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+ Plus / add [ Sum / Total] Minus / Subtract /Deduct [ Difference] Times / Into/ dot /of /Multiply [Product / Multiplication ]

, /, Division , Divisible , Remaindera(dividend-) b(Divisor-)= c(Quotient-) Plus or Minus = Equal / Is Approximately Equal Is not Equal Is greater then {5> 2} Is not greater then {5

20}

Is greater than or equal to ( / )

% Percentage( 100 )

Infinity /

Varies as / is Proportional Implies/or If and only if Pi

1,2,3...n[,\,] Constant/

x,y,z Variable /


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2x x + x

=

a+bx+c Expression [a, bx,c Term]0 n0 =n , n0 =0 , 0/n =0 , n/o = (anything 0) = Undefined ()|x| [x] Absolute Value ( ) Negative Positive Square Root , =2, =3 Cube Root , =3, =4 n Root n x 1/n

X y

= Summation ,X n

* +- Bracket Logarithmsa x ( n= )

[ + , ]

10 n!n Factorialn n (n-1) (n-2)1 [ 5!=54321]

npr Permutation [ n npr ,npr= n(n-1) (n-2) (n-3) ..(n-r+1) Ex:- 6p3=654 ]ncr Combination/ /,ncr=


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A=*,, ,+ A , a,b,c,d Intersection /cap [ /

] [AB={x:xA xB}] Union/cup [

]=> ( ) [AB={x:xA xB}] Element of / Belongs to / [Ex: bA] Is not an Element of/not Belongs to

/ Subset of [A /B / ]/ Superset

Empty Set

A\B [B A , A / A ] A-B={x:xA xB}

A Complementary set [U\A=U-A={xU : xA }P(A) Power Set [A n P(A)

2n]

NZQR N( / +n),Z( +n,0,+n)Q(0,+n, ),R ( ), ( ) Q=R-Q

Straight line ( ) Ray ( ) Line Segment ( ) Similar to Almost Equal to Is Equivalent to/ Congruent


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Angle / RightAngle Measured Angle Perpendicular To Is Parallel to Therefore / Hence Since / Because / Triangle Rectangle/Square Circle

(Unit) ()

3 (Digits) / 3 Ex:- 318 3+1+8=12 ,

(Unit) (tens) 4

Ex:- 544 , 4 444 (Unit) () 5 3 2

(Unit), (tens) (Hundredth)

8 Ex:- 77 264 ,2648 , 77264 8 (Digits) / 9

Ex:- 288 2+8+8=18 ,9 , 288 9

(Unit) () 2, 5, 10

(oo) , 4, 25, 100

(000) , 8, 125, 1000


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0,1,2,3,4,5,6,7,8,9

1 100 0 11

2 9 (2,3,4,5,6,7,8,9) 20

1 21

87654321

8(Crores) 7(Nijut) 6(lacs) 5(Ajut) 4(Thousands) 3(Hundreds) 2(Tens) 1(Units)4321=41000+3100+210+1


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{-n.-5,-4,-3,-2,-1, 0, +1,+2,+3,+4,+..+n}2 {0,2,4,6,8,.2n}

2 {1,3,5,7,9.(2n+1)}

Even Even=Even , Odd Odd=Odd , Even Odd=Even

Even + Even=Even , Odd + Odd=Even , Even Odd=Odd

Even / Even=Even , Even /Odd=Odd , Odd/Even=Odd

Odd Odd =Odd , Odd Even =Odd , Even Even=Even , Even Odd =Even

(2,4,6.) (3,5,7..)

{ n,n+1,n+2,n+3,.}

( even prime number)

(Odd Prime number)

1 100 25 1060 1 200 46 1 500 95 1 1000 168 ( 2 ,3

3 , )


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1 100

1-10 2,3,5,7 4

11-20 11,13,17,19 4

21-30 23,29 2

31-40 31,37 2

41-50 41,43,47 3

51-60 53,59 2

61-70 61,67 2

71-80 71,73,79 3

81-90 83,87 2

91-100 97 1

(4422322321)

(1232232244)

/

Fraction ()= ( , x y ) , = Rules of fractions

+ = - = + = = + - = = - = = =


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=

a c = b

2

> ( Ex:- , )

< ( Ex:- , )


