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#43476 Re: Puzzles and Games » Math Equation Mind Bender » 2005-10-21 22:37:08

I tried many combinations, finally got it. I first drew the conclusion that 3/4 should figure in the denominator. Thereafter, it was juggling with numbers.
I think the problem has a unique solution. Mathsy beat me, but I should say, it didn't take more than 10 minutes! (There was a gap of more than 90 minutes between my first and second periods of five minutes)  smile

#43477 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-21 15:55:34

Problem # k + 34

Two numbers when divided by a certain divisor leave remainders of 431 and 379 respectively. When the sum of these two numbers is divided by the same divisor, the remainder is 211. What is the divisor?

#43478 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-21 15:50:14

Problem # k + 33

What are the values of M and N if M39048458N is divisible by 8 & 11 where M & N are single digit whole numbers?

#43481 Re: Dark Discussions at Cafe Infinity » Wink Murder 5 » 2005-10-17 16:18:50

Sorry, not playing this time. Too busy with work.

#43483 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-16 16:11:36

Solution to Problem # k + 32

x³ = 1
x³ - 1 = 0
(x - 1)(x²+x+1)=0
x = 1 or (x²+x+1)=0
Solving the second equation, we get
x = (-1 ± √3i)/2
Hence, the cube roots of 1 are
1, (-1 - √3i)/2, (-1 + √3i)/2

It can be shown that the three are in Geometic progression with common ratio r= (-1 - √3i)/2
When (-1 - √3i)/2 is multiplied by itself, we get (-1 + √3i)/2
quod erat faciendum

#43484 Re: Jokes » Limericks » 2005-10-16 15:58:09

Insomnia is a new mod
With  the blessings of Rod....

#43485 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-15 17:20:19

Problem # k + 32

Show that the three cube roots of 1 are in Geometric Progression.

#43486 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-15 17:13:49

Problem # k + 31

From a lot of 10 items, of which three are defective, a sample of four is drawn. Which of these is most likely and what is the probability?
(a) One defective item is drawn
(b) Two defective items are drawn
(c) Three defective items are drawn
(d) No defective item is drawn

#43487 Re: Dark Discussions at Cafe Infinity » Random Words » 2005-10-15 17:04:48

Buckminsterfullerene

The name of C60 molecule

#43488 Re: Guestbook » Austraila » 2005-10-15 16:59:14

I come to Australia's rescue....because we are all from Gondwanaland...
Australia isn't really isolated....the only isolated placed in the world is Tristan Da Cunha island.

#43489 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-15 00:01:38

You are right, Mathsy.
For k + 28, you may not require too many words, just mathematical expressions. I know you can do it. To attempt or not is your decision.I shall post the solution soon.

#43490 Re: Help Me ! » Depth in Calculus » 2005-10-14 18:28:15

OMG...
I forgot to square 5/12.
Thats right, I hadn't checked for calculation erros.
Heisenberg's Uncertainity Principle:-
You cannot work at your 100% speed with 100% accuracy smile

#43491 Jokes » More mathematics stuff » 2005-10-14 18:05:46

Jai Ganesh
Replies: 1

1. There were two men trying to decide what to do for a living. They went to see a counselor, and he decided that they had good problem solving skills.
He tried a test to narrow the area of specialty. He put each man in a room with a stove, a table, and a pot of water on the table. He said "Boil the water". Both men moved the pot from the table to the stove and turned on the burner to boil the water. Next, he put them into a room with a stove, a table, and a pot of water on the floor. Again, he said "Boil the water". The first man put the pot on the stove and turned on the burner. The counselor told him to be an Engineer, because he could solve each problem individually. The second man moved the pot from the floor to the table, and then moved the pot from the table to the stove and turned on the burner. The counselor told him to be a mathematician because he reduced the problem to a previously solved problem. 
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2. A somewhat advanced society has figured how to package basic knowledge in pill form.
A student, needing some learning, goes to the pharmacy and asks what kind of knowledge pills are available. The pharmacist says "Here's a pill for English literature." The student takes the pill and swallows it and has new knowledge about English literature!

"What else do you have?" asks the student.

"Well, I have pills for art history, biology, and world history," replies the pharmacist.

The student asks for these, and swallows them and has new knowledge about those subjects.

Then the student asks, "Do you have a pill for math?"

The pharmacist says "Wait just a moment", and goes back into the storeroom and brings back a whopper of a pill and plunks it on the counter.

"I have to take that huge pill for math?" inquires the student.

