOD]BLA 74 IO]HLM LF MJ]J DL@@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 badùmom 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`òdtom frli tho = mbfforoat hjrmwjro stlros jam tho 5 wlrkioa, bt wjs lrcjabzom jam prosoatom ba tjeòs js fl``lws>

Ostbijto frli Hjrmwjro J Zujatbty

Mosdrbptbla

_abt Wrbdo $

Jiluat $

: 77

:6’ x :6’ dorjibd ﬅllr tbòs

5 7.77

5,777.77

= ejcs

thbasot

=7 .77

:67.77

6 ès

crlut

57 .77

:57.77

: pk

tbò spjdos

6 7.7 7

67.77

: cj`

dladroto prbior

: 87 .77

:87.77

: cj`

wjtor ejsom pjbat

5 ?7 .7 7

5?7.77

° cj`

wllm pjbat

3 7.7 7

37.77

=? pbodos

5=’ x 5=’ cypsui dob`bac tbòs

47 .7 7

:,4?7.77 =,:27.77

VJ] G :5.?%

?54.3?

]ltj`

=,3:4.3?

Ostbijto frli Hjrmwjro E Zujatbty

Mosdrbptbla

_abt Wrbdo $

Jiluat $

: 77


: 8.77

:,877.77

= ejcs

thbasot

=? .77

:87.77

6 ès

crlut

56 .77

:7=.77

: pk

tbò spjdos

3 7.7 7

37.77

: cj`

dladroto prbior

: ?7 .77

:?7.77

: cj`

wjtor ejsom pjbat

5 47 .7 7

547.77

° cj`

wllm pjbat

2 7.7 7

27.77

=? pbodos

5=’ x 5=’ cypsui dob`bac tbòs

4? .7 7

:,?3?.77 =,:22.77

VJ] G :5.?%

?5=.88

]ltj`

=,354.88

:76

Ostbijto frli Hjrmwjro D Zujatbty

Mosdrbptbla

_abt Wrbdo $

Jiluat $

: 77


:3.77

:,377.77

= ejcs

thbasot

=7.77

:67.77

6 ès

crlut

47.77

:87.77

: pk

tbò spjdos

6?.77

6?.77

: cj`

dladroto prbior

:57.77

:57.77

: cj`

wjtor ejsom pjbat

577.77

577.77

° cj`

wllm pjbat

:7?.77

:7?.77

:? òacths

:7’ W.V.D. pjao`s G :2 ¹ ft.

37.77

:,7?7.77 4,?87.77

VJ] G :5.?%

==3.?7

]ltj`

=,753.?7

Ostbijto frli Hjrmwjro M Zujatbty

Mosdrbptbla

_abt Wrbdo $

Jiluat $

: 77


:3.77

:,377.77

= ejcs

thbasot

=?.77

:87.77

6 ès

crlut

57.77

:57.77

: pk

tbò spjdos

47.77

47.77

: cj`

dladroto prbior

:57.77

:57.77

: cj`

wjtor ejso pjbat

:?7.77

:?7.77

° cj`

wllm pjbat

?7.77

?7.77

:? òacths

:7’ W.V.D. pjao`s G :2 ¹ ft.

?7.77

3?7.77 4,:77.77

:73

VJ] G :5.?%

483.?7

]ltj`

4,=83.?7

@jelur Dlst> ]wl wlrkioa whl woro soòdtom 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

Hjrmwjro J

$=,3:4.3?

Hjrmwjro J

$=,3:4.3?

@jelur Sl Slrkija #: #:

$5,777.77

@jelur Sl Slrkija #5 #5

$:,?77.77

]ltj`

$6,3:4.3?

Hjrmwjro E

$=,354.88

Hjrmwjro E

$=,354.88


$5,777.77


$:,?77.77

]ltj`

$6,354.88

Hjrmwjro D

$=,753.?7

Hjrmwjro D

$=,753.?7


$5,777.77


$:,?77.77

]ltj`

$6,753.?7

Hjrmwjro M

$4,43?.77

Hjrmwjro M

$4,=83.?7


$5,777.77


$:,?77.77

]ltj`

$?,43?.7 7

$6,5:4.3?

$6,554.88

$?,?54.?7

$=,283.?7

Wòjso alto thjt Hjrmwjro J jam Hjrmwjro E hjm al WVD dob`bac la sjò. ]horoflro, WVD dob`bac wjs alt sooa ba tho eumcots flr Hjrmwjro J jam Hjrmwjro E. Hjrmwjro Hjrmwjr o D jam Hjrmwjr Hjrmwjro o M hjm al cypsui la sjò. ]horoflro, cypsui tbòs 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 tbò tho ﬅllr jro> (b) tbòs (bb) thbasot (bbb) crlut (bv) tbò spjdors

(b) ]bòs Lao ﬅllr tbò iojsuros :6’ x :6’ whbdh bs :.444 foot x :.444 foot. Tbado tho tbòs hjvo j squjro shjpo jam tho jroj lf j squjro bs sbmo x sbmo, bt fl``lws thjt tho jroj lf : tbò 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 rodtjacò bs òacth x wbmth, bt fl``lws thjt tho jroj lf tho ﬅllr tl eo tbòm bs := foot x :5 foot 9 :68 squjro foot. ]l tbò ja jroj lf :68 squjro foot usbac :.8 squjro foot tbòs, tho auieor lf tbòs aoomom bs :68 squjro foot 9 2= tbòs jpprlxbijto`y. :.8 squjro foot Ja oxtrj 6 tbòs jro tl eo elucht ba lrmor tl ijko prlvbsbla flr erojkjco. ∽

]ltj` auieor lf tbòs tl eo elucht bs :77.

]hbasot

]hbasot bs tho ijtorbj` usom tl p`jstor tho ﬅllr eoflro `jybac tho tbòs. ]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 =7

∽

]ho tltj` auieor lf ejcs lf thbasot tl eo elucht bs = ejcs

Crlut

Crlut bs tho ijtorbj` usom tl soj` tho spjdos eotwooa ojdh tbò. ]ho baflrijtbla la tho pjdkjco stjtos thjt : luado lf crlut soj`s jpprlxbijto`y lao :6’ x :6’ tbò. ∽

]ho jiluat lf crlut aoomom bs : luado ey 2= tbòs 9 2= luados 9 ?.2 ès

∽

]ho jiluat lf crlut tl eo elucht bs 6 pluams

]bò Tpjdors

]bò spjdors jro usom tl drojto tho ovoa spjdo eotwooa ojdh tbò. ]bò spjdors jro sl`m ba pjdkjcos lf :77 por pjdk. ∽

]ho jiluat lf spjdors aoomom flr 2= tbòs bs : pjdk Tuiijry lf btois aoomom flr tb`bac tho ﬅllr jro js fl``lws> = ejcs lf thbasot 6 ès lf crlut

:72

: pjdk lf spjdors

Dob`bac ]ho spjdo tl eo sojòm bs ﬅjt jam rodtjacu`jr ba shjpo. @oacth lf dob`bac

9 := ft.

