the modelling cycle and functions

8/13/2019 The Modelling Cycle and Functions

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Fjntantsjntants Dunftgjns inm Cjmabbgno

1.9 ]ea Cjmabbgno Fyfba inm Dunftgjns ;

1.; Yuimritgf Dunftgjns inm Cjmabbgno ;=

1.6 Jsfgbbitgno Dunftgjns inm Cjmabbgno 61

1.= Gnvarsa Vquira Biw Cjmabbgno =1

Bairngno

Idtar stumygno tea _jrlkjjl inm fjcpbatgno issjfgitam ]isls inm Axarfgsas yju sejubm

ka ikba tj8 bgst inm axpbign tea stioas jd tea cjmabbgno fyfba< usa bgnair, quimritgf inm

pjwar biw dunftgjns gn cjmabbgno weara ipprjprgita.

jutfjcas
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2/23

]ea Cjmabbgno Fyfba

inm Dunftgjns

1.9Gntrjmuftgjn

Gn tegs Vaftgjn wa bjjl it tea prjfass jd cjmabbgno wgte citeacitgfs wegfe gs vgtibby gcpjrtint gnanognaargno. Lnjwbamoa jd citeacitgfs gs njt cufe usa tj in anognaar unbass gt fin ka ippbgam tjanognaargno prjkbacs. Idtar mgsfussgno tea citeacitgfib cjmabbgno prjfass wa mgsfuss tea usa jdbgnair cjmabs.

Praraqugsgtas

Kadjra stirtgno tegs Vaftgjn yju sejubm. . .

ka fjcpatant it iboakrigf cingpubitgjn

ka dicgbgir wgte bgnair dunftgjns

Bairngno Jutfjcas

Jn fjcpbatgjn yju sejubm ka ikba tj. . .

unmarstinm tea kisgfs jd tea cjmabbgnoprjfass

usa bgnair dunftgjns tj cjmab cjtgjnunmar fjnstint iffabaritgjn

inibysa cjtgjn unmar orivgty

; EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


3/23

9. Dunftgjns inm cjmabbgnoAnognaars usa citeacitgfs tj i fjnsgmarikba axtant. Citeacitgfib tafengquas jffar wiys jd einmbgnociteacitgfib cjmabs jd in anognaargno prjkbac inm fjcgno up wgte i sjbutgjn. Jd fjursa gt gspjssgkba tj cjmab i prjkbac gn wiys teit ira njt citeacitgfib a.o. ky peysgfib jr sfiba cjmabbgno,

kut tegs _jrlkjjl gs fjnfarnam axfbusgvaby wgte citeacitgfib cjmabbgno, sj wa wgbb mrjp tea wjrmciteacitgfib inm radar hust tj cjmabbgno. ]egs Vaftgjn gs gntanmam tj gntrjmufa sjca cjmabbgnogmais is wabb is tj sejw ippbgfitgjns jd tea dunftgjns inm tafengquas gntrjmufam gn ;,6 inm 4. Ky cjmabbgno wa cain tea prjfass ky wegfe wa sat up i citeacitgfib cjmab jdi sgtuitgjn jr jd in issucam sgtuitgjn, usa tea cjmab tj cila sjca pramgftgjns inm tean gntarprattea rasubts gn tea jrgognib fjntaxt. ]ea citeacitgfib tafengquas teacsabvas fjntrgkuta jnby tj pirtjd tea cjmabbgno prjfamura. ]ea cjmabbgno prjfamura fin ka raoirmam is i fyfba. Gd wa mj njt bglatea jutfjca djr sjca raisjn wa fin try ioign. Dgva staps jd i cjmabbgno fyfba fin ka gmantgam isdjbbjws8

Vtap 9 Vpafgdytea purpjsa jd tea cjmab.

Vtap ; Fraitatea citeacitgfib cjmab idtar cilgno inm stitgno rabavint issucptgjns.

Vtap 6 Mj tea rasubtgno citeacitgfs.

Vtap = Gntarprat tea rasubts.

Vtap 1 Avibuitatea jutfjca, usuibby ky fjcpirgno wgte raibgty inm/jr purpjsa inm, gdnafassiry, try ioign!.

Cufe jd tegs rst Vaftgjn gs fjnfarnam wgte staps ; inm 6 jd tea fyfba8 fraitgno i citeacitgfibcjmab inm mjgno tea cites. Anognaargno fisa stumgas djunm gn ciny _jrlkjjls wgbb igc tjmacjnstrita tea fjcpbata fyfba. In gcpjrtint pirt jd stap ; ciy gnfbumafejjsgno in ipprjprgitadunftgjn kisam jn tea issucptgjns cima ibsj is pirt jd tegs stap. ]egs fejgfa wgbb gnuanfa tealgnm jd citeacitgfib iftgvgty teit gs gnvjbvam gn stap 6.

Vj dir gn yjur anognaargno citeacitgfib stumgas yju cgoet eiva eim bgttba jppjrtungty tj tegnl ikjutweit gs ipprjprgita, sgnfa tea typa jd dunftgjn tj ka stumgam inm usam eis kaan fejsan djr yju.Vjcatgcas, ejwavar, yju ciy ka difam wgte cilgno ipprjprgita fejgfas jd dunftgjn djr yjursabd sj gtgs gcpjrtint tj eiva sjca unmarstinmgno jd weit cgoet ka ipprjprgita gn iny ogvan fgrfucstinfa. Iwabb fejsan dunftgjn wgbb ka ipprjprgita gn twj mgffarant wiys. Dgrstby tea dunftgjn sejubm ka fjnsgstantwgte tea purpjsa jd tea cjmab, wgte lnjwn miti jr teajry jr difts, inm wgte lnjwn jr issucamkaeivgjurs. Djr axicpba, tea purpjsa cgoet ka tj pramgft tea dutura kaeivgjur jd i quintgty wegfegs axpaftam tj gnfraisa wgte tgca. Gn tegs fisa tgca fin ka gmantgam is tea gnmapanmant virgikba

sgnfa tea quintgty mapanms jn tgca. ]ea dunftgjn fejsan djr citeacitgfib iftgvgty sejubm ka jna gnwegfe tea vibua jd tea mapanmant virgikba gnfraisas wgte tgca. Vafjnmby, kairgno gn cgnm teit teacjmabbgno prjfass gs i fyfba inm sj gt gs pjssgkba, inm usuib, tj oj rjunm gt cjra tein jnfa, tearst fejgfa jd dunftgjn sejubm ka is sgcpba is ibbjwam ky tea cjmabbgno fjntaxt. ]ea cign raisjndjr mjgno tegs gs tj ivjgm fjcpbgfitgjn unbass gt gs raibby nafassiry. Pegbjsjpegfibby, in gngtgib fejgfa jdi sgcpba dunftgjn gs fjnsgstant wgte tea dunmicantib kabgad teit cjst peanjcani ciy ka cjmabbamimaquitaby ky sgcpba biws inm teajrgas. Gt gs fjccjn anognaargno priftgfa ibwiys tj usa tea sgcpbastcjmab pjssgkba gn i ogvan sgtuitgjn. Vj, djr tea rst trgp irjunm tea fyfba, tea ipprjprgita dunftgjnsejubm ka tea sgcpbast teit gs fjnsgstant wgte lnjwn difts, kaeivgjurs, teajry jr miti. Gd tea quintgtyjd gntarast gs lnjwn njt tj ka fjnstint, tegs cgoet ka i bgnair dunftgjn. Gd tea rst fejgfa turns juttj ka gnimaquita it tea stioa jd tea fyfba weara tea rasubt gs gntarpratam jr tea jutfjca gs avibuitam(stap 1) tean gt gs raisjnikba tj try sjcategno cjra fjcpbgfitam< i quimritgf dunftgjn cgoet ka teasafjnm fejgfa gd tea rst fejgfa wis bgnair.

