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#43601 Re: Help Me ! » Parallelograms » 2005-08-29 20:16:57
In a parallelogram,
opposite sides are parallel, and equal; opposite angles are equal, and the diagonals (lines inside that intersect) bisect each other.
When you know the length of the diagonals, half of them would be the sides of a traingle they form with one of the sides of the parallelogram.
Use the theorems that (i) when two lines intersect each other, the vertically opposite angles are equal and (ii) sum of the total angles is equal to 360 degrees. This way, all the angles can be known.
Now, use the Cosine Theorem
a² = b² + c² - 2bcCosA
(where A, B, C are three angles of a traingle and a,b,c are the three sides opposite to angles A,B,C respectively)
for knowing the third side of the triangle, which forms a side of the parallelogram. Following this method, the adjacent side too can be found! Since opposite sides of a parallelogram are equal, we know all the four sides!
I know this reply is long, and may not be of much help; that's because some Mathematical problems are difficult to explain without a diagram!
#43602 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-29 20:03:52
Solution to problem#k+3 : kylekatarn is correct.
Problem # k+5
Use each digit 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 exactly once to form two five-digit numbers that when multiplied produce the largest quantity.
#43603 Re: Introductions » Winter Lover » 2005-08-29 16:07:01
Welcome to the forum, John!
Your posts and replies are interesting, keep posting 
#43604 Re: Help Me ! » Intergration Rock Solid!!! Please Help Asap.. » 2005-08-28 20:09:03
Flowers4Carlos, tahnk you for solving the problem.
The steps are easy to understand. Keep up the good work!
#43605 Re: Jokes » Mathematics jokes » 2005-08-28 16:11:55
Thanks Rora, we miss you in this forum!
#43606 Re: Introductions » hiii... » 2005-08-28 16:10:53
Sometimes, it is spelt Djakarta!
#43607 Re: This is Cool » I'm cracking up » 2005-08-27 17:44:06
Mikau, Ahgua.....I am sorry, yesterday, when I was
trying to copy the diagram, I saw two same posts
(maybe, I thought I saw) of the diagram, to simplify,
I tried to delete one, and the entire post and got deleted.
I shall be much much more careful in the future,
and thanks for posting it before I requested you!
Nice question, brilliant reasoning.
#43608 Jokes » Mathematics jokes » 2005-08-26 19:09:21
- Jai Ganesh
- Replies: 279
How do you prove in three steps that a sheet of paper is a lazy dog?
1. A sheet of paper is an ink-lined plane.
2. An inclined plane is a slope up.
3. A slow pup is a lazy dog.
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.
Philosophy is a game with objectives and no rules.
Mathematics is a game with rules and no objectives.
How many mathematical logicians does it take to replace a lightbulb?
None: They can't do it, but they can prove that it can be done.
#43609 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-08-26 18:39:59
Problem #k+4
A polyhedron has 12 faces(sides) and 18 edges. How many vertices does it have?
#43610 Re: Guestbook » cool stuff » 2005-08-26 18:25:16
Computer games, Internet, Coke, Beaches...
#43611 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
#43612 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.
#43613 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?
#43614 Re: Puzzles and Games » What next? » 2005-08-25 16:15:58
A, T, G, C..next comes L
Aries, Taurus, Gemini, Cancer,..Leo.
#43615 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.
#43616 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, _
#43617 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?
#43618 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?
#43619 Re: Dark Discussions at Cafe Infinity » Wink Murder 3 » 2005-08-23 21:14:05
Good wishes to all awaiting GCSE results
#43620 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.
#43621 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?
#43622 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!
#43623 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
#43624 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?
#43625 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!