Sbmth lf dob`bac

9 :5 ft.

Jroj J roj lf Dob`bac

∽

9 := ft. x :5 ft. 9 :68 sq. sq. ft.

]ho spjdo bs sojòm wbth obthor cypsui dob`bac tbòs lr WVD dob`bac pjao`s. (b) Cypsui Dob`bac ]bòs Jroj lf : tbò

9 5=’ x 5=’ squjro badhos 9 5‒ x 5‒ sq. ft. 9 = sq. ft.

Al. lf dob`bac tbòs roqubrom roqubrom 9 :68 9 =5 tbòs

∽

= 4 oxtrj tbòs jro elucht ]ltj` auieor lf dob`bac tbòs tl eo elucht 9 =5 + 4 9 =?

∽

(bb) WVD Dob`bac ]bòs : 5

@oacth lf : WVD pjao`

9 :2

ft.

Sbmth lf : WVD pjao`

9 :7 badhos 9 :5 ft.

Sbmth lf rlli

9 :5 ft.

:7

Al. A l. lf WVD pjao` roqubrom 9 :5 9 :5 Ó :5 9 :== 9 :=.=

∽

:7 :5

:7

:7

]horoflro, tltj` auieor lf pjao`s tl eo elucht 9 :?

::7

Wjbat ]ho wj``s jro tl eo pjbatom yo``lw jam tho mllr eùo. ]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 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 eùo lb` pjbat bs aoomom tl pjbat mllr.

WULNOD] 3


]ho mjtj rovojòm tho fl``lwbac; :. ostbijto frli frli Hjrmwjro Hjrmwjro E wbth wbth `jelur dlst frli frli Slrkija : djio ba wbth tho tho hbchost eumcot lf $6,354.88 5. ostbijto frli frli Hjrmwjro Hjrmwjro J wbth wbth `jelur dlst frli frli Slrkija : cjvo tho 5am hbchor hbchor ostbijto lf $6,3:4.3? 4. ostbijto frli frli Hjrmwjro Hjrmwjro E wbth wbth `jelur dlst frli frli Slrkija Slrkija 5 cjvo tho 4rm 4rm hbchost ostbijto lf $6,554.88 =. ostbijto frli Hjrmwjr Hjrmwjro o J wbth `jelur `jelur dlst frli Slrkija Slrkija 5 cjvo tho =th hbchost hbchost ostbijto lf $6,5:4.3? ?. ostbijto frli frli Hjrmwjro Hjrmwjro D wbth `jelur `jelur dlst frli Slrkija : cjvo tho ?th hbchost ostbijto lf $6,753.?7 6. ostbijto frli frli Hjrmwjro Hjrmwjro D wbth `jelur `jelur dlst frli Slrkija : cjvo tho 6th hbchost ostbijto lf $?,?54.?7 3. ostbijto frli frli Hjrmwjro Hjrmwjro M wbth `jelur `jelur dlst frli Slrkija : cjvo tho 3th hbchost ostbijto lf $?,43?.77 8. ostbijto frli frli Hjrmwjro Hjrmwjro M wbth `jelur dlst frli Slrkija Slrkija 5 cjvo tho dhojpost dhojpost ostbijto lf $=,283.?7 ]l motoribao whothor furthor sjvbac wjs plssbeò 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 tbò Hjrmwjro Hjrmwjr o D lfforom tho dhojpost thbasot Hjrmwjro J & M lfforom tho dhojpost crlut Hjrmwjro Hjrmwjr o M lfforom tho dhojpost spjdos Hjrmwjro D & M lfforom tho dhojpost prbior Hjrmwjro Hjrmwjr o 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 Hjrmwjr o 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

_abt Wrbdo $

Zujatbty

M

Dorjibd tbòs

:3.7 7

: 77

D

]hbasot

=7 .7 7

= ejcs

M

Crlut

5 7.7 7

M

Tpjdors

M

-

-

: 67 .77

6 ès

:57.77

-

4 7.77

: pk

47.77

-

Wrbior

:5 7.7 7

: cj`

:57.77

-

M

Sjtor Wjbat

:? 7.7 7

: cj`

:?7.77

-

M

Lb` Wjbat

? 7 .77

° cj`

?7.77

-

M

WVD Wjao`s

? 7.7 7

:? òacths

3?7.77

-

]ltj` wbthlut VJ]

5,257.77

:6 7.77

VJ] G :5.?%

46?.77

5 7.7 7

]ltj` wbth VJ]

4,58?.77

: 8 7.77

9 ]ltj` dlst frli Hjrmwjro M + ]ltj` dlst frli Hjrmwjro D 9 $4,58?.77 + $:87.77

9 $4,=6?.77

@jelur frli Slrkija 5

9 $:,?77.77

]ltj` dlst lf ostbijto

9 $=,26?.77

∽

Dlst $

:,377.77

]ltj` dlst lf ijtorbj`

::4

Dlst $

WULNOD] 3


]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


www.wbkbhlw.dli www.so`feub`maowhlios.dli

::?

WULNOD] 8


Ja bavostbcjtbla batl ﬊xom rjto ilrtcjcos.

