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#42601 Re: Help Me ! » Integration. Where is the 2 coming from? » 2005-08-23 21:12:52
∫udu = u²/2 + c
∫u is not defined.
In integration, the dx or du component is important.
∫1/x is not defined. But, ∫(1/x)dx = logx + c or lnx + c(as denoted in some textbooks).
Similarly, ∫(x^n)dx = [(x^n+1)/(n+1)] + c.
#42602 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-23 21:04:41
Problem #k+1
In a University, a student has to take necessarily Physics, Chemistry or Mathematics. The students are permitted take any two of them or even all the three of them. If 85 students take Physics, 65 students take Chemistry, 100 students take mathematics, 30 students take both Physics and Chemistry, 40 students take both Physics and Mathematics and none of the students take Chemistry and Mathematics or all three of them, how many students are there in the University?
#42603 Re: This is Cool » A Pi Fundraiser » 2005-08-23 16:24:34
Nice T Shirt, Good cause!
I hope they get more funds than what they expect!
#42604 Re: Dark Discussions at Cafe Infinity » Wink Murder 3 » 2005-08-23 00:24:30
Thats right, my post saying I'm in the game is gone!
Anyhow, once again, I am playing 
#42605 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-22 16:25:14
Problem #k
What is the total number of squares, of all sizes, in a Chess board?
#42606 Re: Help Me ! » money in bags question someone asked » 2005-08-22 16:23:29
Yes, seven bags is right, but I would have put the Dollars in the bags this way:-
1, 2, 4, 8, 16, 32 and 8.
Your solution is correct too!
#42607 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-17 16:29:10
Problem # n+11
A circle of diameter 'a' is cut from a square metal sheet of side 'a'. From the four corner cuttings, four circles are cut. Whats the maximum area of the four circles put together?
#42608 Re: This is Cool » 0x∞=-1 ??? » 2005-08-16 19:26:52
Too complex for the human brain to comprehend.....
wcy showed us 0 x ∞ = -1
and there seems to be no loophole in the proof.
I was almost convinced that 0 x ∞ = 0 x 1/0 = 1, now I'd have to tell my mind it is ±1.
When we take the value -1,
0 x ∞ = -1
Taking square root on both sides,
√ (0 x ∞) = √-1
0 x √ ∞ = i
Therefore, √ ∞ = -i/0 !
wcy, your theory appears to be right!
#42609 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-16 16:27:32
Correct, Mathsy!
Problem # n+10
Mathsyperson, Kylekatarn and wcy are a team for solving problems. The possibility of one solving a problem is 45%, the other is 50% and the third is 55%. What is the probability that a problem would be solved?
#42610 Re: Help Me ! » Need help » 2005-08-15 20:39:56
x³ + 2x² - 9x = 18
x³ + 2x² - 9x - 18 = 0
Putting x=3, we find that it is one of the solutions.
Therefore,
(x-3)(x² + 5x + 6) = 0
x² + 5x + 6 = (x+3)(x+2)
Therfore,
(x-3)(x+3)(x+2) = 0
which gives the following values of x :- 3, -3, -2
PS:_ A cubic equation, that is an equation of degree three, can be solved only by trial and error, as far as I know.
#42611 Re: Help Me ! » total square footage of a quonset hut » 2005-08-15 16:37:12
A quonset hut would be half of a right solid cylinder. Length is given as 205 feet. Width is given as 80 feet, and height 24 feet. But if the width is 80 feet, the height would have to be 25.46479 feet. That is obtained by dividing 80 by pi.
The volume would be pi*r²*h/2 = (3.141592 x 648.4556 x 205)/2
= 208,811.285 cubic feet
#42612 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-15 16:10:51
So the next number would be 6³+6²+6=258
Mathsy, thats very good!
Problem #n+9
From a well shuffled pack of 52 cards, four cards are drawn one after the other. What's the probability that the four of them would belong to different suits?
#42613 Re: Help Me ! » percent difference between 2 zero values » 2005-08-14 18:04:53
If the value of the current month is B and the previous month A,
[(B-A)/A]*100 is the right way of calculating the percentage increase, which you have done. Problem arises when the difference is 0 and both the values are 0. I don't think there is any mathematical solution, but if you could program in such a way that
the formula is applied only when the difference ≠ 0
and when the difference is zero, the percentage change is zero,
your problem could be solved!