EABC (;001)8Vaftgjn 1.98 ]ea Cjmabbgno Fyfba inm Dunftgjns

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4/23

Gt gs gcpjrtint tj raibgsa teit sjpegstgfitgjn gs njt nafassirgby i vgrtua gn gtsabd. ]ea cargts jdfjcpbgfitgjn mapanm upjn tea purpjsa djr wegfe tea cjmab gs kagno djrcubitam. I cjmab jd teawaitear teit anikbas i mafgsgjn jn weatear jr njt tj tila in uckrabbi tj wjrl jn iny pirtgfubir miywgbb ka ritear bass sjpegstgfitam tein teit raqugram tj ogva in iffurita pramgftgjn jd tea icjunt jdrigndibb gn tea vgfgngty jd tea wjrlpbifa jn teit miy.

Gn tea naxt suksaftgjn wa wgbb bjjl it virgjus typas jd dunftgjns teit eiva kaan gntrjmufam sj dirkut gn i mgffarant wiy, fjnfantritgno cjra jn teagr oripegfib kaeivgjur inm teagr piricatars. Iscantgjnam airbgar, ipprjprgitanass gs matarcgnam ky tea axtant tj wegfe tea kaeivgjurjd tea fejsandunftgjn raafts tea kaeivgjur tj ka cjmabbam is tea gnmapanmant virgikba virgas. ]ea kaeivgjur jdi dunftgjn gs matarcgnam ky weatear gt gs bgnair, njn-bgnair, jr pargjmgf inm gts rinoa jd vibgmgty. Ingcpjrtint tisl jd tegs _jrlkjjl gs tj oat yju tj tegnl cjra inm cjra gn cjmabbgno tarcs ikjut teadjrcs inm issjfgitam kaeivgjurs jd dunftgjns. _a seibb ibsj tila tea jppjrtungty jd margvgno sjcaoanaribgtgas drjc spafgf axicpbas.

;. Fjnstint dunftgjns]eara ira twj peysgfib gntarpratitgjns jd fjnstinfy teit ira jd gntarast eara. I vary fjccjn djrc gsfjnstinfy wgte tgca. Cjtgjn unmar orivgty ciy ka cjmabbam is cjtgjn wgte fjnstint iffabaritgjn.Ky mangtgjn, Dgxam [ita Cjrtoioas (gnfraisgnoby pjpubir gn tea bita 9770s) jffar i fjnstint ritajd gntarast jvar i spafgam pargjm. Gn teasa axicpbas, tea fjnstinfy wgbb ka bgcgtam tj i fartigntgca gntarvib. Cjtgjn unmar orivgty wgbb jnby gnvjbva tea fjnstint iffabaritgjn mua tj tea Airtesorivgtitgjnib pubb is bjno is tea cjtgjn gs fbjsa tj tea Airtes surdifa. Gn iny fisa tea iffabaritgjnwgbb jnby ka drjc tea tgca tea jkhaft gs rabaisam tj tea tgca gt stjps. Qndjrtunitaby, gnfraisas gn kisagntarast ritas avantuibby daam gntj cjrtoioa ritas. Vj cjrtoioa banmars ira jnby ikba tj jffar xam

ritas djr i fartign tgca. I citeacitgfib stitacant jd teasa bgcgts gs i stitacant jd tea rinoa jd vibgmgtyjd tea fjnstint dunftgjn cjmab.

Injtear typa jd fjnstinfy gs fjnstinfy gn spifa. Bjno stratfeas jd [jcin rjims wara kugbt gni xam mgraftgjn. Djr it baist pirt jd teagr banotes, rjims eiva fjnstint wgmte. Gn cjmabbgno teadjrcitgjn inm cjvacant jd sagscgf wivas gn tea Airtes frust gt gs fjnvangant tj issuca teit teabiyars drjc wegfe tea Airtes frust gs djrcam eiva fjnstint tegflnass wgte raspaft tj tea Airtessurdifa. Gn teasa fisas tea issucptgjn jd fjnstinfy wgbb jnby ka vibgm wgtegn fartign bgcgts gn spifa.

= EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


5/23

Axicpba 9]ea rita jd jw jd witar drjc i tip gs manjtam isr(bgtras par cgnuta). ]ea tgcadjr wegfe gt gs turnam jn gs manjtam kyt (cgnutas). Vuppjsa teit i tip gs turnam

jn inm teit tea rita jd witar runngno jut jd i tip gs issucam tj ka fjnstint it6 bgtras par cgnuta inm teit gt gs turnam jff idtar 90 cgnutas.

(i) _rgta mjwn i citeacitgfib stitacant jd tea cjmab djr tea jw drjc teatip, gnfbumgno gts rinoa jd vibgmgty.

(k) Vlatfe i oripe jd tea virgitgjn jdrwgte t.

(f) Dgnm in aquitgjn djr tea nuckar jd bgtras jd witar teit eiva run jut jd teatip idtar tcgnutas.

(m) Fibfubita tea vjbuca jd witar teit eis run jut jd tea tip teraa cgnutaskadjra gt gs turnam jff.

Vjbutgjn

(i) r3 6 (0 t 90)

(k)

r (bgtras par cgn)

t (cgnutas)0 1 90 91

9

;

6

Dgoura 98 Dbjw drjc tip

(f)T 3rt (0 t 90)

(m) ]ea tip wgbb eiva run djr savan cgnutas< 6 bgtras par cgnuta x ? cgnutas 3 ;9 bgtras

Njta teit i cjra sjpegstgfitam cjmab wjubm ibbjw djr tea virgitgjn gn jw rita is tea tip gs turnamjn inm turnam jff.


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6/23

6. Bgnair dunftgjns; eis gntrjmufam bgnair dunftgjns jd tea djrcy3ix + k. Vufe dunftgjns ogva rgsa tj strigoet-

bgna oripes. ]ea fjastfgant i gs tea sbjpa. Gdi gs pjsgtgva tea oripe jdyioignst xsbjpas upwirms. Gdi gs naoitgva tea oripe sbjpas mjwnwirms. ]ea fjastfgant kogvas tea gntarfapt jn tea y-ixgs. ]ea

tarcs i inm kciy ka fibbam tea piricatars jd tea bgna. Njta teit tegs gs i mgffarant usa jd teatarc piricatar tein gn tea piricatrgsitgjn jd dunftgjns mgsfussam gn ;.