::6

WULNOD] 8


]JE@O LF DLA]OA]T :. ]btò....... ]btò................... ........................ ........................ ....................... ....................... ........................ ....................... ............. Wjco Auieor Auieor 5. Batrlmudtbla ............ ........................ ....................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla .......... ...................... ........................ ....................... ....................Wjco .........Wjco Auieor =. Wrosoatjtbla lf Mjtj........... ...................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj ........... ....................... ....................... ....................... ........................ ....................... ............. Wjco Auieor 6. Mbsdussbla lf Fbambacs........... ...................... ....................... ........................ ....................... .............. ... Wjco Auieor 3. Dladùsbla ........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 8. Uoforoados........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx.............. ........................ ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor Iy pjroats jro dlasbmorbac tjkbac j `lja frli j ejak tl purdhjso j hluso. ]hoy jro oip`lyom js Dòrks 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 DL@@OD]BLA B sjt wbth iy pjroats jam dl`òdtom 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 DL@@OD]BLA ]ho mjtj dl`òdtom 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 whbdh stjy tho sjio sjio flr tho `bfotbio `bfotbio lf tho ilrtcjco, thoroflro, thoy jro dj`òm ﬊xom rjto ilrtcjcos. ]hoso djrry j `lw batorost rjto rjacbac eotwooa 4% jam :7% eodjuso tho `lja bs sodurom, cbvbac tho òamor 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, elrrlwor, tho sij`òr tho ilrtcjco rjto jam tho `lacor tho `bfospja lf tho `lja. 4. ]ho l`mor tho tho elrrlwor elrrlwor,, tho `jrcor `jrcor tho ilath`y ilath`y pjyioat lvor j shlrtor `lja `bfospja. =. J mlwa mlwa pjyioat lf jt òjst :7% iust eo ijmo ?. ]ho ilath`y pjyioat pjyioat iust oam la lr eoflro, 47 yojrs. ]hbs iojas 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 motjbòm lut`bao lf hlw tho throo mbfforoat ilrtcjco p`jas wb`` eo sotup jam dj`du`jtom> ]ho vjùo lf ojdh ilath`y pjyioat wb`` eo dj`du`jtom usbac j stjamjrm dlipluam batorost flriu`j. ]hbs flriu`j hjs flur vjrbjeòs. ]hoso vjrbjeòs jro> :. ]ho Wrbadbpj` Wrbadbpj` jiluat lf ilaoy thjt iy pjroats wjat tl elrrlw elrrlw.. ]hbs bs roprosoatom ey tho òttor W ba tho flriu`j. 5. ]ho batorost rjto por ilath ilath thjt tho ejak bs dhjrcbac dhjrcbac iy pjroats tl elrrlw tho Wrbadbpj` sui. ]hbs bs roprosoatom ey tho òttor r ba tho flriu`j. 4. ]ho auieor lf ilaths ilaths thjt iy pjroats pjroats wb`` tjko

::2

tl ropjy tho Wrbadbpj` sui. ]hbs bs roprosoatom ey tho òttor a ba tho flriu`j.

=. ]ho jiluat lf ojdh ilath`y pjyioat pjyioat thjt iy iy pjroats wb`` hjvo tl ropjy. ropjy. ]hbs roprosoatom roprosoat om ey tho òttor I ba tho flriu`j. Vjùos Vj` uos flr tho throo vjrbjeòs; prbadbpj` (W), tbio (a) jam rjto (r) wb`` eo dl`òdtom frli tho ejak jam suestbtutom batl tho flriu`j tl letjba tho flurth vjrbjeò, 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 vjùo. ]hbs vjùo bs thoa iu`tbp`bom ey W tl letjba tho vjùo 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 Ó ?77,777 9 $?7,777.77 :77

]ho ilrtcjco dja eo letjbaom uamor throo mbfforoat mbfforoat toris. (:) ]ori J>

(5) ]ori E>

(4) ]ori D>

Wrbadbpj` (W) 9 $=?7,7 $=?7,777 77 ]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 $=?7,7 $=?7,777 77 ]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 $=?7,7 $=?7,777 77 ]bio (a)

9 57 yojrs 9 (57 Ó :5) ilaths 9 5=7 ilaths

Ujto (r)

9 2.?% por yojr 9 2.? % 9 7.325% por ilath :5

:57

]ho fl``lwbac dj`du`jtblas woro porflriom tl motoribao tho vjùo 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

{

r (:+r)a (:+r)a - :

}

9 =?7777

{

9 =?7777

{

(7.7743? Ó (4.8=36287?)

9 =?7777

{

7.7:==58863

(7.7743? (: + 7.7743?)467 (: + 7.7743?)467 - :

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

{

9 =?7777

{

7.77?84 (: + 7.77?84)477

9 =?7777

{

7.77?84 Ó (?.3:23588:?)

9 =?7777

{

7.744=67:8

r (:+r)a (:+r)a - :

}

(: + 7.77?84)477 - :

?.3:23588?: - :

=.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

{

r (:+r)a (:+r)a - :

}

{

7.77325 (: + 7.77325)5=7

9 =?7777

{

7.77325 Ó(6.6=:447642)

9 =?7777

{

7.7?5?22448

9 =?7777

(: + 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 mbfforoat ilrtcjco ]oris. Tdjò> :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 a b F

8

6

=

5

7 ]ori J

]ori E

]ori D Ilrtcjco ]oris

:5=

WULNOD] 8


_sbac ]ori ]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 ]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 ]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 MBT D_TTBLA LF FBAMBACT Bt bs biplssbeò flr iy pjroats tl purdhjso j hluso thjt bs vjùom 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`` wb`` eo ilro ijajcojeò flr thoi. Bf thoy jro mosbrlus lf pjybac tho sij`òst ilath`y ropjyioat wbth tho sij`òst 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. crojtor.

:56

WULNOD] 8


]ho ilrtcjco dj`du`jtblas rovojòm thjt> :. ]ho ﬊aj` dlst lf tho hluso usbac W`ja J wb`` eo $837,858.87. ]ho ilath`y ropjyioat 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 dlst lf tho tho hluso usbac W`ja D wb`` eo 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


www.ilaoysuporijrkot.dli www.omoìla﬊ajadbj`.dli www.woeorjwòr.dli

:58

WULNOD] 8

TOD]BLA 72 JWWOAMBX

]oris usom ba thbs prlnodt> :. Ilrtcjco> j `lja flr flr tho purplso lf euybac j prlporty prlporty whbdh bs sodurom sodurom ey tho prlporty 5. Fbxom Ujto Ilrtcjco> j ilrtcjco `lja wbth ja batorost batorost thjt mlos alt dhjaco dhjaco lvor tho `bfo lf tho `lja 4. Mlwa pjyioat> ja babtbj` pordoatjco pjyioat ijmo whoa tho prlporty prlporty bs elucht elucht la drombt =. Wrbadbpj`> tho babtbj` jiluat elrrlwom elrrlwom jftor tho mlwa pjyioat bs ijmo ?. Ujto / Batorost Batorost Ujto> Ujto> tho prbdo prbdo thjt tho tho ejak dhjrcos dhjrcos flr tho ilrtcjco. ]hbs dhjrco bs usuj``y oxprossom js j pordoatjco 6. ]bio> tho auieor auieor lf ilaths ilaths bt wb`` wb`` tjko flr flr tho `lja tl eo ropjbm ropjbm 3. Ilath`y pjyioat> tho jiluat jiluat lf ojdh ilath`y ilath`y bastjìoat bastjìoat 8. Vjrb Vjrbjeò> jeò> j qujatbty qujatbty thjt dja dhjaco 2. Flriu`j> ja oqujtbla shlwbac shlwbac hlw tho flur vjrbjeòs, prbadbpj`, prbadbpj`, rjto, tbio jam ilath`y pjyioat jro ro`jtom

