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M&²y m&Ñiai[:  Kc mh_v  Kc g[ni (v(vF ²yili[  (v(vF Kc b>Fi[  T*>kigiLi an[ li>bigiLimi> Kc b>Fi[

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Presentation on theme: "M&²y m&Ñiai[:  Kc mh_v  Kc g[ni (v(vF ²yili[  (v(vF Kc b>Fi[  T*>kigiLi an[ li>bigiLimi> Kc b>Fi["— Presentation transcript:

1 m&²y m&Ñiai[:  Kc mh_v  Kc g[ni (v(vF ²yili[  (v(vF Kc b>Fi[  T*>kigiLi an[ li>bigiLimi> Kc b>Fi[

2 - Äyipir)k (nN<yi[ l[vi - nfini mh_im)krNni uÑ[Sn[ (s¹F krvi - m*D) ri[kiN pr a(Fktm vLtr m[Lvvi - vAt&n) (k>mt a>g[ni (nN - Kc dB[ g[ni (nN<yi[ l[vi

3 {1} IAYr Kc t Kc< {1.1} IAYr Kc t& Kis kr)n[ T*>ki giLimi> Kc k[ie f[rfir Yt[i nY) t[n[ (AYr Kc aiv[ C[. diKli tr)k[ {1} kirKini miT[ rKiy[l mkinn&> BiD&> {2} kiym) AYifn[ c&kvvimi> aivt&. v[tn. {3} m&D) prn&> Äyij. {4} prvini f) aikZ(_imi> ji[e Skiy C[ k[ uRpidn OD hi[y k[ OF hi[y t[m Cti> IAYr Kc j C[. uRpidn S*ºy hi[y Ryir[ pN IAYr Kc rh[ C[. uRpidnni a[kmi[ uRpidn Kc< X Y D F E C A O

4 {1} IAYr Kc t Kc< {1.2} aIAYr Kc pN vwir[i Yiy, uRpidn GT[ t[i Kc pN GTiD[i Yiy an[ j[i uRpidn S*ºy Yiy t[i Kc< pN S*ºy Yiy t[n[ a(AYr Kc< kh[ C[. di.t.: kici miln[i Kc< bLtNn[i Kc< d](nk mj*rn[ c&kvvimi> aivt&> v[tn. uRpidnni a[kmi[ uRpidn Kc< X Y D A E C O B aikZ(_imi> OE aIAYr Kc f[rfir Yiy C[. S*ºy uRpidn[ ai K< pN S*ºy hi[y C[. uRpidn vFti t[ vF[ C[ an[ uRpidn Gtti t[ GT[ C[.

5 {1.3} k&l {IAYrKc aiv[ C[. uRpidnni a[kmi[ uRpidn Kc< X Y O -IAYr Kc< an[ aIAYr Kc< vµc[ni[ tfivt a[ mi#i p\miNni[ C[, p\kirni[ nY). - b>n[ kc *ki giLimi> j mh_vn) C[. li>bi giLin) ØIOTa[ bFi[ j Kc< aIAYr Kc< hi[y C[. aIAYr Kc<

6 {2} sr[riS Kc< : sr[riS Kc< a[Tl[ a[km d)q Kc<. K&l Kc<n[ k&l uRpidn vD[ BigviY) sr[riS Kc< mL[ C[. k&l Kc< k&l uRpidn di.t. p[Q)n) am&k vAt&ni 1000 a[kmi[n&> uRpidn kr{ C[ an[ ji[ t[n&> k&l Kc< $i. 5000 hi[y ti[, 5000 1000 sr[riS Kc< $i. 5 YS[. sr[riS Kc< =

7 uRpidnni a[kmi[ a[km d)q sr[riS IAYr Kc< X Y D O B sr[riS IAYr Kc< r[Ki k&l IAYr Kc< k&l uRpidn sr[riS IAYr Kc vF& hi[y C[ j[m uRpidnmi> vFiri[ Yti> (AYr Kc cit& hi[viY) a[kmd)q (AYr Kc GTiDi[ Yiy C[. sr[riS IAYr Kc< = 2.1 sr[riS IAYr Kc a[kmi[n) s>²yi vD[ BigviY) p\i¼t Yiy C[.