Bgnair cjmabs djr dibbgno rjflsGn cjmabbgno gt gs wgsa tj usa i njtitgjn wegfe ts gn wgte tea ippbgfitgjn. _ean cjmabbgno vabjfgtyunmar fjnstint iffabaritgjn, wa seibb rapbifa tea mapanmant virgikba ykyv (djr vabjfgty), inm teagnmapanmant virgikbaxkyt (djr tgca). ]ea iffabaritgjn wgbb ka manjtam ky tea syckjbi. Fjnsgmartea cjtgjn jd i rjfl mgsbjmoam drjc tea tjp jd i fbgff (61 c egoe) ky i vgbbign murgno tea bcgno jd itergbbar. ]ea bc prjmufar cgoet ka gntarastam gn ejw bjno tea rjfl wjubm tila tj dibb tj tea orjunmkabjw tea fbgff inm ejw dist gt wjubm ka trivabbgno it orjunm gcpift. ]ea rjfl ciy ka issucamtj eiva i fjnstint mjwnwirm iffabaritgjn jd 7.5 c s; wegfe tea iffabaritgjn mua tj orivgty. ]eavabjfgty(vc s9)jd i rjfl, dibbgno drjc tea tjp jd i fbgff 61 c egoe, fin ka cjmabbam ky tea aquitgjn

v3 7.5t (0 t ;.?)

wearatgs tea tgca gn safjnms idtar tea rjfl stirts tj dibb. ]egs djbbjws drjc tea dift teit iffabaritgjngs tea rita jd feinoa jd vabjfgty wgte tgca. Gd tea iffabaritgjn gs fjnstint inm tea jkhaft stirts drjcrast, tean tea vabjfgty gs ogvan sgcpby ky tea prjmuft jd iffabaritgjn inm tgca. ]ea uppar bgcgt djrtgs tea tgca it wegfe tea rjfl egts tea orjunm caisuram wgte i stjp-witfe (ikjut ;.? s gn tegs fisa).Dgoura ; sejwsvis i dunftgjn jdt. Tabjfgty gs i bgnairby gnfraisgno dunftgjn jd tgca inm gts oripe gsi strigoet bgna pissgno terjuoet3 0, v3 0. Njta teit virgjus issucptgjns ira naamam tj jktign teaqujtam rasubt jd i bgnair virgitgjn gn spaam wgte tgca8 gt gs issucam teit teara gs nj igr rasgstinfa,

nj spgnngno inm nj wgnm.

0

90

;0

0.1 9 9.1 ; ;.1 6

Tabjfgty (c s 9)

]gca (s)0

Dgoura ;8 Oripe jdv3 7.5t djr tea dibbgno rjfl

Gn weit wiy sejubm tea aquitgjn djrvka ibtaram gd tea vgbbign wara ikba tj terjwtea rjfl mjwnwirmsit 1 c s9: Prjvgmam wa ira caisurgno pjsgtgjn jr mgspbifacant mjwnwirms, i mjwnwirms vabjfgtygs pjsgtgva. Njw wa eiva teitv3 1 weant3 0. Vj i naw cjmab djrv gs

v3 7.5t+ 1 (0 t ]9)

Vgnfa teay ira kjte mjwnwirms, tea gngtgib vabjfgty sgcpby imms tj tea vabjfgty it iny tgca rasubtgnodrjc dibbgno unmar orivgty. Njta teit]9 gs kagno usam njw djr tea uppar bgcgt jnt (gnstaim jd ;.?)kafiusa ;.? gs (ipprjxgcitaby) tea tgca tilan tj dibb 61 c drjc rast ritear tein wgte in gngtgibmjwnwirms vabjfgty. (Qsgno tea syckjb]9 sivas us trygno tj wjrl jut gts vibua djr tea cjcant!)

Njta teit i oanarib djrc jd tea cjmab djr cjtgjn unmar fjnstint iffabaritgjn jd ciongtumaic s;

ogvan in gngtgib spaamkc s9 gsv3it+k. Gn tea cjmab hust fjnsgmarami3 7.5 inmk3 1.

4 EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


7/23

]islislDjr tea ikjva axicpba cjmabbgno i dibbgno rjfl8

(i) Matarcgna weatear]9 gs cjra jr bass tein ;.?.

(k) Vlatfe i oripe jdv djr0 t ]9.

Wjur sjbutgjn

Inswar

(i)]9 wgbb ka bass tein ;.? sgnfa tea rjfl wgbb ka cjvgno distar terjuoejut gts masfant.

(k) ]ea oripe gs stgbb i strigoet bgna kut mgspbifam upwirms fjcpiram wgte Dgoura ;.

0

90

;0

60

0.1 9 9.1 ; ;.1 6

Tabjfgty (c s 9)

]gca (s)0

Oripe jdv3 7.5t+ 1 djr tea dibbgno rjfl

Fjnsgmar njw ejw tea dunftgjn djrv wgbb feinoa gd tea vgbbign gs avan cgoetgar tein wa pravgjusbytejuoet inm terjws tea rjfl upwirms wgte in gngtgib spaam jd1 c s9 gnstaim jd sgcpby mgsbjmognogt jr terjwgno gt mjwnwirms. Gn tegs fgrfucstinfa, tea gngtgib vabjfgty gs mgraftam upwirms, inm sgnfapjsgtgjn gs kagno caisuram mjwnwirms, tea gngtgib vabjfgty gs naoitgva. _a fin usa tea aquitgjnv3 7.5t+kioign. ]egs tgcav3 1 weant3 0, baimgno tjk3 1 inm

v3 7.5t 1 (0 t ];)


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8/23

]ea naw tgca it wegfe tea rjfl egts tea orjunm gs manjtam ky];. ]ea rjfl wgbb rgsa kadjra dibbgnotj tea ojunm tegs tgca sj]; wgbb ka biroar tein]9.Drjc tea cjmabbgno pjgnt jd vgaw, teara gs jna jtear sgongfint tgca kadjra tea rjfl egts tea orjunm.Dgoura 6 sejws tea naw oripe jdvioignstt. Njtgfa teit teara gs i tgca it wegfev(wegfe stirts it1) gs zarj. _eit mjas tegs cain:

0

90

;0

0.1 9 9.1 ; ;.1 6

Tabjfgty (c s 9)

]gca (s)0

1

Dgoura 68 Oripe jdv3 7.5t 1 djr tea dibbgno rjfl

Is tgca ojas ky, tea dift teit orivgty gs fiusgno tea rjfl tj iffabarita mjwnwirms cains teit tearjfls upwirm cjtgjn wgbb sbjw. Gts vabjfgty wgbb mafraisa gn ciongtuma untgb gt raifeas zarj. Ittegs pirtgfubir gnstint tea rjfl wgbb ka it gts egoeast pjgnt inm gts vabjfgty wgbb feinoa drjc upwirms(naoitgva) tj mjwnwirms (pjsgtgva) pissgno gnstintinajusby terjuoe zarj gn tea prjfass._a fin fibfubita tegs tgca ky sukstgtutgno zarj djrv inm wjrlgno jut tea fjrraspjnmgnot.

0 3 7.5t 1, sj t3 1

7.53 0.19.

]egs cains teit tea rjfl gs stitgjniry ikjut i eibd safjnm idtar kagno terjwn upwirms. Vuksaquantbytea rjfl wgbb dibb untgb gt egts tea orjunm. Kut teara gs yat jna cjra tgca teit ciy ka sgongfintgn tea cjmabbgno fjntaxt fejsan eara. Murgno gts hjurnay tj tea orjunm 61 c kanaite tea fbgff-tjp,tea rjfl wgbb piss tea tjp jd tea fbgff ioign. Njta teit wa ira cjmabbgno tea cjtgjn jd i pirtgfubirpjgnt, siy tea bjwast pjgnt, jn tea rjfl. I raib rjfl, wgte ipprafgikba sgza, wgbb jnby piss tea tjpjd tea fbgff, wgtejut binmgno jn gt jr egttgno gt, gd gt gs terjwn i bgttba djrwirm is wabb is up. Inywiy,gn prgnfgpba wa fjubm usa tea dunftgjn teit wa stirtam wgte, raprasantgno tea vabjfgty jd in jkhaftdibbgno drjc rast unmar orivgty, tj wjrl jut ejw bjno tea rjfl wgbb tila tj piss tea tjp jd tea fbgffeivgno raifeam tea egoeast pjgnt gn gts pite. I sgcpbar catejm gs tj iroua teit, is bjno is tea rjflgs terjwn drjc tea fbgff tjp bavab (tegs raqugras tea vgbbign tj ka bygno mjwn!), tea rjfl sejubm tilaaxiftby tea sica tgca (ipprjxgcitaby 0.1 s) tj raturn tj tea bavab jd tea fbgff tjp is gt tjjl tj rgsaikjva tea fbgff tjp tj tea egoeast pjgnt gn gts pite. Vj wa sgcpby mjukba 0.1 s tj mamufa teit tearjfl pissas tea fbgff tjp ioign ikjut 9 s idtar kagno terjwn.