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,

, , , , , , ,


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- , -(0,1,2,3.n ), ()-16 , (a/b

-a b ) , -

a/b -a b ) ,

( ) , ( ) , , , , , e Ex:- , , , , ,

I1, V5, X10, L50, C100, O500, M1000

Greek Alphabet

Alpha Beta Gamma Delta Epsilon Zeta Eta

Theta Iota Kappa Lambda Mu Nu Xi Omicron

Pi Rho Sigma Tau Upsilon Phi Kai Psi

Omega

,

,

20 =5221

, Ex:- 35/5=7 , 35/7=5 5 735 357 5

,


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,

-

..


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2304 (Square Root )

74 28 1) 2) , 3) 74 64 , = 8 :4) 8 74 64 5)

74 64

10 28

1028 ( )

6) 8 82 = 16 ( )

7) 16 1028 1028

8) 6 16 66=996 7 ( 16 7 7 = 1169) 1028

9) 1028 996 32 862 = 172 32

10) , 86 11) 74 28 32 7396

86


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BODMAS

[{(Braket)}]of /Division() Multiplication () Addition (+) Subtraction(-)

=x , x-a =b-x => x= Formula:-- =

1008 = 2222337=243271

= (4+1)(2+1)(1+1)=30

Formula:-- x =ambncl =(m+1)(n+1)(l+1)

2\1008

2\504

2\252

2\126

3\633\21

7


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n

Let the Numbers =x and (x+1)

According to the Question, (x+1)2 x2 = n x

= , = +

= ( a , b , c d) ..

= ( a , b , c d) ..+

= ( a , b , c d) .. + /

= .. ..

.. = ..

.. =

.. =


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-

(a) 2 (b) 3 = 61 = 6

10 =(610)

= ..

=

=

-M A, M = M A [ A = ]N B, N = N B

= M + N = AM +BN

=


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Varies as / is Proportional

-

,,,

, =

= , =

a, b, c ,

a:b =b:c

a+b+c = S ()

a = S

a:b = x:y = (xl): (yl) = xl : yl b:c =l:m = (ly): (my)= yl : my

a:b:c = xl : yl : my

Formula:-- = a + b + c = n


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Formula:-Required Amount: =

Required ratio

Water =

3 =6

Formula:-- = 7 + 3 = 10

30 = 30

( ) = 21

30 = 30 ( )

= 9

, =

3 : 7

x 3 : 7 21 : (9 + x) = 3 : 7 x = 40

7 : 5

10 = 30

0/0 3

= 7 : (3+2) = 7 :5 1 = 3

6


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100 (100)

x % = N (90) P % (75% )

Formula:--Let the Number be = x

X P% = N X 75% = 90What Percentage % is R(90) of N(120)?

N X% =R

120 x% =90: 100

100

,100

,

, 100

-25% = (100 + 25 ) = 125

125 = 100

,, 100 ,, ,, ,, = = 80 = 00 80)% =20%


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Formula:-

[ % =

]

[ % =

]]

(Increase ) + (Decrease )

, % %

25% , %

25% % , 25%

Formula:-% Change =

100%

Result + Increase

Result Decrease = 0 00 100% =100% [ ]


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Formula:--5% , 100 + 5 =105100 = 105

,, 1000 ,, ,, ,, =

= 1050

5 = 1050 1000 = 50 1 ,, ,, ,, = 50/5 = 10

Formula:-

= 10

Solution:= 100x = 100y

= = 10000 xy20% = (100+20)x =120x

10% = (100-10) = 90y

= 120x 90y = 10800xy = 10800xy 10000xy = 800xy 10000xy = 800xy

,, ,, 100 ,, ,, ,, =

=8% Formula:-

x First Value ( ) % y Second Value ( ) % ,

/ (Increase) + / (Decrease) (Answer) + ,

(Answer) ,


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Formula:-- +

C% = (+5) + (+5) +

Formula:-- ,

F=S = 10

C% = (10) + (10) +

Formula:-- , F=S = 5

, +

C% = (+5) + (+5) +

F= + 25%

S = 5%

C% = (+25) + (

5) +

C% = (-20) + (+20) +


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C% = (+20) + (+20) +

C% = (+10) + (+20) +

Formula:-Mix % =

Formula:- - Rest (n) = 100x (f% + s% + t% )x

Formula:- -pass = n x% (a/b)

