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Catalogs Discussion Forums -> Integral Calculus -> Help with Integration Questions -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
6 replies   

k no beatin abt d bush


1) by practice of course


2) draw d grafs to get an idea nd proceed using simple geometeical methods or integration if required....if itz mod u wont need much of integration....can b solved by simpl geometry

Catalogs Discussion Forums -> Lounge -> Nice one :) -> Go to message
This Post 10 points    (Olaaa!! Perrrfect answer.   in 2 votes )   [?]
7 replies   

white.....coz its north pole.....nd itz a polar bear....as evry wall faces south in north pole

Catalogs Discussion Forums -> Algebra -> functions -> Go to message
This Post 10 points    (Olaaa!! Perrrfect answer.   in 2 votes )   [?]
4 replies   

heyya it shud b:


f(x) = 1 +{ sinx / 1 - sin2x}


       = 1 + sinx/cos2x


       range(-inf,inf)---------->>1 is included!!


cheers!


sinx----->>(-1,1)


cos^2 x--->>(0,1]


so we'll have -infinity too

Catalogs Discussion Forums -> Integral Calculus -> plz see this question -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
6 replies   

newton leibniz rule fr continuous fns.........plz refer ur texts fr this......

Catalogs Discussion Forums -> Integral Calculus -> plz see this question -> Go to message
This Post 14 points    (Olaaa!! Perrrfect answer.   in 4 votes )   [?]
6 replies   

df/dx = log(x + rt(1 + x2))


let df/dx = p(x)


p(x) = log(x + rt(1 + x2))


p(-x) = log[rt(1 + x2) - x]-------------(1)


-p(x) = - log (x + rt(1 + x2))


           =  log [1/(x + rt(1 + x2))]


         = log[rt(1 + x2) - x] / (x2 + 1 - x2)-------------(2)


         = p(-x)


so p(x) is an odd function


so its integral.........f(x) is an even function

Catalogs Discussion Forums -> Algebra -> Write 271 as the sum of positive real numbers so as to maximize their product -> Go to message
This Post 7 points    (Olaaa!! Perrrfect answer.   in 2 votes )   [?]
11 replies   

@sachin gupta.....


dats d mistake we all made d last tym.........


its not mentioned 2 nos.--got it!


accordin to ma soln.....the max pdt is e271/e ~~~approx....(2.7)100.....which is way higher than ur 135.5^2


 


xperts......reply

Catalogs Discussion Forums -> Algebra -> Write 271 as the sum of positive real numbers so as to maximize their product -> Go to message
This Post 10 points    (Olaaa!! Perrrfect answer.   in 2 votes )   [?]
11 replies   

oops........stupid me!


it s not mentioned 2 + real nos...is it........


let me assume the number of numbers to b 'n'


so


x1 + x2 + ....+ xn   >=  n (x1x2.....xn)1/n


.......pdt....<= (271/n)n


so pdt is a function of number of terms


so p(n) = (271/n)n.........


logp = n log(271) - nlogn


1/p * dp/dn = log271 - logn - 1


dp/dn = p[log (271 / n) - 1]


dp/dn = 0 ------->> log(271/n) = 1 or p=0


n = 271/e or p = 0


but p cant be zero so


n = 271/e


n x1 = nx2 = .......= nxn = 271


so...


x1 = x2 = x3=.......=xn = e


so the positive real numbers required are:


271/e................n times..........


x1 = x2 = x3=.......=xn = e.........


uhhhhhh........now anothr prob.....,m gettin not gettin n as an integer.......ne1 help.....

Catalogs Discussion Forums -> Algebra -> Find the remainder -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
13 replies   

check this out


solved last year:


http://www.goiit.com/posts/list/algebra-number-theory-13315.htm


 


cheers!