9/23

]islisl]egs ]isl fjnfarns tea dibbgno rjfl cjmab hust mgsfussam.

(i) Imm bgnas tj i slatfe varsgjn jd Dgoura 6 tj raprasant vabjfgty is i dunftgjn jd tgca gd tea rjfl gs

(g) mgsbjmoam (gg) terjwn wgte vabjfgty6 c s9 mjwnwirms (ggg) terjwn wgte vabjfgty ;c s98

Wjur sjbutgjn

Inswar

0

90

;0

60

0.1 9 9.1 ; ;.1 6

Tabjfgty (c s 9)

]gca (s)0

1

(k) _eit mj yju mamufa ikjut tea affaft jd tea gngtgib vabjfgty jn tea oripe jd vabjfgty ioignst tgca:

Wjur sjbutgjn

Inswar]ea affaft jd feinogno tea gngtgib vabjfgty (gn sgza jr gn sgon) gs sgcpby tj mgspbifa tea strigoet bgnaupwirms jr mjwnwirms wgtejut feinogno gts sbjpa.

(f) Gciogna teit tea bcgno wis jn tea Cjjn wgte rjuoeby jna-sgxte tea orivgtitgjnib pubb jd Airte.Dgnm i bgnair dunftgjn teit wjubm masfrgka tea vabjfgty jd i mgsbjmoam rjfl8

Wjur sjbutgjn

Inswar

v37.5

4t 9.4t

(m) _eit mj yju mamufa ikjut tea affaft jd feinogno tea iffabaritgjn mua tj orivgty jn tea oripejd vabjfgty ioignst tgca:

Wjur sjbutgjn

Inswar]ea oripe jd vabjfgty ioigns tgca gs stgbb bgnair kut tea feinoa gn tea iffabaritgjn mua tj orivgtyfeinoas tea sbjpa.


7


10/23

Vj, gn tea fjntaxt jd cjmabbgno cjtgjn unmar orivgty, tea gngtgib vabjfgty matarcgnas tea vartgfibmgspbifacant jd tea bgna, gts gntarfapt jn tea v-ixgs, inm tea iffabaritgjn matarcgnas tea sbjpa.Ioign, ogvan tea cjmabbgno fjntaxt, kjte jd teasa gnuanfa tea rinoa jd vibgmgty jd tea cjmab sgnfateay ibtar tea tgca tilan djr tea rjfl tj raife tea orjunm inm tegs xas tea uppar bgcgt jn tgca.Bgla vabjfgty, iffabaritgjn eis mgraftgjn is wabb is ciongtuma. Is bjno is pjsgtgjn gs kagno caisurammjwnwirms, inm jnby orivgty gs fjnsgmaram tj ift, dibbgno jkhafts mj njt prjvgma iny axicpbas jdnaoitgva iffabaritgjns - kut rjflat cjtgjn mjas. _eara mjwnwirms iffabaritgjns ira raprasantam ispjsgtgva, in upwirms iffabaritgjn wgbb ka naoitgva. Vj i cjmab jd tea cjtgjn jd i rjflat iffabaritgnoiwiy drjc tea Airte fjubm gnfbuma i fjnstint naoitgva iffabaritgjn. Ejrgzjntib iffabaritgjn, siyjd i rjim vaegfba, gn tea sica mgraftgjn is pjsgtgjn is kagno caisuram, gs raprasantam is pjsgtgva.Mafabaritgjn, djr axicpba wean tegs vaegfba gs kagno krilam, gcpbgas teit vabjfgty gs mafraisgno wgtetgca, inm gs raprasantam is naoitgva. Gn citeacitgfib cjmabbgno, gt gs usuib tj radar tj iffabaritgjn,weatear gt raprasants pjsgtgva iffabaritgjn jr mafabaritgjn.

Vuppjsa teit wa ira masfrgkgno tea cjtgjn jd i rjflat tilgno jff vartgfibby murgno gts gngtgib kjjstar

stioa jd 90 s. _a cgoet cjmab tea iffabaritgjn is i fjnstint

;0 c s

;

. ]ea naoitgva sgon irgsaskafiusa mjwnwirms gs kagno tilan is tea pjsgtgva mgraftgjn kut tea iffabaritgjn gs upwirms. Vgnfatea rjflat gs stirtgno drjc rast, in ipprjprgita dunftgjn gs

v3 ;0t (0 t 90)

]egs sejubm masfrgka tea virgitgjn jd gts vabjfgty wgte tgca untgb tea anm jd tea gngtgib kjjstar stioajd gts goet. Dgoura = sejws tea fjrraspjnmgno oripe jd vabjfgty ioignst tgca. Njta tea wiy gn wegfetea oripe sbjpas mjwnwirms tj tea rgoet. ]egs dunftgjn masfrgkas in gnfraisgnoby naoitgvavabjfgty istgca pissas, fjnsgstant wgte in gnfraisgno upwirmsvabjfgty. ]ea fjrraspjnmgno oripe djr i pjsgtgvaiffabaritgjn jd tea sica ciongtuma wjubm sbjpa upwirms tjwirms tea rgoet.

t

(c s 9)

(s)0

;00

900

; = 4 5 90

v

Dgoura =8 Tirgitgjn jd vabjfgty jd rjflat murgno tea gngtgib kjjstar stioa.

]islislGciogna teit i sitabbgta gs dibbgno tjwirms Airte it 1c s9 wean i kjjstar rjflatgs ram djr 1 s iffabaritgno gt iwiy drjc tea Airte it 90 c s;.

(i) _rgta mjwn i fjrraspjnmgno bgnair dunftgjn teit wjubm masfrgka gts vabjfgty murgno tea kjjstarstioa.

Wjur sjbutgjn



11/23

InswarGd pjsgtgjn gs caisuram mjwnwirms, iffabaritgjn iwiy drjc tea Airte ciy ka wrgttan is 90c s;.]ea gngtgib vabjfgty tjwirms tea Airte ciy ka manjtam ky(+)1c s9 sjv3 90t+1 (0 t 1).Gd pjsgtgjn gs caisuram upwirmsv3 90t 1 (0 t 1).