, = 100

= (100+25 ) 125

125 =100

,, ,, 100 ,, ,, ,, ,, 80 = (100 80 ) = 20


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,

100 =25

,, 64 ,, ,, ,, ,, =

, = (6416) 48

,

40 = 100

,, 48 ,, ,, ,, ,, =

120

= (12048) 72

, = (72 16) 56

,

,

Formula:-- = (100 70 10)% = 20% = (100 80 10)% = 10% = (20 + 10 + 10)% = 40% = (100 40)% = 60% 60 , = 100

,, ,, 360 ,, ,, ,, ,, ,, ,, =


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= (60 40)% = 20% = (70 40)% = 30% = (40 + 30 + 20)% = 90%

= (100 90)% = 10%[1 10% ]100 = 10

,, 200 ,, ,, ,, ,, ,, ,, =

, , ,

, ,

()

[ , ]

X = Y 1 = (X Y) [ , ]Z =

[ , ]


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1 1 2

,

Formula:- M1 D1 = M2 D21) M2 = 2) D2 =

Solution :

100 =(500 100) = 400 5 ,500 = (20 5)15 1 ,, ,, ,, ,, ,, = (15 500)

400 ,, ,, ,, ,, ,, =

00 [ 500 ,

, ]

Formula:--X m = 1

1 ,, ,, = Y 1 = X Y 1 = (

+

) =

=1

,, 1 ,, ,, ,, = Formula:- T =


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Formula:- T =

Formula:- T =

Formula:- T =

Formula:- T =

[ ]

SolutionX 20 = 1

X 1 = Y 1 =

Z 1 =

X , Y Z 1 = ( ) = 1

,, 1 ,, ,, ,, = 8


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Formula:--1 = 1/8

,, 6 ,, ,, ,, = 6/8

= (1 ) = X 1 = 20

,, ,, ,, = (20 ) =20/4 = 5

Formula:-- X 1 = 1/ 20

5 ,, ,, =

0

X5 X , Y Z = (1 ) =

X , Y Z 1/8 = 1 ,, 1 ,, ,, ,, = 8 ,, ,, ,, ,, = = 6

= X , Y Z + X 5= 6 + 5 = 11


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1 1 1 2

2 2

Formula:--3 20 = 1

3 ,, ,, 1 ,, ,, = 0

1 ,, ,, 1 ,, ,, = 0 4 ,, ,, 1 ,, ,, = 0 = [ ,

, ],

5 20 = 1

1 ,, ,, 1 ,, ,, = 0 10 ,, ,, 1 ,, ,, = 00 = 0 4 10,

1 = ( +

0 ) =

= 1 1 ,, ,, ,, = 6Formula :

T2 =


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Formula:- T =

t

U = Up , D = Down

T = 1= 77Min

Formula:-- ( )n = 1 ( )

=

=

= +

=

, U V [U > V]

,

(Relative Speed) = U +V ,

(Relative Speed

)= U

V

/ / X T

T X ,, 1 ,, ,, ,, =

=


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p

Lt

T =( Lp + Lt) ,, 1 ,, ,, ,, =

=

Formula:-- ,1 (60 60) = 45 = (45 1000)

60 ,, ,, = 0 0 750 60 ,

= +

750 = + 100 = 650Formula:- = 45 =

[ T Cnver Seed in km/hr to m/sec multiply speed by ]

=650x

T = , (Relative Speed) = , (Relative Speed) = T =

= 11 Second [1 km/hr = meter/second ]


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Formula:-

T =

= 0T = 0 0 = 9 Second [1 km/hr =

meter/second ]

Formula:-T = T = 0 0 0

(Principal / Capital / Sum )[Invested]

/ / ( Interest / Extra money for Interest) [ ]

/ [Per-annum ]

(Rate of Interest) [ , 100 1 ]

/-/ (Amount/ Interest-principal/Increased Principal)

= +

P t = p t 1


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r

,100 1 r

1 1 P 1

P tn

I = I = npr [r = r% = r/100]

[ ]

A =P +I

A = P + nPr = P (1 + nr)

P =

[r = r% = r/100]

