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2

Th44s $VVVVk mXk33s zzs33 VVf th33 SzztrXs Xnd Szz$-SzztrXs stXt33d X$VVv33 fKr33s33ntXt44VVn VVf th3344r XKKV44cXt44VVn fVVr V33Xrn44ng 'Xth33mXt44csschVVVVV V33v33V 44n X wXy d44ff33r33nt frVVm whXt 44s tXzzght Xt Kr33s33nt, 33m$VVdy44ng th33 Kr44nc44KV33s VVf XVg33$rX fVVr 33mK44r44cXV XcczzrXcy.

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3

44. hy V33d44c 'Xth33mXt44cs 

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4

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d33V44ghtfzzV chXKt33rs VVf th33 )!th c33ntzzry mXth33mXt44cXV h44stVVry/.

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m33thVVds.

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4444. V33d44c 'Xth33mXt44cXV 5VVrmzzVX33

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S44XT33331 SzzTXS

 

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T%44T33331 SzzB 7 SzzTXS

 

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652= 6 X 7 / 25 = 4225;

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O352

= O3 X O4/25 = O8225;

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2

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2 

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2+5

2

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= X (X + O) . O02+ 25.

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2 fVVr X = 4, x=O0

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= [ X2.O0

2+2Xb.O0 + X.O0 + b

2+ b] O0

2+ 5

2 

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8/17/2019 Mandana

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44.33.,, O / 20 = 0.O / 2 = .O0 ( 0 t44m33s, O r33mX44nd33r)St33K. 2 : D44v44d33 O0 by 2

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O)

44.33.,, !.!!*( * t44m33s, ! r33mX44nd33r "

St33K. 3 : D44v44d33 5 by 2

44.33.,, 0.05O2 ( 2 t44m33s, O r33mX44nd33r )

St33K. 4 : D44v44d33O2 44.33.,, O2 by 2

44.33.,, 0.0526 ( 6 t44m33s, NVV r33mX44nd33r )

St33K. 5 : D44v44d33 6 by 2

44.33.,, 0.05263 ( 3 t44m33s, NVV r33mX44nd33r )

St33K. 6 : D44v44d33 3 by 2

44.33.,, 0.05263OO(O t44m33, O r33mX44nd33r )

St33K. 7 : D44v44d33OO 44.33.,, OO by 2

44.33.,, 0.05263OO5 (5 t44m33s, O r33mX44nd33r )

St33K. 8 : D44v44d33O5 44.33.,, O5 by 2

44.33.,, 0.05263O5O7 ( 7 t44m33s, O r33mX44nd33r )

St33K. 9 : D44v44d33O7 44.33.,, O7 by 2

44.33.,, 0.05263O57O8 (8 t44m33s, O r33mX44nd33r )

St33K. O0 : D44v44d33O8 44.33.,, O8 by 2

44.33.,, 0.05263O5789 (9 t44m33s, NVV r33mX44nd33r )

St33K. OO : D44v44d33 9 by 2

44.33.,, 0.05263O5789O4 (4 t44m33s, O r33mX44nd33r )

St33K. O2 : D44v44d33O4 44.33.,, O4 by 2

44.33.,, 0.05263O578947 ( 7 t44m33s, NVV r33mX44nd33r )

St33K. O3 : D44v44d33 7 by 2

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13/16

OO

44.33.,, 0.05263O578947O3 ( 3 t44m33s, O r33mX44nd33r )

St33K. O4 : D44v44d33O3 44.33.,, O3 by 2

44.33.,, 0.05263O5789473O6 ( 6 t44m33s, O r33mX44nd33r )

St33K. O5 : D44v44d33O6 44.33.,, O6 by 2

44.33.,, 0.05263O578947368 (8 t44m33s, NVV r33mX44nd33r )

St33K. O6 : D44v44d33 8 by 2

44.33.,, 0.05263O5789473684 ( 4 t44m33s, NVV r33mX44nd33r )