Catalogs Discussion Forums -> Algebra -> Find the remainder -> Go to message
This Post 22 points    (Olaaa!! Perrrfect answer.   in 5 votes )   [?]
13 replies   

simple....use congruence modular theory:


2222 nd 7 r coprime to each other


so eulers totient function phi(n)= 7(1 - 1/7)= 6


so


22226 = 1(mod 7)


so


(22226)925 = 1925(mod 7) = 1 mod7


so


22225550 = 1mod7------------(1)


 


now


2222 = 3mod7


22222 = 9mod7 = 2mod7------(2)


22223 = (-1)mod7------(3)


so 22225555 = 1*2*(-1)mod7 = (-2)mod7 = 5 mod7


remainder is 5


cheers!


 

Catalogs Discussion Forums -> Mechanics -> rates assured for correct answer -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
5 replies   

now fer explanation:


consider car A movin in rite with u m/s


and car B movin in left with v m/s


.....


now relative velocity of A wrt B is.....U - V (caps are fer vectors nd lower case fer scalars)


relative displacement is S = 8 m/s


S = (rel.velocity)(time)


  = U -V....coz time is 1s


now U = +u


and V = - v(takin rite to left as negative)


so s = u + v


8 = u + v


similarly


wen both travel in same direction it is


0.8 = u - v.........


solve u get above ans

Catalogs Discussion Forums -> Mechanics -> rates assured for correct answer -> Go to message
This Post 5 points    (Olaaa!! Perrrfect answer.   in 1 votes )   [?]
5 replies   

let velocities b ---u and v


now dis is easy coz it in 1 second......


so sum of velocities mus b 8 and diff mus b 0.8


so ans is obv....4.4 and 3.6-----(b)

Catalogs Discussion Forums -> Algebra -> Write 271 as the sum of positive real numbers so as to maximize their product -> Go to message
This Post 0 points    (Olaaa!! Perrrfect answer.   in 0 votes )   [?]
11 replies   

hey


u c itz positive real nos......


so d first thing u shud look at is


x + y/2 >= rt(xy)


so itz obviously (135.5)^2........


in maximisin probs the value u luk fer mostly lies in middle

Catalogs Discussion Forums -> Algebra -> wow!!! what a gr88 problem....plzz try it... -> Go to message
This Post 5 points    (Olaaa!! Perrrfect answer.   in 1 votes )   [?]
9 replies   

awryt....itz a try....


k m assuming dat he is buildin d cube from bottom up....row by row......


for bottom row---he needs4 vth 3face colored......4 vth 2 face colored nd 1 vth 1 face colored.......


he picks em out in


8C4 * 12C4* 1C1  ............nd aftr selection....the 3color cubes can b placed on black face in 3/6 ways......nd rotated in 1/4 ways.......------>so in 1/8 ways


2 color cubes can b placed in 2/6 ways nd rotated in 1/4 ways.......---->>1/12


1color cube can b placed in 1way and rotated in 1/4----->>1/4.......


proceed lyk dis fer othr rows!


m still not sure


 


 

Catalogs Discussion Forums -> Algebra -> wow!!! what a gr88 problem....plzz try it... -> Go to message
This Post 2 points    (Olaaa!! Perrrfect answer.   in 1 votes )   [?]
9 replies   

hmmm...


there'll b


12 smaller cubes vth 2 black faces


8 with 3black faces


6 vth 1 black face


1 vth no face black


we'll consider each category separately......


now one 2 face colored cube can occupy the position of anothr 2 face colored cube....nd so on......each can b fitted in2 d place of anothr of itz kind nd not newer else......


so we find the number of ways.....fer each category.....nd divide by total no.of ways.......nd there u have it!


this is basic idea!


vll post complete solution l8r......am i r8 little_genius??


PS: dont 4get the along vth position of cube color of d side mus also b taken in2 account!

Catalogs Discussion Forums -> Mechanics -> After what interval will the minute and hour hand of a clock coincide with each other? -> Go to message
This Post 5 points    (Olaaa!! Perrrfect answer.   in 1 votes )   [?]
3 replies   

whoa-----ive been fooling arnd......got an idea.....


in 12 hrs hands vll meet 11 tyms....


so answer


12/11 hrs

 
 
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