(k) Vlatfe tea fjrraspjnmgno oripe jd vabjfgty ioignst tgca gd pjsgtgjn gs caisuram mjwnwirmstjwirms Airte8

Wjur sjbutgjn

Inswar

(c s 9)

(s)

; = 4

=0

;0

0

;0

v

t

Vitabbgta vabjfgty (pjsgtgjn caisuram mjwnwirms tjwirms Airte)

(f) Vlatfe tea fjrraspjnmgno oripe jd vabjfgty ioignst tgca gd pjsgtgjn gs caisuram upwirms iwiydrjc tea Airte8

Wjur sjbutgjn

Inswar

(c s 9)

(s)

; = 4

=0

;0

0

;0

v

t

Vitabbgta vabjfgty (pjsgtgjn caisuram upwirms iwiy drjc Airte)


99


12/23

(m) It weit tgca wjubm tea vabjfgty jd tea sitabbgta ka zarj:

Wjur sjbutgjn

Inswar

_eanvgs 0,0 3 90t + 1, sjt3 0.1. ]ea sitabbgta eis zarj vabjfgty tjwirms tea Airte idtar 0.1 s.

(a) _eit gs tea vibua jd tea vabjfgty it tea anm jd tea kjjstar stioa:

Wjur sjbutgjn

Inswar_eant 3 1, agtearv 3 90 9 + 1 3 1, sj tea vabjfgty gs 1 c s9 iwiy drjc tea Airte, jr,usgno tea safjnm aquitgjn gn (i),v3 90 1 3 1, baimgno tj tea sica fjnfbusgjn.

Jtear fjntaxts djr bgnair cjmabs

Bgnair dunftgjns ciy irgsa gn jtear fjntaxts. Gn aife jd teasa sgtuitgjns, tea sbjpa inm gntarfaptvibuas wgbb eiva sjca cjmabbgno sgongfinfa. Gnmaam tea kaeivgjur inm eanfa tea sugtikgbgty jd ibgnair dunftgjn, jd tea djrcy 3ix+k, wean cjmabbgno iny ogvan sgtuitgjn wgbb ka matarcgnam ky

tea vibuas jdiinm k.

]islislMurgno ;0 cgnutas jd rign, i fybgnmrgfib rign kirrab teit gs gngtgibby acpty gs bbamtj i mapte jd 9.1 fc.

(i) Fejjsa virgikbas tj raprasant tea bavab jd witar gn tea kirrab inm tgca. Vlatfe i oripe raprasantgno

tea bavab jd witar gn tea kirrab gd tea gntansgty jd rigndibb racigns fjnstint jvar tea ;0 cgnuta pargjm.

Wjur sjbutgjn

9; EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


13/23

InswarGn tegs inswar e fc gs usam djr tea bavab jd witar caisuram drjc tea kjttjc jd tea kirrab inm tcgnutas djr tgca.

t (cgnutas)

0

0.1

9

9.1

0 1 90 91 ;0

e (fc

e3 0

)

e

Eagoet (mapte) jd rignwitar gn i kirrab.

(k) _rgta mjwn i bgnair dunftgjn teit raprasants tea bavab jd witar gn tea vassab tjoatear wgte gtsrinoa jd vibgmgty.

Wjur sjbutgjn

Inswar]ea gntansgty jd rigndibb gs stitam tj ka fjnstint, sj tea rita it wegfe tea kirrab bbs ciy ka tilan isfjnstint. ]ea orimgant jd in ipprjprgita bgnair dunftgjn rabitgno bavab jd witar (efc) caisuram drjctea kjttjc jd tea vassab inm tgca (t, cgnutas) caisuram wjubm ka 9.1

;0 3 0.0?1 inm in ipprjprgita

bgnair dunftgjn wjubm ka e3 0.0?1t+ f. Vgnfa tea kirrab gs acpty tj stirt wgte, e 3 0 wean t30, gcpbygno teit f3 0. Vj tea ipprjprgita bgnair dunftgjn inm gts rinoa jd vibgmgty ira axprassam kye3 0.0?1t, (0 t ;0).

(f) Vtita iny issucptgjns teit yju eiva cima8

Wjur sjbutgjn

InswarGt gs issucam teit tea kirrab eis i ungdjrcby fybgnmrgfib frjss saftgjn, teit nj witar gs racjvammurgno tea rigndibb inm teara ira nj ejbas jr bails up tj 9.1 fc mapte.

(m) _rgta mjwn tea icanmam djrc jd yjur inswar tj (k), gd tea vassab fjntigns ; fc jd witar gngtgibby.

Wjur sjbutgjn

Insware3 0.0?1t+ ; (0 t ;0)


96


14/23

]islislVuppjsa teit yju trivab jdtan drjc Njttgnoeic tj Cgbtjn Laynas wegfe gs imgstinfa jd 5? cgbas ibcjst ibb jd wegfe gs ibjno tea C9 cjtjrwiy. Qsuibby gttilas 9.1 ejurs. Vuppjsa ibsj teit, jn jna jffisgjn, yju eiva ioraam tj pgflsjcajna up it tea Bagfastar hunftgjn (;9) jd tea C9. ]egs gs ;1 cgbas drjc teastirt jd yjur hjurnay gn Njttgnoeic. Gd yju stirt yjur hjurnay it 5 i.c., weit tgcasejubm yju imvgsa djr tea pgfl-up:

Wjur sjbutgjn

Inswar(Oripegfib catejm)

Issuca i fjnstint spaam djr tea wejba hjurnay. ]egs cains teit gd 5? cgbas gs fjvaram gn 9.1 ejurs,tean eibd tea mgstinfa (=6.1 cgbas) gs fjvaram gn 0.?1 ejurs inm sj jn.

0

;0

=0

40

50 0.=6

0.1 9 9.1

;1

I mgstinfa jd;1 cgbas wgbb kafjvaram gn 0.=6 ejurs

]ea ivarioa spaam gs 5?

9.13 15 cpe.

]egs gs ibsj tea orimgantjd tea oripe

mgstinfagn cgbas

tgca gn ejurs

9= EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


15/23

Inswar(Vyckjbgf catejm)

Bat mcgbas ka tea mgstinfa trivabbam gn tgca tejurs. ]eanm

t 3 15t. ]egs gs vibgm jnby djr tea

muritgjn jd tea hjurnay (0 t

9.1). ]ea aquitgjn fin ka usam tj nm tea tgca it wegfe m3 ;1.Njw;1 3 15tinm sjt3

;1

153 0.=6906==5 3 0.=6 (tj twj mafgcib pbifas). Agtear wiy, ogvan teit

0.=6 e gs ikjut ;4 cgnutas, i pjssgkba suooastgjn gs teit tea pissanoar sejubm ka imvgsam 5.;4 i.c.djr tea pgfl-up. Kut tea issucptgjn jd fjnstint spaam eis gts bgcgtitgjns. Gt wjubm ka sidar tj siyka teara ky 5.;0 i.c. kut ka prapiram tj wigt pareips untgb 5.60 i.c.

]islislI bjfib iutejrgty eis jjm fjntrjb pbins gn wegfe tea acaroanfy inm rasfua sarvgfasira ibartam wean tea rgvar bavab rgsas tj frgtgfib vibuas. I bgnair cjmab gs usam tjastgcita tea virgitgjn jd eagoet wgte tgca. Idtar i pargjm jd fjntgnujus eaivy rigntea bavab jna miy wis 9.1 c it 5 i.c. inm 9.5 c it ; p.c.