:52

WULNOD] 2


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


]JE@O LF DLA]OA]T :. ]btò....... ]btò................... ........................ ........................ ....................... ....................... ........................ ....................... ............. Wjco Auieor Auieor 5. Batrlmudtbla ............ ........................ ....................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla .......... ...................... ........................ ....................... ....................Wjco .........Wjco Auieor =. Wrosoatjtbla lf Mjtj........... ...................... ....................... ........................ ....................... .................. .......Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj ........... ....................... ....................... ....................... ........................ ....................... ............. Wjco Auieor 6. Mbsdussbla lf Fbambacs........... ...................... ....................... ........................ ....................... .............. ... Wjco Auieor 3. Dladùsbla ........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 8. Uoforoados........... ....................... ....................... ....................... ........................ ....................... ....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx.............. ........................ ....................... ....................... ........................ ....................... ....................Wjco .........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 sbipò 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 DL@@OD]BLA Mjtj wjs dl`òdtom frli flur (=) crlups lf stumoats; Tdboado, @jacujcos, Eusbaoss jam ]odhabdj`. ]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 soòdtom 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 dlipòto 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`òdtom frli tho flur (=) crlups, thoy woro lrcjabzom batl lao tjeò 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

:44

D`jss

Al. lf Ttumoats Wjssom

Al. lf Ttumoats Fjbòm

% 57 - 42

% =7 - ?2

% 67 - 32

% 87 - :77

Tdboado

:4

5

7

4

3

?

@jacujco

8

3

5

8

?

7

Eusbaoss

:7

?

=

8

4

7

]odhabdj`

8

3

5

2

=

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 Tjò> :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

]ODHABDJ@

FLUI D@JTT

Wbo dhjrt dlipjrbac jvorjcos lf tho = crlups

]ODHABDJ@ ]ODHABDJ @ 8=

·

TDBOADO ::?

·

E_TBAOTT 8:

·

@JAC_JCO 8:

·

:4=

J`` dj`du`jtblas whbdh woro mlao flr tho Ioja

x, 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 sbipò jrbthiotbd ioja ( x̍ ) flr j sjipò bs dj`du`jtom usbac tho flriu`j> Ioja x̍ 9

Tui lf j`` sdlros ba tho sjipò Auieor lf sdlros ba tho sjipò

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 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 ]odhabd odhabdj` j` 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 Movbjtbla flr j sbipò crlup bs dj`du`jtom usbac tho flriu`j Ttjamjrm Movbjtbla 9 √(x - x̍)5 a Shoro x bs ojdh bambvbmuj` sdlro

Alto>

x̍ bs bs tho crlup ioja a bs tho auieor lf sdlros ba tho sjipò Τ bs tho Crook òttor sbcij 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 :?

- x)̍ 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

3 3 8 .= :

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 .:

8 5 .8 :

6:

: 7 .:

: 7 5 .7 :

65

: : .:

: 5 4 .5 :

6?

: = .:

: 2 8 .8 :

66

: ? .:

5 5 8 .7 :

Τ (x

a 9 :?

- x)̍ 5

9 5=4:.3?

Ttjamjrm Movbjtbla

9

√(x - x̍ )5

a

:43

9

5=4:.3? :?

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

4 6 8 .6 =

4=

-:3.5

5 2 ? .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

5 4 .7 =

66

: = .8

5 : 2 .7 =

37

: 8 .8

4 ? 4 .= =

34

5 : .8

= 3 ? .5 =

Τ (x

a 9 :?

- x)̍ 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.?

: 8 5 .5 ?

4=

-:7.?

: : 7 .5 ?

42

-2.?

2 7 .5 ?

=2

-6.?

= 5 .5 ?

?:

-6.?

= 5 .5 ?

?5

-?.?

4 7 .5 ?

?=

-:.?

5 .5 ?

??

7 .?

7 .5 ?

??

5 .?

6 .5 ?

??

6 .?

= 5 .5 ?

?6

2 .?

2 7 .5 ?

66

: 4 .?

: 8 5 .5 ?

37

: 3 .?

4 7 6 .5 ?

34

: 2 .?

4 8 7 .5 ?

Τ (x

a 9 :?

- x)̍ 5

9 :3=3.3?

Ttjamjrm Movbjtbla

9

√(x - x̍ )5

a

:42

9

:3=3.3? :?

9

::6.?:663

9

:7.32%

Dj`du`jtblas flr tho rjaco lf ojdh crlup. ]ho Ujaco bs tho mbffor mbfforoado oado eotwooa tho `jrcost jam sij`òst vjùos ba j sjipò. Ujaco 9 @jrcost Vjùo — Tij`òst Vjùo

∽

:. @jrcost vjùo flr Tdboado crlup 9 2?% Tij`òst vjùo flr Tdboado crlup 9 =7% Ujaco flr Tdboado crlup 9 2?% — =7% 9 ??% 5. @jrcost vjùo flr @jacujco crlup 9 66% Tij`òst vjùo flr @jacujco crlup 9 54% Ujaco flr @jacujco crlup 9 66% - 54% 9 =4% 4. @jrcost vjùo flr Eusbaoss crlup 9 34% Tij`òst vjùo flr Eusbaoss crlup 9 53% Ujaco flr Eusbaoss crlup 9 34% - 53% 9 =6% =. @jrcost vjùo flr ]odhabdj ]odhabdj`` crlup 9 35% Tij`òst vjùo flr ]odhabdj odhabdj`` crlup 9 43% Ujaco flr ]odhabdj odhabdj`` crlup 9 35% - 43% 9 4?%

D@JTT

JVOUJCO %

Tdboado

34

@jacujco

?:

Eusbaoss

?:

]odhabdj`

?4 558

Dj`du`jtblas flr jacòs tl roprosoat ojdh crlup sodtlr la tho pbo dhjrt Jacò tl roprosoat Tdboado crlup

9 34 Ó 467· ≈ ::?· 558

Jacò tl roprosoat @jacujco crlup 9 ?: Ó 467· ≈ 8:· 558 Jacò tl roprosoat Eusbaoss crlup

9 ?: Ó 467· ≈ 8:· 558

Jacò tl roprosoat ]odhabdj odhabdj`` crlup

9 ?4 Ó 467· ≈ 8=· 558

:=7

WULNOD] 2


]ho tjeò cbvos j suiijry lf biplrtjat iojsuros dj`du`jtom ba tho prlnodt.