8 uRpidnni a[kmi[ a[km d)q sr[riS aIAYr Kc< X Y O sr[riS aIAYr Kc< r[Ki k&l aIAYr Kc< k&l uRpidn sr[riS aIAYr Kc vFiri[ Yiy C[. aiY) sr[riS aIAYr Kc<n) r[Ki U aikirn) hi[y C[. sr[riS IAYr Kc< = 2.2 sr[riS aIAYr Kc a[km[i vD[ BigviY) j[ ai>k p\i¼t t[n[ sr[riS a(AYr Kc aiv[ C[. Sr&aitmi> t[ GT[ C[. am&k (b>d& pC) vF[ C[.

9 sr[riS k&l Kc n[ r[Kini[ srviLi[ dSi<v[ C[. 2.3 sr[riS k&l Kc U>c&> hi[y C[, kirN k[ S$aitmi> uRpidn ai[C&> hi[y C[. an[ IAYr Kc cie C[. J[m j[m uRpidn vF&jiy C[ t[m t[m IAYr Kc cie C[ t[Y) sr[riS k&l Kc< GT[ C[. Am&k hd pC) sr[riS Kc< vF[ C[. kdni g[rliBi[ ai miT[ jvibdir C[. uRpidnni a[kmi[ a[km d)q sr[riS Kc< X Y O sr[riS aIAYr Kc< r[Ki sr[riS IAYr Kc< r[Ki sr[riS k&l Kc< r[Ki

10 uRpidnni a[kmi[ s)mi>t Kc< X Y O {3} s)mi>t Kc a[k a[kmn&> uRpidn krviY) k&l Kc Yti> f[rfirn[ s)mi>tKc aiv[ C[. T*ki>giLimi> IAYr Kc ki[e f[rfir Yti[ nY). miT[, s)mi>t Kc Yti[ f[rfir dSi<v[ C[. s)mi>t Kc< r[Ki k&l Kc Yy[li[ frfir uRpidnni a[kmi[mi> Yy[li[ f[rfir s)mi>t Kc< = s)mi>t Kc cilk)y (nN K*b j mh_vni[ C[. p[Q)ni[ mh_im nfia[ (b>d&a[ nkk) Yiy C[, jyi> s)mi>t Kc t aivk srKi> Ye rh[.

11 uRpid n a[kmi[ IAYr Kc< {$} aIAYr Kc< {$} k&l Kc< {$.} s)mi>t Kc< {$} sr[. IAYr Kc< {$} sr[. aIAYr Kc< {$} sr[. k&l Kc< {$} 110011001200-10011001200 21001200130010050600650 31001375147517533.3458491 41001400150025 350375 51001500160010020300320 61001700180020016.7283.3300 71002000210030014.30280.7300 81002400250040012.25300312

12 (v(vF Kc tr s>b>Fi[: 1.sr[riS Kc<a[ k&l Kc<n[ uRpidnni k&l a[kmi[ vD[ BigviY) p\i¼t Yiy C[ 2.p[Q) gm[ t[Tl&> uRpidn kr[ Cti> T*>kigiLimi> IAYr Kc ki[e f[rfir Yti[ nY) 3.s)mi>t Kc t Kc< vFti[ hi[y C[, Ryir[ k&l Kc< vFti jti dr[ vFti[ hi[y C[. 4.s)mi>t Kc< jyir[ sr[riS Kc< krti vF& hi[y C[, Ryir[ sr[riS Kc< GT[ C[. 5.s)mi>t Kc< jyir[ sr[riS Kc< krti vF& hi[y C[, Ryir[ sr[riS Kc< vF[ C[. uRpidnni a[kmi[ Kc< X Y O sr[riS aIAYr Kc< r[Ki sr[riS IAYr Kc< r[Ki sr[riS k&l Kc< r[Ki s)mi>t Kc< r[Ki

