lomaxx:


this is on permutation and basic counting principle.
In how many ways can 3 guests sit together in 7 row of seats.

tempest01:

Cheap, do u want the answer or u need the answer?

tempest01:

e don tey sha but:::::::::::::::  ⁿP_r=n!/(n-r)! = 7!/(7-3)!= 42 , mine

Eemeekaa:

Find d value of n in 2^n+3^n=12^n.

lomaxx:

[/color][color=#990000]i wonder if the problem is as you put it , i.e, the original problem you were given to solve or you just made it up. I tried it sha and discovered that there is no algebraic method of solving this, you can only use calculus<so far as i know>

for n=0
2^0 + 3^0 > 12^0



for n=1
2^1 + 3^1=5

12^1= 12
So there is a single solution and d solution is between 0 and 1.
And there is no algebraic way of solving this.


My brother there is an algebraic method of solving it. Just admit that you don't know it. Anyway I admit you are smart for guessing that the answer is between 0 and 1.

Obinoscopy:

Ozorhumphery:

arctan(1+x) means the tan inverse of (1+x).
Let f(x) =arctan(1+x)/(1-x) also let 'u'=arctan(1-x) and 'v'=(1-x)
> f(x)=u/v applying quotient rule of differentiation:
> f'(x)={vdu/dx - udv/dx}/v^2
>du/dx =? dfrenting 'u' wrt x, du/dx = 1/{1+(1+x)^2}
vdu/dx =(1-x)(du/dx)
>dfrenting 'v' wrt x, dv/dx =-1, udv/dx = -arctan(1+x),
v^2 =(1-x)^2,
so substituting the values obtained in the quotient rule above and taking 'n'=(1-x), 'm'=(1+x) to enhance simplification gives:
>{(n+(1+(m)^2)(arctanm)}/((1+m^2)n^2} as the answer.
This solution can be understood at least by an average Alevel mathematician.

Ozorhumphery:

[color=#990000][/color]

if u =arctan(1+x)     du/dx can be precisely gotten,because if   for example:
y=arctanu, therefore dy/du =1/ (1+u^2) from first principle.

Ozorhumphery:

Na wah for youoooo, na so u go take write the aptitude test?