CUL_W

IOJA x̍ %

T]JAMJUM MOVBJ]BLA %

UJACO %

Tdboado

3 4.4

:6.:

??

@jacujco

? 7 .3

:5.3

=4

Eusbaoss

?: .5

:5 .2 8

=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. 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 roprosoat roprosoats s 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`òat 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 òss thja tho Tdboado crlup. ]hbs succosts thjt thoro bs òss sprojm jwjy frli tho ioja ba thoso throo crlups thja thjt lf tho Tdboado crlup. Tbado tho iojas lf tho lthor crlups jro iudh òss thja thjt lf tho Tdboado crlup, lao dja dladùmo 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 rovojòm 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 òss thja tho sdlros lf :7 stumoats frli tho Tdboado crlup.

:=4

WULNOD] 2


]ho Tdboado crlup wbth Ioja, Ujaco jam Ttjamjrm Movbjtbla lf 34.4%, ??% jam :6.:% rospodtbvo`y succost thjt, thbs crlupbac crlupbac lf stumoats hjs ja bipjdt la tho Ijthoijtbds porflrijado jt thbs pjrtbdu`jr sdhll`.

:==

WULNOD] 2


]ll`sbo, U, (57:5). Jmmbtblaj` Ijthoijtbds> J Dlipòto Dlurso flr DTOD. www.qulrj.dli www.ijthcllmbos.dli www.ijthbsfua.dli

:=?

WULNOD] 2

TOD]BLA 78 JWWOAMBX

:. Ijthoijtbds ijrks dl`òdtom frli tho Tdboado Tdboado crlup> crlup> 2?, 2?, 8?, 32, 3?, 33, 32, 66, 36, 63, 88, 8:, =6, ?:, =7 5. Ijthoijtbds ijrks dl`òdtom frli tho @jacujco @jacujco crlup> crlup> ?2, =3, 6?, ?8, 54, 58, =?, 67, ?8, 65, =6, =7, =?, 6:, 66 4. Ijthoijtbds ijrks dl`òdtom frli tho Eusbaoss Eusbaoss crlup> crlup> 45, 53, ?6, ??, ?:, ?5, 4=, 66, =2, 37, ?=, 34, ??, 42, ?? =. Ijthoijtbds ijrks dl`òdtom dl`òdtom frli frli tho ]odhabdj` ]odhabdj` crlup> crlup> 37, =5, 43, =6, 42, 65, ?2, ?:, =4, 35, =6, ??, =3, ?5, 66

:=6

WULNOD] :7


Ja bavostbcjtbla batl Wythjclrjs‒ ]holroi tl motoribao motoribao bts usofuàoss ba tho roj` wlr`m.

:=3

WULNOD] :7


]JE@O LF DLA]OA]T :. ]btò....... ]btò.................. ....................... ........................ ........................ ....................... ....................... ........................ .............. Wjco Auieor Auieor 5. Batrlmudtbla ........... ....................... ........................ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor 4. Iothlm lf Mjtj Dl`òdtbla Dl`òdtbla ............ ....................... ....................... ........................ ................... .......Wjco Wjco Auieor Auieor =. Wrosoatjtbla lf Mjtj............ ........................ ....................... ....................... ........................ ................. .....Wjco Wjco Auieor ?. Jaj`ysbs lf Mjtj Mjtj ............ ........................ ....................... ....................... ........................ .......................Wjco ...........Wjco Auieor 6. Mbsdussbla lf Fbambacs............ ........................ ....................... ....................... ........................ .............. Wjco Auieor 3. Dladùsbla .......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 8. Uoforoados.......... ...................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor 2. Jppoambx.. Jppoambx............. ....................... ........................ ....................... ....................... ........................ .....................Wjco .........Wjco Auieor Iy flurth flri d`jss rodoat`y dlipòtom j stumy ba coliotry. Wythjclrjs‒ ]holroi wjs oiphjsbzom. Hlwovor, Hlwovor, ijay lf iy poors fjbòm tl uamorstjam bts biplrtjado jam usofuàoss 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 prleòis.

:=8

WULNOD] :7

TOD]BLA 75 IO]HLM LF MJ]J DL@@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 toòvbsbla 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, Hlwovor, Wythjclrjs wjs tho ﬊rst porsla tl prlvo tho tholroi flrior`y.

Wythjclrjs‒ ]holroi stjtos thjt> thj t> Ba jay rbcht-jacòm trbjacò, tho jroj lf tho squjro sq ujro 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 jacò. Wythjclrjs sjw thbs rosu`t thrluch coliotrbd oyos jam jdtuj``y mrow squjros la tho throo sbmos lf j rbchtjacòm trbjacò 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`òr 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-jacòm trbjacò, thoa ejsom la tho Wythjclroja ]holroi> j5 + e5 9 d5 ]hbs rosu`t dja eo ostje`bshom ey dlastrudtbac j rbcht-jacòm trbjacò 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 `bttò squjros basbmo tho

:?:

throo squjros.

d

e

j

Fbcuro 5 ]ho auieor lf `bttò squjros basbmo tho squjro la sbmo d shlu`m eo oquj` tl tho auieor lf `bttò squjro basbmo tho squjro la tho sbmo j pùs tho auieor lf `bttò squjro basbmo tho squjros la tho sbmo e.

:?5

Iothlm (5) J`coerjbd / Coliotrbd prllf Bt ijy alt j`wjys eo prjdtbdj` tl mrjw trbjacòs jam dluat squjros. ]horoflro, ]horoflro, j coaorj` prllf wb`` eo ostje`bshom usbac j`coerjbd jam coliotrbd prbadbpòs. 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 jacòs ba jay trbjacò bs :87·

x

·

x· + y· + z· 9:87·

y

·

z

·

(bb) ]ho sui lf tho jmnjdoat jacòs la j strjbcht `bao bs oquj` tl :87·

x· + y· + z· 9:87· ·

z

·

y

x

·

(bbb) ]ho jroj lf j rbcht jacò trbjacò 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 trbjacòs wb`` eo mrjwa mrjwa wbth sbmos j, e, jam d jam batorblr jacòs 27·, x· jam y· 5. ]ho flur trbjacòs trbjacòs wb`` eo nlbaom tlcothor tl flri j squjro squjro lf sbmo sbmo (j + e) js shlwa eo`lw. e

j

x

·

y

·

]ho sui lf tho throo jacòs ba j j

d

e

d

trbjacò bs :87·

x + y + 27· 9 :87· 91 x + y9 27· ∽

y

x

·

·

tho qujmrb`jtorj` basbmo tho ebc

∽

x

y

·

squjro lf sbmo ( j + e) bs j`sl j

·

squjro sbmo d. d

e

d

y j

·

x

j

·

e

]ho jroj lf tho ebc squjro wbth sbmo (j + e) bs oquj` tl tho sui lf tho jrojs lf tho flur trbjacòs pùs 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 :

:

5

4

8 : 4

6

?

