II C'lQlC5

�

A em,x)m 10 x 25

B eQ)x)m 05 x 150

= 250

750

1000/10

�· m� P �· «l3 •� AJlll'1 Q� 8� itim v �. d� �aeo. eSc)�ea,Md$ai�!OD®��itilif•�a0.��·c,s,P�v �·�Q�,.��(Q���.t:lSl!>�PimQ(JJrogm:im,8��

o{Oi§l"'c> l = �(M!:) --+ �,�

O=(Amu-mv)-(mu-lmv)

⇒ 0=(..t-l)u+(A.-l)v

⇒ 0=(,'l-IXu+v)

⇒1=1.

(u+v)=e(u+v)

:. e=J.

0

0

2. .,.a:,·�� d4)C il(g� � t=O� � em �uf ��� r::i1t'i �f:IFxk£ttd!A� Sc1d & ... £ICm(o � ·..SJ<6stJ, � t= T@ � �� Sdz41€nd .,ed·& �.� ecm el). ,�()'8') �.iS co6e em =cb �ae, .,_ � �G4cd.� � �a,e �·� � �. T. f e0:1 g�� $B>Gil.oe6$e.o�..

V

A

T fT

e,06® cm = OAB �'"1lif..,� �"e"' = !(t + f T)xfT.. . 2 . g

. =:\f+g)

3

3. ot� PA-BCD�� 3{)"i!M� �·� �.hl ••�e·•�mfd �.en��-����.Ata���sg&)e.��·t;·��·mfiO� �id·tc c:iB. Jj� qfJo � M,�� �� &) qu,d AB� CD &w. � �e .cnSf> ��� ae �. �aa. � � � toE>e ��� e,W����.�����·�eo�

*F· 2rng

x+ 2y= zfkom�25'! ⇒i+2y=0 ⇒2y=-x. 0

E. = mg_ / for P: T-mgsin3o· = mf

F : mg .J. for 2mg: 2mg- 2'f = 2m F

0

0

4. � Mkg� � � -� 111.lgj � a,e tic1J c:,adm_ � q;i�� =D oh!ffl��eoa��-��-����@d�el)ll����:�1.Jl.-�.tm�---..i(>-0)�.�� �f):,Jdood���-eitm�P-�W·� qadfJl5J� s,:, �

�G.' V ms;-t C!tl>. � � � �qm&, � tff Sf) �

nn +- [:11---••-=r-........,,r!i?J-+ F

. IOOOP r;-"\ 9111�•�@eco F=-v-N ......... ,. •.. (1) • "-V .

0

E.=mg_ ➔ forM: F-J.M-T�Mf ·.u ......... (2) · 0\E_=mg_ ➔ form: T-hn=mf '."·--------� (3)

(D j

. · IOOOP · · ·. ·�t� (l), (2) 10:> (3)⇒.-. -. -AM -T =¥I

. . V

.

. 1000.P

. . · M > ,;_ . ⇒-·-.-)41-T=-(T-lm):;

.v: ··· m, ',;,

5

5. ·� (fo� • .,.i,..2j�?ai+l:Q =ll �· O,,t)e ��A 8:13 Bez:i!e:i,���ore�; c,111$ «{>O).� �· � �. AOB =� ae�zdis,. . .

. . ,4

C�.·o,tcB�-�t�c.,,.13�.0C�y���esc>Sd.(l s· . e£lQ ���-

--

a,isJ �&ec.,: OA ·OB= (-[+2l)·(2at+af)

;:,;-2a+2a =0

0 :.AOB=;-©

OC=OA+AC

=OA+OB

== (-J +2!!H +(2+a)J:. CD

CD

0

6. 0Aa»OB�r&:l���.WOqE:le�"dem�. �m,2al:Q:lacSW�AB�������' G� '48$��e-e, AOB=:f � oJB·=a@e ,-cnm.

· .AOG = aQlcl �. � � � $&&".u,tt,,· ·

0

B CD

A· w

• :r . . .

AOB =2

, @iEJ2ff A, 0 cos, Bw6� (,o3) �-®ex.,AB � e:lasm� �ttdmt� G �-

:.AG= OG.

�AOG=OAG=a. CD

0 Ti =Wcosa. 0

T2

=Wsina. 0

---·-----

w

B

7

7. A�Bo�O&:c��·��Q!iSG:i���;P(AUB)=¾•

P(A'UB')=¾ u» PCB I A)=¼ as�•�t11. P�)� P(B)�� ..