13 6. sitmi> a[km sr[riS Kc ai[Ci[ hi[y, Ryir[ s)mi>t Kc< an[ sr[riS Kc< an[ sr[riS Kc< srKi Yiy C[. 7. s)mi>t Kc< ji[ sr[riS Kc< krti ai[Ci[ hi[y ti[ sr[riS aIAYr Kc< GT[ C[. 8.s)mi>t Kc< ji[ sr[riS aIAYr Kc< krti vFir[ hi[y ti[ sr[riS aIAYr Kc< GT[ C[. 9. sr[riS Kc t Kc t Kc n[ Kc t Kc< K*b zDpY) vF[ C[. uRpidnni a[kmi[ Kc< X Y O sr[riS aIAYr Kc< r[Ki sr[riS IAYr Kc< r[Ki sr[riS k&l Kc< r[Ki s)mi>t Kc< r[Ki

14 {4.1} T*>kigiLimi> Kc b>Fi[: T*>ki[giLi[ a[Tl[ smyni[ a[vi[ giLi[ k[ j[ dr(myin IAYr siFni[n&> p\miN bdl) Skit&> nY) mi#i aIAYr siFni[ j bdl) Skiy C[. miT[ kh) Skiy k[ p[Q)n&> uRpidn vF) Sk[ C[, pN t[n&> kd vFt& nY). T*kigiLimi> Kc b>Fi[n)c[ni #iN ²yili[ni aiFir[ krvimi> aiv[ C[.  sr[riS IAYr Kc< an[ uRpidn  sr[riS aIAYr Kc< an[ uRpidn  sr[riS k&l Kc< an[ uRpidn  s)mi>t Kc< an[ uRpidn

15 uRpidnni a[kmi[ a[km d)q sr[riS IAYr Kc< X Y D O B sr[riS IAYr Kc< r[Ki k&l IAYr Kc a[km[i vD[ BigviY) j[ ai>k p\i¼t t[n[ sr[riS (AYr Kc aiv[ C[. sr[riS (AYr Kc vF& hi[y C[. uRpidnmi> vFiri[ Yti> (AYr Kc cit& hi[viY) a[kmd)q (AYr Kc GTiDi[ Yiy C[.a[Tl[ k[ a[km d)q IAYr Kc vlN Friv[ C[ pr>t& ApS kh)a[ ti[ “rectangular hyperbola” hi[y C[. 1. sr[riS IAYr Kc< an[ uRpidn: sr[riS IAYr Kc a[kmi[n) s>²yi vD[ BigviY) p\i¼t Yiy C[.

16 sr[riS aIAYr Kc vFiri siY[ sr[riS a(AYr Kc vFiri[ Yiy C[. aiY) sr[riS aIAYr Kc kirN p[Q)ni IAYr siFnni[ mh_im upyi[g Ye gyi> bid, a(AYr siFni[mi> vFiri[ krti uRpidnmi> Gtti dr[ vFiri[ Yvi pim[ C[, miT[ a[km (dq aIAYr siFni[n) uRPidkti Gtvi pim[ C[. 2. sr[riS aIAYr Kc< an[ uRpidn : k&l aIAYr Kc a[km[i vD[ BigviY) j[ ai>k p\i¼t t[n[ sr[riS a(AYr Kc aiv[ C[. uRpidnni a[kmi[ a[km d)q sr[riS aIAYr Kc< X Y O sr[riS aIAYr Kc< r[Ki

17 sr[riS k&l Kc n[ r[Kini[ srviLi[ dSi<v[ C[. 3. sr[riS k&l Kc< an[ uRpidn : sr[riS k&l Kc U>c&> hi[y C[, kirN k[ S$aitmi> uRpidn ai[C&> hi[y C[. an[ IAYr Kc cie C[. j[m j[m uRpidn vF&jiy C[ t[m t[m IAYr Kc cie C[ t[Y) sr[riS k&l Kc< GT[ C[. am&k hd pC) sr[riS Kc< vF[ C[. kdni g[rliBi[ an[ GTt) p[diSni[ (nym ai miT[ jvibdir C[. uRpidnni a[kmi[ a[km d)q sr[riS Kc< X Y O sr[riS aIAYr Kc< r[Ki sr[riS IAYr Kc< r[Ki sr[riS k&l Kc< r[Ki