St33K. O7 : D44v44d33 4 by 2

44.33.,, 0.05263O57894736842 ( 2 t44m33s, NVV r33mX44nd33r )

St33K. O8 : D44v44d33 2 by 2

44.33.,, 0.05263O57894736842O ( O t44m33, NVV r33mX44nd33r )

NVVw frVVm st33K O9, 44.33.,, d44v44d44ng O by 2, St33K 2 tVV St33K. O8 r33K33Xts thzzs g44v

0  EEEEEEEEEEEEEEEEEE . . O / O9 =0.05263O57894736842O VVr 0.05263O57894736842O

1VVt33 thXt w33 hXv33 cVVmKV33t33d th33 KrVVc33ss VVf d44v44s44VVn VVnVy $yth33 d44v44s44VVn $y O9 VVcczzrs.

$" 'zzVt44KV44cXt44VVn '33thVVd2VXVzz33 VVf O @ O9

544rst w33 r33cVVgn44z33 th33 VXst d44g44t VVf th33 d33nVVm44nXtVVr VVf th33 VXst d44g44t 44s 9.

5VVr X frXct44VVn VVf th33 fVVrm 44n whVVs33 d33nVVm44nXtVVr 9 44s th33 VXst

cXs33 VVf O @ O9 Xs fVVVVVVws2

5VVr O @ O9, /Kr33v44VVzzs/ VVf O9 44s O. Xnd VVn33 mVVr33 thXn VVf 44t 44s O >

Th33r33fVVr33 ) 44s th33 mzzVt44KV4433r fVVr th33 cVVnv33rs44VVn. 33 wr44t3nzzm33rXtVVr Xs O Xnd fVVVVVVw th33 st33Ks V33ftwXrds.

St33K. O : O 

8/17/2019 Mandana

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O2

St33K. 2 : 2O(mzzVt44KVy O by 2, Kzzt tVV V33ft)

St33K. 3 : 42O(mzzVt44KVy 2 by 2, Kzzt tVV V33ft)

St33K. 4 : 842O(mzzVt44KVy 4 by 2, Kzzt tVV V33ft)

St33K. 5 : O6842O(mzzVt44KVy 8 by 2 =O6, O cXrr4433d VVv33r, 6 Kzzt tVV V33f

St33K. 6 : O36842O( 6 X 2 =O2,+O [cXrry VVv33r]

= O3, O cXrr4433d VVv33r, 3 Kzzt tVV V33ft )

St33K. 7 : 736842O ( 3 X 2, = 6 +O [CXrryVVv33r]

= 7, Kzzt tVV V33ft)

St33K. 8 : O4736842O (Xs 44n th33 sXm33 KrVVc33ss)

St33K. 9 : 94736842O ( DVV – cVVnt44nzz33 tVV st33K O8)

St33K. O0 : O894736842O

St33K. OO : O7894736842O

St33K. O2 : O57894736842O

St33K. O3 : OO57894736842O

St33K. O4 : 3O57894736842O

St33K. O5 : 63O57894736842O

St33K. O6 : O263O57894736842O

St33K. O7 : 5263O57894736842O

St33K. O8 : O05263O57894736842O

NVVw frVVm st33K O8 VVnwXrds th33 sXm33 nzzmb33rs Xnd VVrd33r tVVwXrds V33ft cVVnt44n

Thzzs O / O9 = 0.05263O57894736842O

44t 44s 44nt33r33st44ng tVV nVVt33 thXt w33 hXv33

44) nVVt Xt XVV zzs33d d44v44s44VVn KrVVc33ss

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O3

4444) 44nst33Xd VVf d44v44d44ng O by O9 cVVnt44nzzVVzzsVy, jzzst mzzVt44KV4433d O by 2

th33 r33szzVtXnt szzcc33ss44v33Vy by 2.