The pharmacist replied "Well, you know math always was a little hard to swallow." 
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3. A Mathemetician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture.
E says "How do you understand this stuff?"
M: "I just visualize the process"
E: "How can you POSSIBLY visualize somrthing that occurs in 9-dimensional space?"
M: "Easy, first visualize it in N-dimensional space, then let N go to 9"
--------------------------------------------------------------------------------------------------------------
4. There was once a very smart horse. Anything that was shown it, it mastered easily, until one day, its teachers tried to teach it about rectanguar coordinates and it couldn't understand them. All the horse's aquaintences and friends tried to figure out what was the matter and couldn't. Then a new guy (what the heck, a computer engineer) looked at the problem and said,
"Of course he can't do it. Why, you're putting Descartes before the horse!"

#43492 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-14 16:32:04

Problem # k + 30

If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

#43493 Re: Help Me ! » Depth in Calculus » 2005-10-14 16:28:29

Volume of the concial tank is 1/3*pi*r²*h
We know the diameter is 10 feet, therefore, radius is 5 feet.
The height is 12 feet, therefore radius is 5/12*h
V = 1/3*pi*(5/12 *h)²*h
V = 1/3*pi*5/12*h³
V = 5/36*pi*h³
dV/dt = 5/36*pi*3h² dh/dt
We know dV/dt=10 ft³/min
Therefore, when h=8,
10 = 5/12*pi*64*dh/dt
dh/dt = (10*12)/(5*pi*64)
dh/dt= 120/320*pi
dh/dt = 0.1194 ft
I haven't checked for calculation errors!

#43494 Re: Introductions » i hate subject fields. » 2005-10-13 22:39:23

I tried translating English to German, then German back to English. After three cycles, this is what I got. You can see how different, meaningless the passage is after the three cycles.


There is tremendous happiness in making others happy, despite our own situations. Shared grief is half the sorrow, but happiness when shared, is doubled. If you want to feel rich, just count all the things you have that money can't buy.

There is enormous luck, if one forms others lucky, despite our own situations.  Divided wrong is half ensures, but luck, if it is divided, is geverdoppelt.  If you liked to feel rich, straight lines counting pulse all things, which have you that money cannot buy.

There is enormous luck, if one forms lucky others, despite our own situations.  Divided wrongly half guarantees, but luck, if it is divided, is geverdoppelt.  If you hand counting pulse, straight straight lines to believe liked all things, which have you that money cannot buy.

There is enormous luck, if one forms lucky others, despite our own situations.  Divided one wrongly half warranties, but luck, if it is divided, is geverdoppelt.  If you hand counting pulse over, the straight straight straight lines liked all things, which have you to the faith that money cannot buy.

#43495 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-13 20:44:46

Excellent! I used a

method for finding the solution.
Well done,  you have made a great start!

#43496 Re: Help Me ! » Integration by substitution » 2005-10-13 19:02:47

A little further.....
(-1/6) ln( 1-2x^3 )=
ln[1/(1-2x^3)^1/6]
MathsIsFun had done it right, I posted this
.... just to complicate things big_smile

#43497 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-13 16:58:27

Problem # k + 29

If each interior angle of a regular polygon is 150 degrees, how many sides does it contain?

#43498 Re: Maths Teaching Resources » Basic Algebra for Form1 students in secondary schl » 2005-10-13 16:29:16

I was first taught the difference between variables and constants.
Thereafter, the lessons were on simple operations of addition, division, multpilication, subtraction, extracting roots, exponentiation etc.
The next step was solving linear equations in one variable, simultaneous equations of two, three variables. A little later I learnt solving quadratic equations and their properties. I forgot to mention, I was also taught plotting graphs and solving equations with graphs.
The Binomial theorem was the last I was taught, and Pascal's triangle too.

#43499 Re: Jokes » Proof :- e equal to one » 2005-10-13 16:12:34

You are right, this was a proof I found in a Mathematics Jokes page.
It is obviously faulty, and you have said where the error lies. I too had figured it out, but left it open for discussion.

#43500 Jokes » Proof :- e equal to one » 2005-10-13 00:06:08

Jai Ganesh
Replies: 4

Proof :- e equal to one
Theorem: e=1
Proof:
2*e = f
2^(2*pi*i) x e^(2*pi*i) = f^(2*pi*i)
We know e^(2*pi*i) = 1

Therefore:
2^(2*pi*i) = f^(2*pi*i)
2=f
Thus:
e=1

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