P =

[ ,, ]


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P r

n C = p

= (C) (P)= P P

=

=

Solution-700 5 = 105

100 ,, 1 ,, ,, =

Formula:-I =

105 =

r =

, X 5 - = 2X

= - = 2X X = X

X 5 = X

100 ,, 1 ,, ,, = = 20 = 20%


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Formula:- ( ) =

=

r 0

1 2

Formula:--100 1 = (10 8 ) = 2

100,, ,,, ,, 5 ,, ,, ,, = (5 2 ) = 10 10 = 100

,, 200 ,, ,, ,, = 00 000 Formula:-I = 200 = p =2000

Formula:--5% , 100 10 = ( 5 10) = 50

10010 = ( 100 + 50 ) = 150150 = 100

,, 5000 ,, ,, ,, = 00 0000 Formula:-P =

P =


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Formula:--300 4 = 1200 1

500 5 = 2500 1

(1200 + 2500 ) = 3700 1 3700 1 148

100 ,, ,, 1 ,, ,, = 0000 = x % = x/100

, I1 =00

00

, I2 = 00 00

, I1 + I2 =148

00 00 + 00 00 = 148 x = 4%Formula:-I = r =

r = 00 00 00= 4%


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+ 5 = 500

+ 5 = 460

[ ]

2 = 40 1 ~ ~ = = 203 ~ ~ = 203 = 60

= (46060) = 400

400 1 20

1 ~ 1 ~ ~ 20/400

100 ~ 1 ~ ~20

400 00

Formula:-C = p

C = 600 C = 726


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(Cost Price ) CP :- / (Selling Price )SP:- (Profit) = (SP)

-

(CP)/(Profit /Gain) P:-(loss) = (CP) - (SP)/ (Loss)L:-

,

-

X % x %

x

C x % ,

=

X% c = ( C + )

X %C = ( C )

C P ,

=

Furmula: 1

(Profit %) = 00

Profit % = 00 %


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Furmula: 1

(Loss %) =

loss % = 00

0

Furmula:

(n) , (n+1) (n+2) ,

, ?

(loss) = /-

loss % = 000

Formula:- =n , First Value=F%, Second Value=S% = n [ + , ]

= 12

Formula:- =

= 00 00 0


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Solution = (150 + 20 )=170170 = 20

,, 100 ,, ,, ,, = 0 000 Formula:-

=

+ [ =

]

=

Cost = 150 +20 =170 % =0 000

Formula:-=

Cost = 00 0000 0

Formula:-= Cost = 00 0000 0

Solution: 100 , 100 P%,

100 = (100 + P )

,, n ,, ,, ,, = 0000 L% ,

100 = (100 -L )

0000 ,, ,, ,, = 00 00 0000 [P% , L% p% 5%(L%)

]


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Formula:--15%,

100 = (100 +15 ) =115

,, 280 ,, ,, ,, = = 322 8% ,

(100 -8 )92 = 100

,, 322 ,, ,, ,, ,, = = 350

Formula : ( )= 30 30 20% =24

(Profit) =(

Profit = 0

Formula:- = R% ( )

Cost= 00 00


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Solution %

10% = (100 10) = 9020% = (100 + 20 ) = 120

(120 90) = 30 30100

,, ,, 40 ,, ,, ,, ,, Formula:-

=

40 10% 20% ,

10% + 20% =40 15% = 40 1% = 0

100% = 0 00 Formula:-

=

= 00 0 0


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Solution: 3 % 20% = (100 20) = 8040% = (100 + 40 ) = 140

40% 100 = 140

,, 80 ,, ,, ,, 0 000 = 11210% , = (100 10 ) =90

= (112 -90) = 22

22= 100,, 50 ,, ,, ,, =

00 0

Formula:10% , Sells1 = (100 10) = 9020% = (100 20 ) = 80 ,

profit, 80 40% =32

,Sells2 = + = 80 + 32 = 112

=

[ Absolute Value Negative Positive]

Cost = 00 0


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Solution:5 = 4

1 ,, ,, = ,

4 = 5 1 ,, ,, = = - =

=

0

[ ]