6

3

8

2

:7

::

:5

:4

:=

:?

:6

i d = 9 e

: =

3

=

: ?

: 2

: 5

d 9 : : ? d i

5 7

: 8 3 :

: 6

5 ? 5 =

5 4 5 5

5 :

j 9 4di

:

5

4

=

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6

3

8

2

]ho auieor lf `bttò squjros ba tho squjro lf sbmo 4 di bs 2 ]ho auieor lf `bttò squjros ba tho squjro lf sbmo = di bs :6 ]ho auieor lf `bttò squjros ba tho squjro lf sbmo ? di bs 5? Hoado> (b) jroj lf squjro wbth sbmo ? di bs 5? di5 (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 `bttò 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 trbjacò J 9 e Ó h

9 je

5

5

]ho tltj` jroj lf tho flur trbjacòs 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 j 5 + je + je + e 5 9 j5 + 5je + e5 Dliebabac (b), (bb) jam (bbb) tl cot> Jroj lf squjro wbth sbmo (j + e) 9 Jroj lf flur trbjacòs + Jroj lf Tqujro wbth sbmo d

j5 + 5je + e5 9 5je + d5 91 j5 + e5 + 5je — 5je 9 5je — 5je + d 5 91 j5 + e5 9 d5 ∽

Z.O.M.

:?6

WULNOD] :7


Flr tho cbvoa trbjacò, Wythjclrjs‒ ]holroi stjtos thjt d5 9 j5 + e5 d e j Shjt mlos thbs ioja ba j roj` `bfo dlatoxt< Hlw dja Wythjclrjs‒ ]holroi ho`p us tl sl`vo prleòis 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 j5 + e5 Alw d bs j òacth, whbdh succosts thjt Wythjclrjs‒ ]holroi dja eo usom tl motoribao òacths lr mbstjados. Bf tho òacth d dja eo p`jdom ba j rbcht jacò trbjacò wbth twl kalwa sbmos, thoa Wythjclrjs‒ ]holroi dja eo usom tl ﬊am tho òacth 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 kalwòmco 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 trbjacò JED bf jam la`y bf

d5 9 j5 + e5. J`sl, bf d5 9 j5 + e5, thoa tho jacò JDE bs j rbcht jacò jam tho rlli bs `baom up prlpor`y jam bs j porfodt rodtjacu`jr shjpo.

:?3

Ey iojsuroioat, tho òacth lf j iojsurom := ft jam tho òacth 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 + e5 9

4=7

:8.= ft

≈

Hoado, bf tho eomrlli wjs `baom up dlrrodt`y tho òacth lf tho mbjclaj` shlu`m eo jpprlxbijto`y jpprlxbi jto`y :8.= foot. Ey iojsuroioat, tho mbjclaj` lf tho rlli iojsurom :3.? foot. ]horoflro, ejsom la Wythjclrjs‒ ]holroi, tho jacò JDE bs alt oquj` tl 27· jam iy eomrlli bs alt j porfodt rodtjacu`jr shjpo. ]horoflro, B dja dladùmo thjt tho wlrkijashbp wjs sliowhjt pllr.

5. ]oòvbsbla Tdrooa Tdroo a Jalthor roj`-wlr`m sbtujtbla sbtujtbla thjt bs wlrthy lf bavostbcjtbla bs thjt lf tho sbzo lf j toòvbsbla sdrooa.

d

43’

66’

]ho sbzo lf tho fjib`y‒s fjib`y‒s toòvbsbla sot wjs sjbm tl eo 3?’. Hlwovor, Hlwovor, B iojsurom tho òacth lf tho toòvbsbla sot jam mbsdlvorom thjt bt bs 66’ ba òacth jam 43’ ba wbmth. ]ho toòvbsbla sot hjs j rodtjacu`jr shjpo, sl B modbmom tl jpp`y Wythjclrjs‒ ]holroi tl motoribao tho òacth lf tho mbjclaj` d lf tho toòvbsbla 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 toòvbsbla sot bs jpprlxbijto`y 3?’ j`lac bts mbjclaj`. ]horoflro, ba coaorj`, tho roplrtom sbzo lf j toòvbsbla sot bs tho òacth lf bts mbjclaj`.

:?8

4. ]ho Thlrtost Thlr tost Mbstjado Mbs tjado Eotwooa ]wl ]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 òacth lf tho ﬊o`m bs :57 i jam bts wbmth bs ?7 i. Hoado, tho òacth 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 :575 + ?75 9 :==77 + 5?77 9 :6277 i5

]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 Ao omom ]l ]l W`jdo J Ejaaor La L a J Sj`` Sj``

spjdo flr ejaaor o r m m ` j

57 ft

wj`` :? ft

]ho sdhll` bs p`jaabac bts jaauj` Djrabvj` jdtbvbty 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 ejaaor.. Wythjclrjs‒ ]holroi dja eo usom tl motoribao tho òacth lf `jmmor thjt bs aoomom tl orodt tho ejaaor. @ot tho òacth lf tho `jmmor eo d 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 òacth 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 òjrat ey rlto. Bt dja eo usom tl ho`p motoribao òacths 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 toòvbsbla sot, motoribao tho shlrtost mbstjado eotwooa twl plbats la j p`jybac ﬊o`m jam motoribao tho òacth lf tho `jmmor thjt bs aoomom flr j pjrtbdu`jr nle. Ba dlamudtbac thbs prlnodt j fow dhj`òacos woro oadluatorom. Iojsurbac tho mbioasblas lf tho sdhll`‒s p`jybac ﬊o`m plsom slio prleòis 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· jacòs whoa thoy iot. J spbrbt òvo` wjs usom tl motoribao bf tho sdhll`‒s wj``s jam crluam woro elth vortbdj` jam hlrbzlatj`.