A'vB'=(Ar.B)', �� P((AnBY)=I-P(AriB) 0E).

5 1 �5 .:.P(AriB)=1-6

=6. �

P(BIA) P(Br.A) ⇒ P(A)= 6 =�. �

0(A) :¼ 3 \._::_J

s. �. � is,e� i;e�. �- �� 1 ·� �«riQ tl1J<$ qt8. •� � �2��� §� �*1:11· �•·� �-,&t@iif·.� ®e�� �

�� eLGie.

(i) ·�mc>.mm�·������:,,__(ii) � cna! ◄ � � �� .� C!J� !lee,

��

5 I 5 (i)8��6=-X-=-.

0 9 2 18 s 0

( .. ) Si;i 4 3 2 I n e:-,!:1J6=-x-x-=-.

9 8 7 21 0

9, �- a>azs, �c.,:i,J a,.Q._b, b� !Sl!I Y�t �-o.;I;,_Jflipo i�• 00> $c � � .a<b � <N)® � � � � lr'

<il®e��a'.Xl�-�Xt9111�,�-qv:2!.�lli��1'� !a!) �.a�b�

0

:.3a+3b+ab=21 --------·······- (l) 0 -�

l&, Zt,Z:2,; .. ,Xfo� � � � � �-� toa 9�. Xjg �El�

� � .. �- � �� .� Wal> �qp.,llJM' � t!I� -!W�

�qsmm.

0 .-. I: x,2 = 990.

1 .. , 0

0

11.(a) ce, a" S6c:t �ui ���em j. � Z.aem

��c���·�•�ai:i� -4" �,����u����ciel:lf��fl

ii� er@$, <� o>�) � �� � � ·� �+i

----'!ooi·�----+ CSoRr,6.-&l.C��ilMd�•,r---rfR-Ja =- 0 z.a .� ®&lm· R � et,u, ss ��

u. a� g��·��. ,; > t:�a&,«>e·�� •�se � ll!ldzmn.(Ji) S �tc)t.Sf c,c,�· � a 1ml h·

1 ·� � 1'1{� � � z:s,d$.

B ·ea-.iof!Vll!.l Sc>�· �.-0.� ltnr,p JO»I� � � � �t'>; ��c) *� <l� � � v.km.11-l� �=de� eomo G'.l� �; � usin8 < I'< ii 41!). �Zib�·� i9& m:,.ec,m � � G'.l•m 0tS c�� �. �.:� � • ioia eom � �m!f!® �tt)O � �· � �.� '9 � �-

�oo �s � ��� � � �� �· ,z._2a cile �2'>; @®@ a=sin--t {ii5?'9) �-

a

C R

tr Ut· 0 R;:::ucos-·i=-----( 5 . . 4 .Ji

-a= usin�t-_!_gt2 --------(2(2!)4 2

1 2R2

(1) aJa (2) ⇒ -a=R--g-2 u 2

0

0 ⇒ gR2 -u1R-u2a=0

--------- ·---

B

.'. R = u2 ±./u4 +4u2ag.

2g

⇒ R>2a.

:. G:>C �o:>��0 C!>2S'lat.J-r�.

0

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

. (b) f_(S.E) =➔ u 0[(B,E)=v 0 [(B,S)=: J?.0

f_(B, S) = ru�. E) + K.(E,:R©

= f_(E, S) + f_(B, E)- -

=PQ+·QR

=PR.

. .·

tfDG)� e?b)l�'-'= R1QR2 0

usin0<v<u

=,r-2a; �53, QR2R1 =a.(�

u

• _ • • -1 (usinB) .. a-sm -- .

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

/ 2ucos0:. ti + t 2 =--=--�---,,---,--­

u2 cos2 0-(v2 -u2 sin2 0)

2/ucosO 2 • � =2 2 (·: cos 0 + sm" 0 = 1)

u -v .