18 uRpidnni a[kmi[ s)mi>t Kc< X Y O 4. s)mi>t Kc< an[ uRpidn: vFirini> a[k a[kmn&> uRpidn krviY) k&l Kc Yti> f[rfirn[ s)mi>tKc aiv[ C[. T*ki>giLimi> IAYr Kc ki[e f[rfir Yti[ nY). miT[, s)mi>t Kc Yti[ f[rfir dSi<v[ C[. s)mi>t Kc< r[Ki s)mi>t Kc GT[ C[ a[n&> kirN vFt) s)mi>t p[diS k[ vFti mLtrni[ (nym C[ Ryir pC) s)mi>t Kc kirN GTt) s)mi>t p[diSni[ (nym C[.

19 T*>kigiLimi> Kc b>Fi[n) r[Ki ¹viri smj*t) 1.uRpidn vFti> sr[riS IAYr Kc jiy C[ an[ t[Y) r[Kini[ QiL äN hi[y C[. 2.sr[riS aIAYr Kc GT[ C[ an[ am&k (b>d& bid t[ vFvi mi>D[ C[. 3.sr[riS k&l Kc GT[ C[ an[ Ryir pC) t[ vF[ C[. aiY) t[n) r[Kini[ U aikir hi[y C[. 4.s)mi>t Kc GT[ C[ an[ pC) vFvi mi>D[ C[. 5.s)mi>t Kc d&a[ C[d[ C[. 6.s)mi>t Kc hi[y C[, Ryir[ sr[riS Kc t Kc t Kc< vF[ C[. 7.s)mi>t Kc hi[y ti[ sr[riS aIAYr Kc t Kc vFir[ hi[y ti[ sr[riS aIAYr Kc< vF[ C[. uRpidnni a[kmi[ Kc< X Y O sr[riS aIAYr Kc< r[Ki sr[riS IAYr Kc< r[Ki sr[riS k&l Kc< r[Ki s)mi>t Kc< r[Ki

20 4.2 li>bi giLimi> Kc b>Fi[ libi>giL[ aIAYr siFni[ upri>t IAYr siFni[ni p\miNmi> pN vFiri[ GTiDi[ kr)n[ p[Q)n&> kd bdl) Skiy C[. aim li>b[ giL[ bFi[ j Kc bigiLin) sr[riS Kc kigiLin) sr[riSn) sr[riS aIAYr Kc<n) r[Kin) j[m U aikirn) hi[y C[. Tfivt mi#i a[Tli[ j hi[y C[ k[ t[ vFir[ C)Cr) k[ spiT hi[y C[. j[ miT[ni kirNi[ - X BC D E F uRpidnni a[kmi[ s)mi>t Kc< Q Y O R ST V libi>giLin) sr[riS Kc<n) r[Ki 1. li>b[giL[ IAYr Kc< pN aIAYr Kc< bn[ C[. 2. li>b[ giL[ siFni[n&> (vBijn Sky bn[ C[. 3.j$)yiti[n[ an&lx)n[ siFni[ni upyi[gmi> f[rfir Sky bn[ C[. bij&n) aikZ(_imi> HH’ r[Ki libi>giLin) sr[riS Kc c j&di j&di kd p\miN[ bdlit) uRpidnn) T*kigiLin) sr[riS Kc<n) r[Kiai[ C[. - k[Tli>k aY<SiA#i)ai[ ai r[Kin[ “aiyi[jn r[Ki” tr)k[ pN ai[LKiv[ C[. H’ H

21 li>bi giLin) sr[riS Kc<n) r[Kini lxNi[ 1.U aikirn) hi[y C[. tfivt mi#i a[Tli[ j hi[y C[ k[ t[ vFir[ C)Cr) k[ spiT hi[y C[. 2.j[m j[m vF& mi[Ti kdni[ ¼liºT upyi[g l[t) jiy t[m t[m S$aitmi> sr[riS Kc jiy C[, pr>t& pC) vF[ C[. 3.li>bigiLin) Kc kirN k[ li>bi giLin) Kc d& pr ApS<ti nY). X BC D E F uRpidnni a[kmi[ s)mi>t Kc< Q Y O R ST V libi>giLin) sr[riS Kc<n) r[Ki H’ H


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