=

0

,, ,, 100 ,, ,, ,, =

Formula


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Solution:X = 1

1 ,, ,, =

Y = 1 1 ,, ,, = = =

=

,, ,, 100 ,, ,, ,, = 00

Formula =

=

00

Solution: = (380+20)400 400 =20

,, 100 ,, ,, ,,

Solution:10% = (100-10) 90

5% = (100+5) 105

= (10590) 15 15 100

,, 45 ,, ,, ,, ,, 300


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Solution:20% = (100+20) 120

10% = (100-10) 90

20% , 100 = 120

,, 90 ,, ,, ,, = =108

% , = (100

)

= (100 ) 31

2 =100

,, 31 ,, ,, ,, ,, = 200

Solution:x % , = 0 0

( 0 0 ) = 100 ,, n ,, ,, ,, = y % , = 0 0 100 = ( 0 0 ) ,, ,, ,, ,,=

= n


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Solution:36 =12

100 ,, ,, ,,

20% , 100 = (100 + 20) 120

20% ,

= 120

20 ,, ,, ,,

Solution:15% 1200 + 1200 15% (1200 15

100 )

1200+180 = 1380

5% 1380 1380 5%

1380 69 = 1311

Solution:5 = 2

100 ,, ,, = 4040% ,100 (100+40) 140

140 =40

35 ,, ,, ,, ,, = 10


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Solution:12=20

1 ,, ,, ,, = 53

1 = = 2

5

3=

1

3

53 = 1

3

,, 100 ,, ,, 20 [ ]

Solution:3 = 1

1 ,, ,, ,, =

2 = 1

1 ,, ,, ,, = 2

1 = = 1

2 1

3=

16

[ ]1

3 = 1

6

,, 100 ,, ,, 50


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Solution:, 5 = x

1 ,, ,, ,, =

4 = x

1 ,, ,, ,, =

1 = =

=

=

,, 100 ,, ,, 25


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1 Lac = 105

1 Million = 106 = 10 lac

1 Crore =107 =10 million

1 Billion = 109 (USA) =1012(Eu)

1 Trillion = 1012(USA) = 1018(Eu)

1 kilogram= 2.2 (lbs) pounds

1 Seer = .93 kg

1 mound = 40 seer = 37.2 kg

1 quintal = 100 kg

1 ton = 1000 kg

S.I International Systems of Units 1960

CGS Centimeter . Gram .Second

M.K.S Meter . Kilogram . Second

F.P.S Foot .Pound .Second

12 Inch = 1 foot , 3 foot = 1 Yard , 1760 Yard = 1 mile

RelationshipDistance Area Volume1 Inch = 2.54 Centimeter 1 Inchs2= 6.45 cm2 1 liter = 1000 Cubic Centimeter

1 Meter = 39.37 Inch 1 Hectare = 10000 meter2 1 Cubic meter = 1000 liters

1 mile = 1.61 kilometer 1 Katha = 720 feet2 1 Cubic foot = 28.31 liters

1 Nautical Mile = 1.853km 1 Acre = 4047 meter2 1 gallon = 3.78 liters(us) = 4.54 liters(uk)

1 km2 = 247 Acres 1 Cubic Centimeter= 1 gram

1 m_t_r = 100 C_ntim_t_r = 39.37 In]hs = 3.28 `__t = 1.0936 Yr^s = 0.00062 mil_s1 kilogram = 1000 grams = 2.2 pounds = 35.27 Ounces = 0.157 Stone(uk)1 meter 2 = 10.76 feet2 =1550 Inchs2 = 10000 centimeter21 Square kilometer = .3861 mile2 = 100 hectares = 247 acres1 mile2 = 2.589 kilometers2 = 259 hectare = 640 acres1 Celsius = 33.8 Fahrenheit = 274.15 kelvin


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F S F + S F SF S = F S = 30 = 20 + 15 F S F S

1 12

12 = 3600 ,, ,, ,, ,, = 0N = n 0

1 0

H M = ()() HM = [() ]

0 / 0

Examples: = = [>0]

= 0

=

0


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:

()

()(x )

x

()

()

()x

:

, A= q n, q = n =

(

,, W = q x n, q = ,

n = x =w = nx

, d = v t., v = t=

, Q(t) = Q0 q t, Q0=

q =

t=

Q(t) = t(+ )

P = b r, b =

r == = S%P== b S%


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