CD

----·------------------------

U.(�)d��I\BCD�.�2mQ�� g �·�=lo�-��-6:td-�AD!lliO 1· :.:. C

(a)

BC���-�-AB���flll� p,

I c� � � e&. � � AB;::2ti�_ BAI}= a � ate,c,$i}0<a<f �.oosa=¾�M:4(ld��IM� ..4_ D �Ill! ec qio}D � �- eaa � 1 (> 211) �- ��

. tf&)mr- t1>�2:I Bf3 800. q� s®O � � c= � � � <t� cd=z,JQQ m 9 P q,,qfld i. � � -� tti� fl �- � {l � � � �i». <1{� ��tn�P�AB��� .. a�-BCb._i:n&,��4i&>� � &l ii?- � �

-� � �� � ffi �-� �-� p� ��-

_1'.lEJ '< P.� A1.1>03 �-� � �11: ��.(b) �t.t ci:m::s, � m Jl A.UlO B��� l(>�) �dg:

�:a�� �:�:�-211!�.Cq�� ,®l):z, � (Jt� CtaG. �;� � qd'G,· a� ��®i:> � ¢�� e-lll!dl. C-�-!fc:,$e <; _. ID'J B q,.q O� 9 &3.:tcd me=�������-�­�r::, � l:llClb lft2». Clld'e �-� A� Cllll$D � eib� C. "<><eOO -� ®l:!I � -Sdtd mo-d � � �� �ei�. c;."" � � � �- ·fr'=..l(i-oostn &e00� .. ! e®!i! 8� OC lllt� � � �- a

..L

T T RI c ·

R· I

mg

F

R2 _....

A D

2mg

e A

���

®

g:{P,Block)=f / g (Q,Block) = f ..-

lSleJ� [(Block, E) = F �

. '

tr�

10 � � ®� u <©�118 �> 1 e,.@OJ.Cl. <e-cteG> � - 2011·1 � �� � � � �- 13

0=2mF +m(F- f)+m(F- f cos a)

3⇒0=4F-f-fx5

5F � :. f =:=2 -----------(1) �

P qoc.QDcJ ,I mg sin a -T = m(f -Fcosa) ------ ------ (2)

T =m(f-F) -------�-----(3)

0 &- ·,��

_(2) + (3) ⇒ mgx1=m(f-F)+m(f-Fx¾)

⇒ 4g=5J-5F+5f-3F

⇒ 4g=l0f-8F 0�3'f (l) ⇒ 4g= 25F-8F

4 ⇒ F=Ug. 0(1)⇒/=]0g

17

l s=ut+-at2

:

0

0

@ri--f-o

® c-1--o

�

------·-----·---------------

(b)

k

A

:o,

P.E.=0 :--{ -------------- ------�-2mg

mg

l . · 2 1 · 2 -x2mx(a0) +2x-xmx(a0) +2mgacos0-mg(k-a0)-mg(k+a0) =-2mgk+2mga2 2 �

::;. 2a02 =-2gcos0_+2g ®

02 g . 0 :. =--(I-cos ). a

_F=mg:

C etJc;roo/'; R-2mgcosB = -2m • a82

⇒ R = 2mgcos0- 2mg(I-cos0) .

�1PEJO KE 10 Equation 5

0

13. �!::.\) �m a a,:, sc��m:i � mg� «l'{q� � -�zxt ¢mf 0�d a®":ilod � 3i:z co:i:sr � � o� � � �$ -� tf<'• <Kil�•� m·� (1� 4't'I? .<fti:D. q� o ��-../ii�� c> � �c, z:w� er:ee.c,i;rl� �m xomlS.l, a-s:x< 3¢ � i+.!(x-2a'.)=0� �m � ae� <II®®.

. a .

c,de q�iS � � � em�· c®m �- lll� •W tf�� � �o �trxi mllll'@ e:,oe!!'a$. t}� �m

. a S X < 3a �.00. f = ! ( 4ax - ,I) cile ecl�!b. . ..

X=x-2a�@ «>� qoi=n�:-a�X<a�G» "x2 ·=!(it -x2 )�u1 9�=<Sm$; � A �- ��- -� � � 19l>. -�·�.������:��-fi'"e �-�a®.�� -� * �- -oS! � 09 � �<:! � ezm:4� c§ � ��-!l:SX�a� ;f =!(r�.:x-2:)� � <'ttz:Di � B ��me)

l:DQ� q� � � i:iie.� � -��� ll� tsi6� e� ¢l!j qaf �- �� ¢- Qfe· it�-� "e> � fl6· t1rJe0.Sa � .. .,,s.� 6'fg � �o.x-,;o,m.

a�x<3a: �!.03

T=mg(x-a) 0 a

{j

f._ =mg_: '1te-'�0@zi' 0 m o,� ,l,;mg-T:::mx ®

mg(

· ) ...⇒ mg-- x-a = i"l'JX

⇒ x+ g (x-2a)=0. fs\a .