VVbs33rvXt44VVns :

X) FVVr Xny frXct44VVn VVf th33 fVVrm O / X9 44.33.,, 44n whVVs33 d33nVVm44nXtVVr 9 44s th33 d44g44t

Xnd X 44s th33 s33t VVf r33mX44n44ng d44g44ts, th33 vXVzz33 VVf th33 frXct44VVn 44s 44n r33c

r33K33Xt44ng bVVVck’s r44ght mVVst d44g44t 44s O.

b) WhXt33v33r mXy b33 X9, Xnd th33 nzzm33rXtVVr, 44t 44s 33nVVzzgh tVV fVVVVVVw th33 s

3344th33r 44n d44v44s44VVn VVr 44n mzzVt44KV44cXt44VVn.

c) StXrt44ng frVVm r44ght mVVst d44g44t Xnd cVVzznt44ng frVVm th33 r44ght, w33 s3333 ( 44n O9)

Szzm VVf Ost

 d44g44t + O0th

 d44g44t = O + 8 = 9

Szzm VVf 2nd

 d44g44t + OOth d44g44t = 2 + 7 = 9

- - - - - - - - -- - - - - - - - - - - - - - - - - - -

Szzm VVf 9th d44g44t + O8th d44g44t = 9+ 0 = 9

FrVVm th33 XbVVv33 VVbs33rvXt44VVns, w33 cVVncVzzd33 thXt 44f w33 f44nd f44rst 9 d4

b33 d33r44v33d Xs cVVmKV33m33nts VVf 9.

44) Thzzs Xt th33 st33K 8 44n d44v44s44VVn KrVVc33ss w33 hXv33 0.05263O5O7 Xnd n33xt st33K. 9 g44v33s

0.05263O578

NVVw th33 cVVmKV33m33nts VVf th33 nzzmb33rs

0, 5, 2, 6, 3, O, 5, 7, 8 frVVm 9

9, 4, 7, 3, 6, 8, 4, 2, O fVVVVVVw th33 r44ght VVrd33r

44.33.,, 0.05263O57894736842O

NVVw tXk44ng th33 mzzVt44KV44cXt44VVn KrVVc33ss w33 hXv33

St33K. 8 : O4736842O

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O4

St33K. 9 : 94736842O

NVVw th33 cVVmKV33m33nts VVf O, 2, 4, 8, 6, 3, 7, 4, 9 frVVm 944.33.,, 8, 7, 5, O, 3, 6, 2, 5, 0 Kr33c33d33 44n szzcc33ss44v33 st33Ks, g44v44ng th3

 

!.!*)3O*D894D384)O .

d" h33n w33 g33t (033nVVm44nXtVVr 7 1zzm33rXtVVr" Xs th33 KrVVdzzct 44n th3KrVVc33ss, hXVf th33 wVVrk 44s dVVn33. 33 stVVK th33 mzzVt44KV44cXt44VVn th

m33chXn44cXVVy wr44t33 th33 r33mX44n44ng hXVf VVf th33 Xnsw33r $y m33r33VcVVmKV33m33nts frVVm 9.

33" 3344th33r d44v44s44VVn VVr mzzVt44KV44cXt44VVn KrVVc33ss VVf g44v44ng t

s44ngV33 V44n33 fVVrm.

XVg33$rX44c KrVVVVf 2

Xny vzzVgXr frXct44VVn VVf th33 fVVrm O @ X9 cXn $33 wr44tt33n Xs

O @ X9 ? O @ ( (X > O " + - O " wh33r33 + ? O!

O

? EEEEEEEEEEEEEEEEEEEEEEEE

( X > O " +

 [O - O@(X>O"+

] 

O  ? EEEEEEEEEEE

[O - O@(X>O"+]-O

( X > O " +

O

? EEEEEEEEEE

[O > O@(X>O"+ > O@(X>O"+)> ----------

] 

( X > O " +

= O/(X+O)x + O/(X+O)2x

2 +O/(X+O)

3x

3+ ----Xd 44nf44n44tzzm

= O0-O

(O/(X+O))+O0-)

(O/(X+O)))+O0

-3(O/(X+O)

3) + ---Xd 44nf44n44tzzm