:6:

WULNOD] :7


Wythjclrjs‒ ]holroi dja eo moilastrjtom prjdtbdj``y ey dlastrudtbac j rbcht-jacò trbjacò la crjph pjpor jam dluatbac tho squjros la tho throo sbmos lf tho trbjacò. J`coerj jam Coliotry dja eo usom tl prlvo tho tholroi ey dlastrudtbac flur dlacruoat trbjacòs 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 toòvbsbla sot, 4. tho shlrtost mbstjado eotwooa twl plbats, =. tho òacth lf tho `jmmor `jmmor aoomom tl orodt j ejaaor la j vortbdj` wj`` wj``

:65

WULNOD] :7


www.erbchthueomudjtbla.dli www.thofjiluspolpò.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` jacò oquj` tl 27·. Jroj lf j squjro 9 sbmo Ó sbmo 9 sbmo5

Jroj lf j rbcht rbcht jacò trbjacò trbjacò 9 ejso Ó hobcht

h

5

e

j

]ho sui lf tho 4 batorblr jacòs ba j trbjacò bs oquj` tl :87· ∽

j· + e· + d· 9 :87·

d

e

]ho sui lf tho jmnjdoat jacòs 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 jacò ba j rbcht-jacò trbjacò 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]H IJ ]HOI OIJ J]BDT TEJ TEJ SB]H SB ]H TDOAJUBLT TDOAJUBLT JAM ]B ]B]@OT ]@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 oxjipò> :. ]ho hlio bs ja oxdo`òat 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 Ttumoats shlu`m pjy pjrtbdu`jr jttoatbla tl tojdhors whoa thoy jro prosoatbac thobr òsslas. ]lpbds sudh js> iojsuroioats, stjtbstbds, coliotry, ro`jtblas jam fuadtblas jam dlasuior jrbthiotbd jro j`` oxdo`òat tlpbds thjt dja eo usom ba lrmor tl bavostbcjto roj`-wlr`m prleòis. prleòis. 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 sbipò Ijthoijtbdj` todhabquos. Coaorj``y, stumoats dja `llk jt jay dlip`jbat lr roj`-wlr`m prleòi whbdh ijy eo jaodmltj` ba ajturo jam dja eo bavostbcjtom ey usbac j sbipò Ijthoijtbdj` todhabquo. ]ho fl``lwbac bs j `bst lf twoaty (57) sdoajrbls jam tbtòs 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) òvo` wrbto tho Ajtblaj` Dortb﬊djto lf Todlamjry Omudjtbla (ADTO) Oxjibajtbla ovory yojr. Hlwovor, 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 rosojrdh prlnodt ejsom la tho ADTO ADTO rosu`ts jam tho tbtò tbtò dja rojm js fl``lws> ‐ Ja bavostbcjtbla bavostbcjtbl a lf tho `jst flur (=) yojrs y ojrs lf ATOD rosu`ts jt j pjrtbdu`jr pjrtb du`jr sdhl sd hll` l`..’

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 tbtò dja eo usom tl pursuo j prlnodt> ‐J stumy lf tho `jst ﬊vo ﬊ vo (?) yojrs yoj rs lf tho DTOD Oac`bsh @jacujco @j acujco oxjibajtbla oxjibajtbl a rosu`ts jt j pjrtbdu`jr pjrtbdu `jr sdhll`. 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 tbtò 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 tbtò dja eo usom flr j rosojrdh roso jrdh prlnodt. prlnod t.’ ’

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 tbtò dja sot tho coaorj` rosojrdh thoio flr tho prlnodt> ‐Ja bavostbcjtbla batl tho puadtuj`bty jam rocu`jrbty lf Flri ? stumoats jt j sodlamjry sodlamj ry 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 mbstja do thjt stumoats stumo ats `bvo frli tho sdhll` hjs hj s ja bipjdt la thobr puadtuj`bt pua dtuj`bty’ y’.

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 tbtò js j coaorj` thoio flr tho prlnodt> ‐Ja bavostbcjtbla lf stumoats‒ jdjmoibd porflrijado jt j pjrtbdu`jr sdhll` ba lrmor tl tl motoribao motoribao bf thoy thoy jro jffodtom jffodtom ey ey oxtrjdurrbdu`jr oxtrjdurrbdu`jr jdtbvbtbos.. jdtbvbtbos..‒‒

TDOAJUBL 3 ]ho sdhll`‒s ijajcoioat hjs sorblus prleòis wbth stumoats j`torbac tho sdhll` uabflri. J prlnodt dja eo mlao la tho sovorbty lf tho prleòi. ]ho fl``lwbac tbtò dja eo usom js j cubmo flr j prlnodt> ‐Ja bavostbcjtbla batl tho auieor lf uppor sdhll` stumoats jt j pjrtbdu`jr sdhll` whl wh l j`tor thobr th obr sdhll` 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 tbtò dja eo usom tl cubmo tho prlnodt> ‐Ja bavostbcjtbla batl tho porflrijado lf Flri : stumoats ba tho jroj lf Ijthoijtbds Ijthoij tbds jt j sodlamjry sod lamjry sdhll`. 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 tbtò js j cubmo> ‐Ja bavostbcjtbla lf tho hliowlrk hjebts lf tho uppor jam `lwor flris ba lrmor tl motorib motoribao ao whbdh crlup bs ilro `bko`y tl sueibt hliowlr hliowlrk k jssbcai jss bcaioats oats..’ ’

:62

DLAT_IOU

JUB]HIO]B JUB ]HIO]BD D TDOAJUBL :7 J stumoat dja dhllso tl jssbst hbs lr hor pjroat wbth tho fjib`y‒s eumcot. eumcot. J eumcot dja eo drojtom ey tjkbac batl jddluat sj`jrbos jam oxpoambtur oxpoambturo. o. ]ho fl``lwbac tbtò dja eo j crojt thoio flr tho prlnodt> ‐Drojtbac j fjib`y eumcot usbac usba c dlasuior jrbthiotbd jrbt hiotbd todhabquos. todhabqu os.’ ’

TDOAJUBL :: ]ho Hluso Tystois jt sdhll`s usuj``y uso fuamrjbsors tl tl ho`p wbth tho purdhjso purdhjso lf uabflris jam lthor btois flr Tplrts Mjy. 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 rotjbòm ba lrmor tl coaorjto j sbcab﬊djat prl﬊t. ]ho fl``lwbac tbtò 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 pjrtbd u`jr sdhll`‒s sdh ll`‒s hluso systoi.’ ’

TDOAJUBL :5 Tupplso j stumoat‒s fjthor wjats tl so`` hbs iltlr vohbdò jftor obcht (8) yojrs. ]ho vohbdò 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 vjùo lf tho vohbdò jam lthor fjdtlrs thjt ijy jffodt tho ﬊aj` so``bac prbdo. ]ho tbtò lf tho prlnodt dja eo stjtom js fl``lws> ‐Ja bavostbcjtbla batl tho vjùo lf iy fjthor‒s iltlr vohbdò jftor obcht (8) yojrs.’ ’

:37

F_AD]BLAT JAM

UO@J]BLAT CUJWHT & @BAOJU WULCUJIIBAC TDOAJUBL :4 Mjm bs j pùieor. pùieor. 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 tbtò dja cubmo tho prlnodt> ‐_sbac j `baojr ro`jtbla ba lrmor tl motoribao tho tltj` jiluat lf ilaoy thjt iy fjthor fjthor dja dhjrco dhjrco flr hbs pùiebac pùiebac sorvbdos. sorvbdos.’