\...J

mg. 3a

PE 10

·--------------------

16

·---�-X:::x-2a⇒X=x © me>� aSx<3a � -a�X <a.

X2 "." ! {4o(X + 2a)-(X +2a)2 } 0

=!{402 -X2 } for-a�X<a 0 :.A=2a.(D--------

---------

--------·------�--,.---------

---------·-------·-------.----.----------------·------------

z,!)c)ir,' <$rs! sm�"'� lfl"'®�Z'l' eoiQ!:>c) c,9 s�m� i= � (·.-e = l) .. _kl =K(iJ2 -X2 )

X=a0�6� X=� eO.

ga=K(B2 -a2 ) �a \...V

⇒B=✓2a .(D

a

I, -= -, z3CSJ t, = - - @O.

ft tel _

� 2 - 2 g

---------------------------------- ---------------- . �

-------- ------�

14.(a) A� B m_@)m m,eCmG, AOE>a Q �fl<, §le<m' �� A� B e63:ms, e=e:c �=>Z:1:> 853� @(W�lsi� 8� a� J, �- O�� C �l¼M:SI � ��- c = (l- J.) a+ lb c.:tcf3 GiB@� d&l O<l < L et&.

A(.;-too CB �� a,b1D1>•,t �� .� � 6 � C�:i,c:, A1J� � �- aa;ei,, aed .AC� CB=.). :_(1-A) a6m.t cte�mZI).

��, oc� AIJB� ��m QcS Sm§. lbl(•��) � laf(b·c)@i) c,e� daiW,,l.�

t: E

(b) Ol� A:IJCD '°'13 AS= l m too ,ac = .... 1m � � C);,> qti>c:5 /\ cmicfl ���-�-&:>em Sw 2/§,3, 4/i,.P. io:> .!J �

ae ag� P.A. DA,.DC. (JJ;t •. CEl!O-J .lJEt.r � � ��€>t0 D .· . C ���c) �;�-&e-� �-� <!il), P== 4� Q-=8� �. �a�� �-�z!. BAroo DA �ear�-��-�-�,�t��e:i,-� .J5m

01ea. t1.lf> �QBd � �$ z.fii �� � ��� � •. ¢'1�-� ���- A'----'B

� � $C� �-� �-ms BA�� A-Ba tn.6l r,,<S Im

i�aro��.

i.e. AC:CB=A:(1-A) CD

19

a·c b·c 0⇒ =-===-=- s

If! I !QI

A

10 - � GJ� IT (�f@:11!�· o0oil'.)a)) I q.00),CI; (C,.�) � • 2017 I·�� � � � ,crz;tS!. Z\) .1

(b) E

3

A

1fll

er!{E::Jilc.o �a:f®c.o2Sl8 C'!ltnts">c.o D2n �o»,

➔ 3-5+Qcos60° -Pcos60° =0

⇒ P-Q=-4, CD

C

B

CD

t -2✓3 -4✓3 +Qsin60°

+Psin60° =0 CD

. ⇒ P+Q=12 0 :. P = 4 and Q = 8� � . � \...::,_I

·--------------------

10 ".�®�II (�d �) I ;.!'O).m. (C;@os) � - 2017 .1 �· C)o@(9�a1 �d !.!>S � qi;t». · 21 . . . • 1 •

H a

➔ X=5+3+8cos60° -4cos60�·=10 0t Y =2✓3 -4✓

3+8sin60° +4�in60° =4✓3

R=✓100+48 =2-fri 0

E

s

1-m

0

H �m �z:sf zs,e BA, e,l!/992:shs>� �a1a e�cibD ;,o�e)2S'> emf1t:i,c., c.,1.8 a,z3§.

ii) . .-6./3-+2,/3(i+a)+✓3(3+4-2)=0 @� -6a+2 + 2a+S =0

a=im, 0 ---------------·---------------

C

15.(a) Q/6 Wa:>:1 c�ZS> � 2a El� c1t>i� c:1ml!Mt.'i'l06 �z;rl o� Socl @�®d ®m mQl� lfil:ll. i:ilO 2W to> �CD 2a §e"f�3� AB i;""'1e.)2Sl A <S'l:S)eru 6xSd � �-�9®0 �Cl qe:iE> l:S)0 �B qtl>68 (;ti@� �Z'I'� 9®c>Soc:! @�ZS>ll ()@<5� �� �!:Sf�e-d m@:i �m. 't.fJiffl cr),-:'.f@cl c.:)25) Bde:f z:oea, �fud � Bottt �-eoma e®a>

B

2a

Q

elm qm6 �O.mo 0®�� oc>�. (<f'?S So.d _'---___ _.._ ______,_ <'Oddz:ile) cori;w� Otoe., @e�-) iz�z:ood �& e!lO � A tnue:f @<D@® qzro e:1tf-s �= µ�. µ � Jj oo@otrlD::rl�.

