[ravi]

Hi Gaurav !
Been missing u ! Nice 2 c u back here ! And don't worry ! Everybody screwed up SimCAT5.
Ravi

[gkathotia]

Hey guys ,
--------------------------
This is for 21/10/2002
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(1) If a+b+c+d=constant , then the product a^p * b^q * c^r * d^s will be maximum
if a/p = b/q = c/r = d/s .

(2)Consider the two equations

a1x+b1y=c1
a2x+b2y=c2

Then ,
If a1/a2 = b1/b2 = c1/c2 , then we have infinite solutions for these equations.
If a1/a2 = b1/b2 <> c1/c2 , then we have no solution for these equations.(<> means not equal to )
If a1/a2 <> b1/b2 , then we have a unique solutions for these equations..

(3) For any quadrilateral whose diagonals intersect at right angles , the area of the quadrilateral is
0.5*d1*d2, where d1,d2 are the lenghts of the diagonals.

(4) Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is ,
the minute hand describes 6 degrees /minute
the hour hand describes 1/2 degrees /minute .

Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute .

(5) The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight.
(This can be derived from the above) .

Any inputs are highly welcome and appreciated ,

Regards
Gaurav

[aakaanksh]

Hi gaurav....
time is ticking and moreover you are also pretty much occupied with some other pressing concerns.
So i guess it would be helpful for us...if u can publish some imp formulae in large digestible quantities,so that we could work on them and make ur effort worth some use.
What does thou sayeth:...pls guys create a vociferous appeal out here so that gaurav pitches in with some good news

[gkathotia]

Lets make it 6-7 formulae per day . That way we would be able to reach something close to 150 + more formulae by the D-day .
WOKAY??
Gaurav

[MUKUL]

Gaurav (Math Expert) & all the math nerds
is there any formula for the perimeter of a quadrilateral & trapezium?
i was doing a sum & got stuck, the only way out that i use is to find all the sides & then add!
but it is time consuming yaar!!
can u give any suggestions?
also when i get stuck at a sum, i quit immediately but later i find i'm able to crack it...........much to my disappointment of course, any suggestions again?
Regards,
Mukul

[gkathotia]

Hye there all
This is the contribution for 25/10/2002:
------------------------------------------------

(1)If n is even , n(n+1)(n+2) is divisible by 24

(2)If n is any integer , n^2 + 4 is not divisible by 4

(3)Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for
[(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]

(4)Area of a triangle
1/2*base*altitude = 1/2*a*b*sinC = 1/2*b*c*sinA = 1/2*c*a*sinB = root(s*(s-a)*(s-b)*(s-c)) where s=a+b+c/2
=a*b*c/(4*R) where R is the CIRCUMRADIUS of the triangle = r*s ,where r is the inradius of the triangle .

(5)In any triangle
a=b*CosC + c*CosB
b=c*CosA + a*CosC
c=a*CosB + b*CosA

(6)If a1/b1 = a2/b2 = a3/b3 = .............. , then each ratio is equal to
(k1*a1+ k2*a2+k3*a3+..............) / (k1*b1+ k2*b2+k3*b3+..............) , which is also equal to
(a1+a2+a3+............./b1+b2+b3+..........)

(7)In any triangle
a/SinA = b/SinB =c/SinC=2R , where R is the circumradius


If others would also pitch in with their inputs this couls become a ready reckoner in QUANT
Regards
Gaurav

[nagging]

speaking of triangles and cosines heres an useful one u left out

cosC = (a^2 + b^2 - c^2)/2ab

sin2A = 2 sinA * cosA
cos2A = cos^2(A) - sin^2 (A)

[gkathotia]

--------------
29/10/2002
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(1) x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 - 14^3)

(2) e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity
(2a) 2 < e < 3

(3) log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [ Note the alternating sign . .Also note that the ogarithm is with respect to base e ]

(4) In a GP the product of any two terms equidistant from a term is always constant .

(5) For a cyclic quadrilateral , area = root( (s-a) * (s-b) * (s-c) * (s-d) ) , where s=(a+b+c+d)/2

(6) For a cyclic quadrilateral , the measure of an external angle is equal to the measure of the internal opposite angle.

(7) (m+n)! is divisible by m! * n! .

[gkathotia]

-------------
02/11/2002
-------------

(1) If a quadrilateral circumscribes a circle , the sum of a pair of opposite sides is equal to the sum of the other pair .

(2)The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .

(3)The equation whose roots are the reciprocal of the roots of the equation
ax^2+bx+c is cx^2+bx+a

(4) The coordinates of the centroid of a triangle with vertices (a,b) (c,d) (e,f)
is((a+c+e)/3 , (b+d+f)/3) .

(5) The ratio of the radii of the circumcircle and incircle of an equilateral triangle is 2:1 .

(6) Area of a parallelogram = base * height

(7)APPOLLONIUS THEOREM:

In a triangle , if AD be the median to the side BC , then
AB^2 + AC^2 = 2(AD^2 + BD^2) or 2(AD^2 + DC^2) .

[gkathotia]

Hiya guys
Back after a brief hiatus , the cause for which can be attributed to the sudden burden of work in office coupled with long working hours(gosh , this is killing me) . anyway i am overdue for a long one and here's it::::



(1) for similar cones , ratio of radii = ratio of their bases.

(2) The HCF and LCM of two nos. are equal when they are equal .

(3) Volume of a pyramid = 1/3 * base area * height

(4) In an isosceles triangle , the perpendicular from the vertex to the base or the angular bisector from vertex to base bisects the base.

(5) In any triangle the angular bisector of an angle bisects the base in the ratio of the
other two sides.

(6) the quadrilateral formed by joining the angular bisectors of another quadrilateral is
always a rectangle.

(7) Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1

( |a|+|b| = |a+b| if a*b>=0
else |a|+|b| >= |a+b|

(9) 2<= (1+1/n)^n <=3

(10) WINE and WATER formula:

If Q be the volume of a vessel
q qty of a mixture of water and wine be removed each time from a mixture
n be the number of times this operation be done
and A be the final qty of wine in the mixture

then ,
A/Q = (1-q/Q)^n

(11) Area of a hexagon = root(3) * 3 * (side)^2

(12) (1+x)^n ~ (1+nx) if x<<<1

(13) Some pythagorean triplets:

3,4,5 (3^2=4+5)
5,12,13 (5^2=12+13)
7,24,25 (7^2=24+25)
8,15,17 (8^2 / 2 = 15+17 )
9,40,41 (9^2=40+41)
11,60,61 (11^2=60+61)
12,35,37 (12^2 / 2 = 35+37)
16,63,65 (16^2 /2 = 63+65)
20,21,29(EXCEPTION)

(14) Appolonius theorem could be applied to the 4 triangles formed in a parallelogram.

(15) Area of a trapezium = 1/2 * (sum of parallel sids) * height = median * height
where median is the line joining the midpoints of the oblique sides.

(16) when a three digit number is reversed and the difference of these two numbers is taken , the middle number is always 9 and the sum of the other two numbers is always 9 .

(17) ANy function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .

(1 Let W be any point inside a rectangle ABCD .
Then
WD^2 + WB^2 = WC^2 + WA^2

(19) Let a be the side of an equilateral triangle . then if three circles be drawn inside
this triangle touching each other then each's radius = a/(2*(root(3)+1))

(20) Let 'x' be certain base in which the representation of a number is 'abcd' , then the decimal value of this number is a*x^3 + b*x^2 + c*x + d

That's all folks for today! Enjoy
Gaurav