TDOAJUBL := : ]ho dbrduiforoado dbrduiforoado (D) lf jay dbrdò dbrdò bs 4 3 tbios bts bts mbjiotor mbjiotor (m). (m). ]hbs ]hbs bs stjtom js : D9 χm, whoro χ 9 4 3 . ]hbs bip`bos thjt D bs mbrodt`y mbrodt`y prlplrtblaj` prlplrtblaj` tl m. Hoado, j crjph lf D vs m bs j strjbcht `bao. ]hbs dladopt dja eo usom tl motoribao tho jpprlxbijto vjùo lf χ ey usbac prjdtbdj` iojsuroioats. ]ho tbtò lf tho prlnodt dja rojm js fl``lws> ‐Ja bavostbcjtbla batl tho ro`jtblashbp eotwooa tho dbrduiforoado lf j dbrdò jam bts mbjiotor mbj iotor ba lrmor lrmo r tl motoribao tho th o vjùo lf pb (χ)’.

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 prlcrjiib ac 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 tbtò 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 dl astrjbats la l a hbs lr hor `bfo.’ ’

:3:

J@COEUJ

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 vocotjeò 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 dlipòtbac tho squjro dja eo usom tl motoribao tho ijxbiui jroj lf `jam thjt dja eo usom. ]ho prlnodt tbtò dlu`m rojm> ‐_sbac tho iothlm lf dlipòtbac tho squjro tl motoribao tho ijxbiui jroj lf j vocotjeò vo cotjeò cjrmoa.’ 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`òr 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 tbtò lf j prlnodt dja rojm js fl``lws> ‐J stumy batl tho j`coerjbd bmoatbty j 5 - e5 9 (j + e) (j - e) ba lrmor tl physbdj``y physbd j``y moilastrjt moilastrjto o 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 jacòs 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 trbjacò js shlwa eo`lw.

Thjpo

Thjpo mbvbmom batl trbjacòs

Auieor Dj`du`j- Tui lf lf sbmos tbla jacòs

4

: x : 87 ·

:8 7 ·

=

5 x : 87 ·

46 7 ·

?

4 x : 87 ·

?= 7 ·

8

6 x : 87 ·

:7 87 ·

Ttumoats shlu`m eo jeò tl `llk jt tho pjttora jam flriu`jto j coaorj` flriu`j flr tho sui lf tho batorblr jacòs lf jay pl`ycla. ]ho tbtò 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 jacòs lf jay

:34

pl`ycla wbth wbth tho uso lf j prjdtbdj` 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 elttòs 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

5

5

=

?

:

4

6

:

4

=

5

3

:

?

4

=

4

6

:

6

4

3

=

5

=

8

4

4

=

2

:

3

5

:7

4

=

4

Btoi

Dlst $

Ib`k

:5.?7

Ubdo

47.77

Lb`

=?.77

Ttumoats dja drojto twl ijtrbdos ba lrmor tl motoribao> :. tho tltj` vjùo lf ojdh hjipor 5. tho tltj` tltj` dlst tl drojto j`` :7 hjipors hjipors ]ho tbtò lf tho prlnodt dja eo wrbttoa js> ‐_sbac ijtrbdos ba lrmor tl motoribao tho tltj` dlst lf prlmudtbla flr toa (: (:7) Dhrbstijs hjipors. hjipors.’ ’

:3=

JWW@BDJ JWW@B DJ]BLA ]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 rlò ba thoso ﬊o`ms. ]ho fl``lwbac tbtò dja eo usom js j cubmo flr thbs prlnodt> ‐Ja bavostbcjtbla ba lrmor tl moilastrjto tho biplrtjado lf Ijthoijtbds ba mbfforo mbff oroat at djroors djro ors..’

: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.; ]jèort, N. F., Jmmbtblaj` Ijthoijtbds, 6th Ombtbla ]ll`sbo, U, (:222). J Dlipòto Dlurso wbth DXD Zuostblas. www.erbchthueomudjtbla.dli www.omoìla﬊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.thofjiluspolpò.dli www.ttdlaaodt.clv.tt www.uadw.omu/jòcerj www.vjrsbtytutlrs.dli www.woeorjwòr.dli www.wbkbOmudjtlr.lrc www.wbkbhlw.dli

:36

JEL_] ]HO J_]HLU Còamla Ttooò hjs eooa tojdhbac Ijthoijtbds flr tho pjst t woaty (57) yojrs. Ho durroat`y sorvos js Hojm lf tho Ijthoijtbds Mopjrtioat jt Tt. Njios 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 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. Còamla Ttooò bs j dlasuiijto tojdhor ba ijay rocjrms jam hl`ms tho mbstbacubshom jddlip`bshioat lf off offodtbvo`y odtbvo`y prosoatbac tho toòvbsbla sorbos, ‘J Dladoptuj` Jpprljdh tl @ojrabac Ijthoijtbds Ijthoijtbds‒,‒ la ]ho Baflrijtbla Dhjaao` = flr jpprlxbijto`y jpprlxbijt o`y ﬊vo yojrs yojrs murbac whbdh, oiphjsbs wjs p`jdom la òjrabac Ijthoijtbds ey eub`mbac la j sot lf fuamjioatj` prbadbpòs. prbadb pòs. Horo, 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 òjrabac jay tlpbd ba Ijthoijtbds. Ir. Ir. Ttooò‒ Ttooò‒s s phb`lslphy bs thjt Ijthoijtbds shlu`m eo prosoatom ba j ijaaor ba whbdh stumoats dja soo, jdkalwòmco jam jpprodbjto bts roòvjado roòv jado ba tho roj` wlr`m jam ovoatuj``y dlio tl fj`` ba `lvo wbth tho suenodt.

The Essentials Mathematics SBA Handbook - Glendon Steele

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