(b) 0-��Doeiam �eot:d Cl� � e'( .AB,Br, AD, BD WJ CD r:iim-rd� .. � ow$2dr:i®m�m 6�� 01.iilc!e� <Sto@d ���-AB = ©ad a �� BC= @)c>c:S .'ia � � . p Q

(a)

r

BAD= BDA =BCD= 30°eE>.�c;;�Ba'!� 150N1mDio�-300Ntnl<1��m.l!>-o AB a>:> BC li36d � c,� �§m A !00c � � �� ei; Poo:i Q &1Jsie �

. qJWJ6 �2R C1ol Sod me� mi� (flm.P = 250 N @el @otrltmfts). @&f qo?S>� '°��m 'gt»:z,:iac �0i:ozm::if � c5oCW. � e .. �e go>l)JQ/e � c,-c},J qJmzil.. @zrog® � �2!'$21) �� z:romm.

A

t0S B -4---'-

0 2 I 12W • R

:z

X F

2a

a

s

�_...,

aRI

w

z:\lDor., CO�!:OJ t R, +R

2 =W

0 2,:j1D8r., Cl�?:D:l _.

0.F=S

(b)

µ> IFI-(R, +Rj

µ;?;✓3W w

µ�✓3

®

0

D

l50x2a+300(2a-f)-P.3a=0 (D

⇒P=250N 0

300N

-----------------------········-···-----------------··---------------

0 6011

1

0

0

0

r

0

200✓3

100✓3

0rf-----,,,C.....--40-0 __ ___:___�

·250✓350 60

°

0

l�f;) a:JtllzBCA e-tllo=® AB 2S0../3N

0 _;.

BC 200../3N ®�--

CD 400N

® DA SOON

® DB 100../3 N

®

25

16. 0zs!msa1 c 10, qoc:i a� �o c>amu,:iz@.?O �-w,f>0com gm � 6� �QZS) mclO @zs!�o Ic @c) 2a �6Bzf �i5l @El eomE>�.

:,r;

p

c.:1:>@1, c:5ioea!&> PQ, PR .oo ST a,m, �52:l> �a,2:1> ezitrlcjc., P � � �·w®8}o1Sm �c,:, wm ede � i::5>1:a>8 tUm- PQ ?SYJ PR 13Jl.f$� �P �� � c:ieiltflS>�c> �-! � c:,s Q ?Oil Rem� , sr a

-a

s,......::;..._ _ _.__�,...,rOJ�� qi1Sl. PQ = PR:. a, ST,= 2a � PO = 2 @E) � ,ws,; 61®� 0 0� QR a:>J ST c:itn �@� ® ®{.).D ezzf'5l!Q @El. me> Ii SUT om e$tm:.)�<D1.5l �mwc., kp §1 Zl?� d� �w � com @tlf� 0 eooqom asJ � c)� �; �- k(>O)� @El. sur�

c:,:l@� c5toc;,d � (fl.S � L � �. � �=6 �oc:) r4®c> Sod Q}� � Bdel:i tl:I®- Di��� t5ld® � B6cf oo,&,®l!i) e:k,b°� @t)®z5, � �- @� cSQ)c) e®r:t}� qt.tD. LtiJm p1llX5m Q)e � JS)d k > ¼ cW �-

�m k= I cr8 w�. Pez:sfe� � � m0m � Lc>� t:.11$ 09 � 'i'Oi5> 8153� ® � ��� <:IS. m < 3pa Q)f) �mvffl2i).

0

--�=---L.><.-.....-----lc----"""\,_--

c --G X

A

u

T

!:. . 0

J apacos0d0

c8c> /lm:a(A0)p �a, x= -2-�---

1,ap

·0

=: Jcos0d0

2

a=-•sm tr

2a =-;;·0

0

---------------------------------·----------

PR

PQ

ST

sur··

ti,oamfm. Do,'��- .·. _ _ \_·.