#42614 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-14 15:28:53
You are correct, NIH !
Problem # n+8
Find the next term of the series
3, 14, 39, 84, 155, _____
#42615 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-12 23:53:01
Problem # n+8
Can you find two numbers composed of only ones which give the same result by addition and multiplication?
#42616 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-12 23:44:28
d/dx (logx) = 1/x and ∫(1/x)dx = logx
#42617 Re: Guestbook » Maths » 2005-08-12 20:07:31
Welcome to the forum, Tahlia!
Keep visiting, new pages are being put on the website! You'd love them too!
#42618 Re: Dark Discussions at Cafe Infinity » The word "Dh00m" is famous. » 2005-08-12 17:13:11
Zach is going places! Well done 
#42619 Re: Dark Discussions at Cafe Infinity » Ah Yes, Infinity » 2005-08-12 17:11:20
Yes, I used logarithm to the base 10 for convenience.
The idea is to show that
Infinity + 1 = Infinity
Infinity + Infinity = Infinity
Infinity x Infinity = Infinity
Infinity ^ Infinity = Infinity
Infinity ^ Infinity ^ Infinity ^ Infinity ........Infinite times = Infinity
This is true because because we can never say for what value of n
log(n)infinity would be undefined.
And this is only the fourth stage of iteration (also referred to as 'tetration').
No wonder, Infinity is beyond comprehension for the human mind!
#42620 Re: Dark Discussions at Cafe Infinity » Ah Yes, Infinity » 2005-08-11 23:54:58
Definition:-
log (x) is denoted as log(1)x
log (log x) is denoted as log(2) x
log[log(logx)] is denoted as log(3)x
and so on.
We know that log of zero or a negative number is not defined.
My question is, for what value of n would log(n) ∞ i.e. log(n)infinity, be not defined?
(eg. log(6)Googolplex is not defined.)
Warning : We are moving from infinite to transfinite 
#42621 Re: This is Cool » 0.9999....(recurring) = 1? » 2005-08-11 22:42:23
a = 1
b=0.0000000000000000...1
a-b=0.99999999....
a²-b²=1²-0.000000....1=0.99999999...
(a+b)(a-b)=a²-b²
a+b = (a²-b²)/(a-b)=0.9999.../0.9999...=1
a=1
therefore b=0 !!!!
therefore a-b=0.999999...=1-0=1 !!!!!
If we are talking of infinite number of zeros after the decimal, before the 1, in b,
the proof is correct!
Because, a²-b² would be equal to a-b.
This is because we have defined 0.0000000000.......1 as 1 ater an infinite number of zeros after the decimal followed by 1,
as kylekatarn denotes 0.(0)1.
However, if the number of zeros is finite, (Don't worry, it is not)
a²-b² would contain more 9s than a-b.
#42622 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-11 22:28:30
Mathsy, you are right.
But, this can be done with Calculus.
Let x^x = y
x logx = log y
Differentiating both side,
xLogx(1) + x(1/x) = d(logy)
logx + 1 = d(logy)
When this is equal to zero,
Logx + 1 = 0
Log x = -1
x = e^-1 = 1/e
This is because logy is minimum when y is minmum
#42623 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-11 22:23:33
Oops, I made a mistake.
If, as I had said earlier, x∈ Real numbers,
my question would have no answer as
(-1 x 10^n) -1 would give a negative odd number for a
large value of n (n ∈ Natural Numbers). And this number raised to itself would give a negative number which would be much lesser than zero!
Therefore, the smallest value would be -∞
I forgot while posting that one that a^-n = 1/a^n
Therefore, the minmum value of x^x is not -∞
I am sorry I wasn't concentrating 100%
#42624 Re: Help Me ! » I need your help » 2005-08-11 22:20:56
You are right, MathsisFun. I am working on this. I shall give you the details next week.
#42625 Re: Help Me ! » I need your help » 2005-08-11 21:17:49
0^0^0 is not defined.
But for 1, as you pointed out, 2^Mx > x^x^x.
For this problem, let us take value of x ≥ 2, x ∈ N