(i) Qsa i bgnair cjmab tj wrgta mjwn in aquitgjn djr astgcitgno tea bavab jd tea rgvar it mgffaranttgcas jd tea miy8

Wjur sjbutgjn


91


16/23

InswarGd tea bavab jd witar gs raprasantam kyBc inm tgca kytejurs idtar 5 i.c. tean i bgnair cjmab djrtea bavab is i dunftgjn jd tgca ciy ka wrgttan

B3it+k

wearaiinmkira fjnstints tj ka djunm drjc tea jtear gndjrcitgjn gn tea prjkbac. Vpafgfibby, gtgs stitam teitB3 9.1 weant3 0 inmB3 9.5 weant3 4. ]ea rst stitacant gcpbgas teit

9.1 3 0 +k jr k3 9.1

]ea safjnm stitacant gcpbgas teit

9.5 3 4i+k

jr, idtar sukstgtutgno djrk,

9.5 3 4i+ 9.1 jr 0.6 3 4i jr i3 0.01

Vj tea aquitgjn djr astgcitgno tea bavab jd tea rgvar it mgffarant tgcas gs

B3 0.01t+ 9.1

(k) Vuooast i sugtikba rinoa jd vibuas jd tgca djr wegfe tea cjmab fjubm ka usam8

Wjur sjbutgjn

Inswar]ea cjmab gs vibgm katwaan 5 i.c. inm ; p.c. inm, suksaquantby, jnby is bjno is tea rgvar bavabrgsas staimgby.

(f) _eit tgca mjas tea cjmab pramgft teit tea bavab jd tea rgvar wgbb raife ; c:

Wjur sjbutgjn

Inswar]ea cjmab wgbb pramgft i bavab jd ; c it tgcat ogvan ky

; 3 0.01t+ 9.1 jr t3 0.1

0.013 90

g.a. 90 ejurs idtar 5 i.c. wegfe gs 4 p.c.



17/23

]islislMurgno jna wgntar, tea rjims gn i rurib irai wara fjcpbataby draa drjc snjw weangt stirtam snjwgno it cgmngoet. Gt snjwam eaivgby ibb ngoet inm miy. Ky 90 i.c. gtwis 97 fc maap.

]j siva cjnay tea bjfib iutejrgtgas wigt untgb tea snjw gs 60 fc maap kadjrapbjuoegno tea snjw iwiy drjc tea rjims. Djrafist wean pbjuoegno sejubm stirt,stitgno iny issucptgjns yju eiva cima.

Wjur sjbutgjn

InswarGd tea mapte jd snjw gs raprasantam kyMfc inm tgca kytejurs idtar cgmngoet tean i bgnair cjmabdjr tea mapte is i dunftgjn jd tgca ciy ka wrgttan8

M3it+k

wearaiinmkira fjnstints tj ka djunm drjc tea jtear gndjrcitgjn gn tea prjkbac jr drjc issucp-tgjns. Is teara wis nj snjw it cgmngoet

0 3 0 +k jr k3 0

Gt gs stitam teitM3 97 weant3 90, g.a.

97 3 90i jr i3 9.7

Vj tea aquitgjn djr astgcitgno tea mapte jd snjw it mgffarant tgcas gs

M3 9.7t

]ea cjmab wgbb pramgft i bavab jd 60 fc it i tgcatogvan ky

60 3 9.7t jr t3 60

9.73 91.?57

g.a. 91.?57 ejurs idtar cgmngoet wegfe gs i bgttba idtar 6.=? p.c.

Issucgno teit tea snjw kugbm up gs staimy a.o. nj mrgdtgno jr feinoa gn prafgpgtitgjn, tegs suooasts

teit pbjuoegno sejubm stirt ikjut 6.=1 p.c.


9?


18/23

Axarfgsas

9. I frjss-feinnab darry usuibby tilas ; ejurs tj cila tea =0 lc frjssgno drjc Anobinm inmDrinfa.

(i) _eit gs tea kjits ivarioa spaam:(k) Margva i bgnair cjmab fjnnaftgno mgstinfa drjc Anobinm inm tgca sgnfa baivgno pjrt. Vtita

iny bgcgtitgjns jd tea cjmab.

(f) Iffjrmgno tj tegs cjmab, wean wgbb tea kjit ka 91 lc inm 61 lc drjc Anobinm:

;. Murgno jna wgntar, tea rjims gn tea fjuntry mgstrgft wara fjcpbataby draa drjc snjw wean gtstirtam snjwgno it ;860 i.c. inm gt snjwam staimgby ibb miy. It ?860 i.c. gt wis 9= fc maap.]j siva cjnay, tea bjfib priftgfa wis tj wigt untgb tea snjw wis ;0 fc maap kadjra pbjuoegnotea rjims. Djrafist wean pbjuoegno wjubm stirt, stitgno iny issucptgjns.

6. Gn i mrjuoet, tea pjpubitgjn jd i pirtgfubir spafgas jd witar kaatba gn i pjnm gs jksarvam tj eivaeibvam wean tea vjbuca jd witar gn tea pjnm eis dibban ky eibd. Cila i sgcpba issucptgjnikjut tea rabitgjnsegp katwaan tea kaatba pjpubitgjn inm tea vjbuca jd witar gn tea pjnm inmaxprass tegs gn syckjbs is in aquitgjn. _eit wjubm yjur cjmab pramgft djr tea pjpubitgjnwean tea witar vjbuca gs jnby jna tegrm jd weit gt wis jrgognibby.

=. I rc prjmufas i spafgibgsam gnstrucant inm, ibtejuoe gt eis tea difgbgtgas tj prjmufa 900gnstrucants par waal, gt riraby prjmufas cjra tein 10. Gt gs nmgno gt mgstfubt tj issass teafjst jd prjmufgno tea gnstrucants inm tj sat raibgstgf prgfas. ]ea rcs iffjuntint astgcitasteit tea rc piys jut 1000 par waal jn xam fjsts (jvareaims, sibirgas atf.) inm teit teaimmgtgjnib fjst jd prjmufgno aife gnstrucant gs 10.

(i) Margva inm usa i bgnair cjmab djr tea virgitgjn gn tjtib fjsts wgte tea quintgty jd gnstru-cants prjmufam. Vtita iny bgcgtitgjn jd tegs cjmab.

(k) _eit gs tea cjmabs pramgftgjn djr tea fjst jd prjmufgno 50 gnstrucants par waal:



19/23

Inswars

9. (i) I mgstinfa jd =0 lc gs fjvaram gn ; ejurs. Vj tea ivarioa spaam gs =0/; 3 ;0 lc e9.

(k) I bgnair cjmab issucas teit tea kjit gs i pjgnt cjvgno it fjnstint spaam inm wgbb jnby

ka vibgm djr ; ejurs (jr =0 lc) wegba tea kjit gs trivabbgno drjc Anobinm tj Drinfa. Gt mjasnjt ibbjw djr virgitgjns gn spaam. Gd tea mgstinfa drjc tea Anobgse pjrt it iny tgca t ejurs gsmanjtam kymlc, teanm3 ;0t.

(f) _ean tea kjit gs 91 lc drjc Anobinm 91 3 ;0t, sjt 3 91/;0 3 0.?1, sj tea kjitgs 0.?1 ejur (=1 cgnutas) drjc pjrt. _ean tea kjit gs 61 lc drjc Anobinm, 61 3 ;0t, sjt3 61/;0 3 9.?1, sj tea kjit gs 9.?1 ejur (9 ejur =1 cgnutas) drjc pjrt.

;. Issuca teit teara gs nj snjw it ;860 i.c. inm teit tea rita jd iffucubitgjn jd snjw gsfjnstint. ]ean, gd tea snjw gs 9= fc maap it ?860 i.c., tea rita jd iffucubitgjn gs ;.5 fcpar ejur. I bgnair cjmab djr tea mapte (mfc) jd snjw tejurs idtar ;860 i.c. gsm3 ;.5t.m

wgbb ka ;0 wean ;0 3 ;.5t, g.a.t 3 ;0/;.5 3 ?.9=6. ]egs fjrraspjnms tj ikjut 7867 i.c. Vjpbjuoegno sejubm stirt it ikjut 78=0 i.c.