2ap

Sdfd ,6, P 9c) drm:sfw ! -m !!:c.e0

a

0 a

0-·

a

0 a 2a

0-+-

tr

xi

-- a trak (Ds. ⇒(4+1rk)x1 =-+a+--+2ak 2 2

� (7lk+4k+3)a ⇒xi=-----.

n-k+4 2

. (.iik+4k+3JE._ !!_ 0I.e. > .n-k+4 2 2

0

s

0

0

p

¢:> 1lk+4k +3 > trk+ 4. r-------------'��--1-----� R

i

,,.,•'

25

------------·-------'------------------..!=::==

R,

s

p

mg t-----��=--1-- - ________ ....,_ R,

�50 [(4ap+1l'a p)+m]x2 =(4ap+,ra p)x1• (D <::> [(4ap+1ra p)+m]x2 =(4ap+1ra p)(1f+7_):!..

,, ,'. 1r+4 ,2

<::} [(4ap+1ra p)+m]x2 =ap(1r+7)� 2

- ap(1r+7) a (D ¢:;> X2 =r L(4ap+1ra p)+m] 2

. ap(n+7) a a i.e. [(4ap +;a p)+ m] 2 >2

<=> ap(Tt+7)>4ap+1ra p+m

<=>m<3ap. 0 ---·----------·--•-. ·------

0

. 10 - � roa'&ool II (�<!!@ oOcDOa,) I (1!.@0:1.tD. (e,.qJ &:lGXll - 2017 I � � �cl t;!>S � �- 29

17. (a) A, B "'3 C C-'f>i ®g IOtsJ. tJ!llll$, e31!m � .�· � ��- � �· a,:, =>c'i e&fe� ,:r� @!>. A �e � :� 4� co,..,� 2d � B� ms·� 2.� w:, � � 4� ti C®d@e&J as e&.1e .�sx, � � (w+ l)d :q �� �- �.� �� �.�OB El tf("mr:n eeiz �· � � � �. � �m r,DmD ID� et<!JS, .� G>m-� ��.a»� Q)� ��-CC)�!) ... :(i)�

(a)

.i� ee, ·'f!l@ � �zn.

toe)"·�� <Dm•� �.�:��ad. �m � �,atJ l tnS �. C@de aN:1116', 06>tn��� •

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0-2- 15 25

.15

e®®8�8Q:z,�p·�mMm�4 ��-

·"' = �#; M) �·<1b'¢.���K���;e£>$M"'?Se�'®w�aS.

.. X Q� t,G� �:fcco 9� QW q,-�Dzn ea!-cco m,c, co1S "'��

§� �!}!!)3e)ts)� 251CO@�zi' ,

P(X) = P(X I A) P(A) + P(X I B) P(B) +�(XI C) P(C). •• --- --- • •• • - ··(I)

(I) ⇒ 2._ = �x.!.+�x.!.+ (m+I) x.!_'tc)'i

18 15 3 15 3 2(2m + I) 3 "--V

5 8 (m+ 1) ⇒---=--'----'--6 15 2(2m + I)

⇒ 3(2m +I)= 5(m + l)⇒ m=2

_0

0

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

3 0·m=2⇒P(XIC)=-. 5 10

P(CIX)= P(XIC)P(C) � P(X) \._y

· 3 I -x� �=J.Q__]_ \...::__,J

5 18

9

. 25 0 --------------·------

(hJ

c�� o6:i�C.5 f ®:IQ:x) c=f•»

x2

X

0-2 IS

2-4 25 3 9

4-6 40 5 25

· 6-8 15 7 49

8-10 5 9 81

Ii =100

= I.rx = 440 =4.4 (D · µ Lf 100

--------· ...... ,._ ... ..,,. _______________________ _

------------·-----·----------------

fx fx2

15 15

75 225

200 1000

105 735

45 405

r1x =44o .f x2 = 2380

?� �3� . 7j

= 2380 -(44)2

fs' 100 JO \....::_)

=✓23.8-19.36 0

=✓4.44

�2.11. 0 ----.... ------------·---·---------------------·------ ------------- ·--- -------·--·--------------------

. 10 0M=4+-x2 S 40

==4.5. 0-·

K= 3(4.4-4.5) 02.11

0.3 ==--

2.11�- 0.14. 0

·········---------------···--···-··-····---·---·-·····-------·---------·-·-·-··