Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#41826 Re: Help Me ! » Hep with Trig. please :) » 2005-08-26 00:09:31
cosecA + cotA = 3
To find cosecA - cotA,
one should remember,
cosec²A - cot²A = 1
From this, we get
(cosecA+ cotA)(cosecA - cotA)=1
Given cosecA + cotA = 3,
3(cosecA-cotA)=1
cosecA-cotA=1/3
cosecA + cotA + cosecA-cotA = 3+1/3 = 4/3
2cosecA = 4/3
cosecA=2/3
sinA=3/2 funny 
#41827 Re: Help Me ! » Variations » 2005-08-25 23:59:17
Lets assume the job can be completed by 5 men in 'x' days.
Therefore, the number of mandays required is 5x.
If one more man is hired, the total number of men = 6 and the number of days required = x-8. Therefore, the total number of mandays = 6(x-8)
Equating the two,
5x = 6(x-8)
5x = 6x - 48
-x = -48 or x = 48.
Therefore, the number of mandays required for the work is 5x48 = 240.
If y men moreare employed for completion of the work in 28 days earlier,
number of men = 5+y, number of days = 48-28=20,
the number of mandays = (5+y)20
but, we already know that the number of mandays required for the work is 240,
therefore,
(5+y)20=240, 5+y=240/20 => 5+y=12, y=7
Therefore, 7 more men would be required.
#41828 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-25 20:26:53
Problem #k+3
A cube of dimensions 10cm x 10cm x 10cm is made up of smaller cubes of dimensions 1cm x 1cm x 1cm. If the outermost layer of smaller cubes are taken off, how many smaller cubes would be left?
#41829 Re: Puzzles and Games » What next? » 2005-08-25 16:15:58
A, T, G, C..next comes L
Aries, Taurus, Gemini, Cancer,..Leo.
#41830 Re: Puzzles and Games » What next? » 2005-08-24 21:38:23
I expected this would happen....... 
A, T, G, C are NOT
Adenine, Thymine, Guanine and Cytosine.
#41831 Puzzles and Games » What next? » 2005-08-24 20:57:48
- Jai Ganesh
- Replies: 7
What comes next in the series?
A, T, G, C, _
#41832 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-24 16:34:02
Problem #k+2
I have a certain number of eggs in my store.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be two eggs left.
If you divide the number of eggs by 4 there will be three eggs left.
If you divide the number of eggs by 5 there will be four eggs left.
If you divide the number of eggs by 6 there will be five eggs left.
If you divide the number of eggs by 7 there will be six eggs left.
If you divide the number of eggs by 8 there will be seven eggs left.
If you divide the number of eggs by 9 there will be eight eggs left.
If you divide the number of eggs by 10 there will be nine eggs left.
If you divide the Number of eggs by 11 there will be NO EGGS left!
What is the minimum number of eggs I can have in my store?
#41833 Re: Help Me ! » Hep with Trig. please :) » 2005-08-24 00:16:35
You are right!
When x=0,
2sinx.cosx + cos^2x = 1
But how do we get a solution x=0?
2sinx.cosx + cos^2x = 1
sin2x + cos^2x = 1,
sin2x = 1-cos^2x
sin2x = sin^2x
this would be true only when x=0
But is there any (other)mathematical way it can be shown that x=0 is a solution?
#41834 Re: Dark Discussions at Cafe Infinity » Wink Murder 3 » 2005-08-23 21:14:05
Good wishes to all awaiting GCSE results
#41835 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.
#41836 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?
#41837 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!
#41838 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
#41839 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?
#41840 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!
#41841 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?
#41842 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!
#41843 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?
#41844 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.
#41845 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
#41846 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?
#41847 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!
#41848 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, _____
#41849 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?
#41850 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-12 23:44:28
d/dx (logx) = 1/x and ∫(1/x)dx = logx