6. Manjta pjpubitgjn kyPinm vjbuca jd pjnm kyT. ]eanP gs prjpjrtgjnib tjT sjP 3lTwearal gs i fjnstint jd prjpjrtgjnibgty. _eanT kafjcasT/6, teanPkafjcasP/6.

=. (i) Manjta tea nuckar jd gnstrucants cima par waal kyN inm tea fjrraspjnmgno fjst kyF. Isuca teitFgnfraisas it i fjnstint rita wgteN (g.a.F gs prjpjrtgjnib tjN). ]ean ibgnair cjmab djr tjtib fjsts (]) gs]3 1000+10N. ]egs wgbb ka vibgm jnby djr0 N 900.

GdN3 50, tean]3 1000 + 10 50 3 7000.

(k) ]ea pramgftam tjtib fjst gs 7000.

=. Catejms djr fibfubitgno orimgantJffisgjnibby yju ciy ka difam wgte twj mgffarant pigrs jd vibuas jr fjjrmgnitaswgte wegfe tj ma-tarcgna tea piricatars jd i bgnair dunftgjn. Put injtear wiy, twj pigrs jd vibuas ira naamam tjmatarcgna tea twj (unlnjwn) piricatars. Pareips, unfjnsfgjusby, yju cgoet eiva usam tegs rasubt

ibraimy wean firrygno jut tea rign kirrab tisl. ]ea orimgant, wrgttan is 9.1;0

gn tea inswar, ciy ka

axprassam ibsj is9.1 0

;0 0 sgnfa tea bgna fjnnafts tea (tgca, bavab jd witar) fjjrmgnitas (;0, 9.1) wgte

(0, 0). Gn oanarib tea orimgant gs ogvan ky

tea feinoa gn tea mapanmant virgikba

tea fjrraspjnmgno feinoa gn tea gnmapanmant virgikba

Jnfa tea orimgant jd tea bgna eis kaan fibfubitam, gt fin ka usam wgte jna jd tea lnjwn pjgnts tjmatarcgna tea gntarfapt. Gd jna jd tea pjgnts gs (0, 0) tea gntarfapt gs zarj.

Vuppjsa teit i naw typa jd iutjcitgf fir gs kagno rjim tastam. ]ea caisurgno taic wints tj lnjwtea cixgcuc iffabaritgjn katwaan 0 inm 60 c s9. Gt pbins tj fibfubita tegs ky issucgno teit gtgs fjnstint inm caisurgno tea tgca tilan drjc rast tj ifegava i spaam jd 60 c s9 it cixgcuc


97


20/23

iffabaritgjn. Gn teagr rst tast tea spaamjcatar raimgno gs 60 c s9 idtar 9; s drjc stirt jd tgcgnoinm cjtgjn. _a fin tegnl jd teasa vibuas gn tarcs jd (tgca, vabjfgty) fjjrmgnitas. It tea stirtjd tgcgno tea fjjrmgnitas ira (0, 0). _ean tea spaamjcatar raims 60 c s9 tea fjjrmgnitas ira(9;, 60). Gd tea iffabaritgjn gs fjnstint tean gts ciongtuma wgbb ka ogvan ky tea orimgant jd tea bgna

hjgngno teasa twj pjgnts. Qsgno tea feinoa gn virgikba gmai, tea orimgant gs

60 0

9; 03 ;.1, inm sj teaciongtuma jd tea iffabaritgjn gs ;.1 c s;. ]ea feinoa gn virgikba rjuta tj fibfubitgno tea orimgantgs in ikrgmoam varsgjn jd i cjra oanarib catejm. ]ea twj pigrs jd fjjrmgnitas ciy ka usam wgtetea oanarib aquitgjn jd i bgna tj wjrl jut tea piricatars jd tea pirtgfubir bgna teit pissas terjuoeteasa twj pjgnts. ]ea issucptgjn jd fjnstint iffabaritgjn baims tj i bgnair rabitgjnsegp katwaantea vabjfgty (v c s9) inm tgca (t s) jd tea djrcv 3it +k wearai inmk ira tea piricatarsfjrraspjnmgno tj orimgant inm gntarfapt raspaftgvaby. ]ea rjim tast ogvasv3 0 weant3 9;. ]easaciy ka sukstgtutam gntj tea oanarib djrc tj ogva

0 3 0 +kinm 60 3 9;i +k.

Wju ciy rafjongsa teit teasa ira sgcubtinajus aquitgjns. ]ea rst ogvask 3 0 wegfe ciy ka

sukstgtutam gntj tea safjnm tj ogvai3 ;.1, fjrraspjnmgno tj in iffabaritgjn jd ;.1 c s;

is kadjra.

Vuppjsa teit tea tast taic firry jut i safjnm tast. Gn tegs tast teay njta wean spaams jd 91 cs9 inm ;? c s9 ira raifeam inm issuca fjnstint iffabaritgjn katwaan teasa tgcas inm spaams.]ea spaamjcatar raims 91 c s9, idtar = safjnms drjc tea stirt jd cjtgjn inm ;? c s9 idtar 7s drjc tea stirt jd cjtgjn. _a ippby tea oanarib catejm tj tea miti drjc tegs tast. ]ea (tgca,vabjfgty) fjjrmgnitas fjrraspjnmgno tj tea raimgnos ira (=, 91) inm (7, ;?). ]ea aquitgjns rasubtgnodrjc sukstgtutgjns gn tea oanarib djrc ira

91 3 =i+k

;? 3 7i+k

_a usa tea abgcgnitgjn catejm jd sjbvgno teasa sgcubtinajus aquitgjns ( 6). ]ea rst jd teasaaquitgjns ciy ka suktriftam drjc tea safjnm tj abgcgnitak.

;? 91 3 7i+k =i k

jr

i3 ;.=.

]ea rasubtgno vibua jdi ciy ka sukstgtutam gntj agtear jd tea aquitgjns axprassgno tea miti tjfibfubitak. Gn tea rst,91 3 = ;.1 +k, sjk3 1.]ea rasubtgno cjmab gs

v3 ;.=t+ 1 (= t 7).

]egs cjmab pramgfts in iffabaritgjn jd ;.= c s;, wegfe gs digrby fbjsa tj tea pravgjus rasubt jd;.1 c s; kut gd wa try tj usa tegs cjmab itt 3 0, weit mj wa pramgft: ]ea cjmab pramgfts teitv 3 1 weant 3 0. ]egs gs njt fjnsgstant wgtet 3 0 kagno tea tgca it wegfe tea vaegfba stirts tjcjva! Vj, avan gd tea iffabaritgjn gs fjnstint katwaan 91 inm ;? c s9, gt mjas njt eiva tea sicavibuas katwaan 0 c s9 inm 91 c s9 is agtear katwaan 91 c s9 inm ;? c s9 inm 60 c s9. Icjra oanarib prgnfgpba gs gbbustritam ky tegs axicpba. Gt ciy ka minoarjus tj usa i cjmab kisam jnfartign miti it pjgnts jtear tein tejsa ogvan ky teasa miti! ]ea kusgnass jd usgno i cjmab jutsgmatea rinoa jd miti djr wegfe gs gs lnjwn tj ka vibgm gs fibbamaxtripjbitgjn. Qsa jd tea cjmab katwaantea miti pjgnts jn wegfe gt gs kisam gs fibbam gntarpjbitgjn. Vj tea oanarib prgnfgpba ciy ibsj kastitam is teit gt gs vary rgsly tj axtripjbita inm gt fin ka rgsly tj gntarpjbita. Navarteabass

;0 EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


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axtripjbitgjn jr gntarpjbitgjn ciy ka pirt jd tea purpjsa djr i citeacitgfib cjmab gn tea rst pbifa.

]ea catejm jd nmgno orimgant inm gntarfapt hust axacpbgam ciy ka oanaribgsam. Vuppjsa teit waira spafgdygno i bgnair dunftgjny 3ix+k weara tea mapanmant virgikba gsy inm tea gnmapanmantvirgikba gsx. _a raprasant twj lnjwn pjgnts ky(p, q) inm (r, s). ]ea orimgant,i, djr tea strigoet

bgna, ciy ka fibfubitam agtear drjc p

rq s jr ky sukstgtutgnoy 3q weanx 3r gny 3ix+k tj

jktign twj sgcubtinajus aquitgjns. Vuktriftgjn jd teasa abgcgnitaskinm ibbjwsitj ka fibfubitam.]ea gntarfapt jd tea bgna jn tea y-ixgs,k, ciy ka djunm ky sukstgtutgjn gny3ix+k, jd agtearp, qinmijrr, sinmi.

]islislQsa tea oanarib catejm tj mamufa tea mgffarant iffabaritgjns (issucgno teit teayira fjnstint) katwaan tea stirt jd cjtgjn inm 91 c s9 inm katwaan vabjfgtgas jd;? c s9 inm 60 c s9.

Wjur sjbutgjn

InswarDjr tea (tgca, vabjfgty) fjjrmgnitas (0, 0) inm (=, 91),

0 3 0i+k

91 3 =i+k

Drjc tea rst jd teasa k 3 0 inm eanfa, gn tea safjnm, i391

= 3 6.?1. Vj tea iffabaritgjn up tj

91 c s9 gs 6.?14 c s;. Djr tea (tgca, vabjfgty) fjjrmgnitas (7, ;?) inm (9;, 60),

;? 3 7i+k

60 3 9;i+k

Vuktriftgno tea rst drjc tea safjnm ogvas

6 3 6isji3 9,

sj tea iffabaritgjn katwaan ;? c s9 inm 60 c s9 gs 9 c s;

Bgnair dunftgjns ciy ka usadub gn afjnjcgfs. I bjt jd ittantgjn gs pigm tj tea wiy gn wegfe macinmdjr i prjmuft virgas wgte gts prgfa. I caisura jd macinm gs tea nuckar jd gtacs sjbm, gd ivigbikba, gn


;9


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i ogvan pargjm. Djr axicpba, tea purpjsa cgoet ka tj matarcgna tea kast prgfa djr i prjmuft ogvanfartign matigbs ikjut fjsts inm wgte fartign issucptgjns ikjut tea wiy tea nuckar jd gtacs sjbm parcjnte virgas wgte prgfa. ]ea prgfa iffafts tea prjt inm eanfa, gn turn, tea nuckar cinudifturamgn raspjnsa tj tea macinm. ]ea nuckar jd gtacs cinudifturam gn i ogvan pargjm gs lnjwn is teasuppby. Gndjrcitgjn ikjut tea virgitgjn jd macinm jr suppby wgte prgfa ciy ka jktignam drjc cirlat

survays. Fjnstint dunftgjns ira njt ipprjprgita gn tegs fjntaxt sgnfa kjte macinm inm suppby virywgte prgfa. Gn tea iksanfa jd jtear gndjrcitgjn tea sgcpbast wiy tj cjmab tea virgitgjn jd agtearmacinm jr suppby wgte prgfa gs tj usa i bgnair dunftgjn.

]islisl_ean tea prgfa jd i buxury fjnsucar gtac gs 9000, i cirlat survay ravaibs teittea macinm gs 900,000 gtacs par yair. Ejwavar injtear survay eis sejwn teitit i prgfa jd400, tea macinm djr tea gtac gs ;00,000 gtacs par yair. Issucgnoteit kjte survays ira vibgm, nm i bgnair dunftgjn teit rabitas macinmY tj prgfa

P. _eit macinm wjubm ka pramgftam ky tea bgnair dunftgjn it i prgfa jd?10:Fjccant jn tea vibgmgty jd kjte pramgftgjns.

Wjur sjbutgjn

;; EABC (;001)8_jrlkjjl 18 Dunftgjns inm Cjmabbgno


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Inswar]ea bgnair dunftgjn wgbb ka jd tea djrc

Y3iP+k (400 P 9000)

]ea bgcgts jnP raprasant tea ogvan rinoa jd miti jn prgfa. Vukstgtutgno tea rst pigr jd vibuas jdY inmP8

900000 3 900i+k

Vukstgtutgno tea safjnm pigr jd vibuas8

;00000 3 400i+k

Vuktriftgno tea rst axprassgjn drjc tea safjnm8

900000 3 =00i sj i3 ;10

Njta teit tea naoitgva orimgant gs fjnsgstant wgte tea dift teit macinm dibbs is prgfa gnfraisas.

Feafl teit tea Feinoa gn virgikba mangtgjn djr nmgnoiwjrls.

Feinoa gn mapanmant virgikba (Y) 3 ;00000 900000 3 900000.

Fjrraspjnmgno feinoa gn gnmapanmant virgikba (P) 3 400 9000 3 =00. ]ea ritgj jd teasa

feinoas gs 900000

;10 3 ;10

]egs vibua jdiciy ka usam wgte tea rst pigr jd vibuas,

900000 3 ;10000 +k

sj

k3 610000

inm tea bgnair dunftgjn rabitgno macinm inm prgfa gs

Y3 610000 ;10P.

\I prafiutgjniry feafl gs tj cila sura teit tegs rasubt gs fjnsgstant wgte tea jtear pigrs jd vibuas._eanP3 400, Y 3 610000 ;10 400 3 610000 910000 3 ;00000, is raqugram.S _eanP3 ?108

Y3 610000 ;10 ?10 3 610000 95?100 3 94;100.

Vj i bgnair rabitgjnsegp katwaan macinm inm tea prgfa djr tegs buxury suooasts i macinm jd 94;100gtacs par yair wean tea prgfa par gtac gs ?10. It i prgfa jd 100,P 3 100, inm tea cjmabpramgfts teit

Y3 ;10 100 + 610000 3 ;;1000.

Vj tea bgnair cjmab suooasts i macinm jd ;;1,000 gtacs par yair wean tea prgfa par gtac gs 100.Vufe i prgfa ejwavar gs jutsgma tea rinoa jd ogvan miti. Fjnsaquantby tea fjrraspjnmgno macinmpramgftgjn raprasants in axtripjbitgjn inm tegs cgoet njt ka rabgikba. Jn tea jtear einm, teaprgfa jd?10 bgas wgtegn tea ogvan rinoa jd miti inm tea fjrraspjnmgno macinm pramgftgjn gs ingntarpjbitgjn. Gd tea ogvan miti pjgnts ira fbjsa tj aife jtear tean gntarpjbitgjn katwaan teasa

pjgnts gs cjra rabgikba tein axtripjbitgjn tj pjgnts durtear iwiy.

the modelling cycle and functions

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