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## #376 2006-01-10 21:58:32

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Probelm # k + 85

If u and v are the roots of the equation x² + ax + b = 0, what are roots of the equation x² -ax + b = 0?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #377 2006-01-11 03:02:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

That's an interesting one. I think it's something like this:

Why did the vector cross the road?
It wanted to be normal.

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## #378 2006-01-11 04:16:41

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

I'm not sure, this is what I get:

Last edited by Ricky (2006-01-11 04:16:58)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #379 2006-01-11 05:09:16

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

I think our answers are the same, and I've just taken a long way round.

Why did the vector cross the road?
It wanted to be normal.

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## #380 2006-01-11 08:34:24

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

Yea, I guess they are.  They looked completely different at first glance.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #381 2006-01-11 11:32:20

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #382 2006-01-14 03:44:50

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #383 2006-01-14 06:33:56

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #384 2006-01-14 08:12:05

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #385 2006-01-14 12:15:28

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Problems and Solutions

darn that k+42, I just cant figure it.  Please someone, put me out of my misery.  I think that you have to incorporate a geometric series somehow, but everything that I try turns to nonsense.

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## #386 2006-01-14 12:47:28

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

Yes, k+42 is an incredibly difficult one. I think it could probably be solved brutally by getting excel to do all the calculations for you, but it's still tough.

Also, I think your answer to k+40 is wrong. I remember it being much smaller.

Why did the vector cross the road?
It wanted to be normal.

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## #387 2006-01-14 16:12:47

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Problems and Solutions

I didn't check if this one has already been solved, but since irspow asked about it, I gave it a go.

Last edited by ryos (2006-01-14 16:15:25)

El que pega primero pega dos veces.

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## #388 2006-01-14 17:13:17

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Four   days Pongal  break, and so  many solutions posted! I  shall reply to all of them after I return from Holiday on  Jan 16. mathsyperson is right, irspow's solution to problem # k + 40 isn't correct. It is much smaller. . Same about ryos' solution to problem # k + 42.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #389 2006-01-15 17:02:39

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

irspow's solution to Problem # k + 59 is correct. I shall wait for some more time before posting the solutions to unanswered problems.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #390 2006-01-15 17:11:31

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Problem # k + 86

Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively. How many boys are studying Science?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #391 2006-01-15 17:42:03

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Excellent, irspow's solution to problem # k + 48 is correct too!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #392 2006-01-16 10:19:05

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #393 2006-01-16 19:36:28

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Well done, irspow

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #394 2006-02-14 02:08:05

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Problem # k + 87

Prove that there exists atleast one multiple of 5 between 10^k and 10^k+1 where k is a Natural number.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #395 2006-02-14 02:42:22

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Problems and Solutions

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #396 2006-02-14 19:18:31

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

I made a mistake while posting problem # k + 87.
The problem should have read 'Prove that there exists atleast one power of 5 between 10^k and 10^k+1 where k is a Natural number.

Problem # k + 88

Show that the sum of any number of terms of the series
1/1*2, 1/2*3, 1/3*4, 1/4*5, 1/5*6,................ is less than 1.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #397 2006-02-15 03:11:01

ganesh
Registered: 2005-06-28
Posts: 23,216

### Re: Problems and Solutions

Problem # k + 89

In a bolt factory, machines A, B, and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random. If the bolt drawn is found to be defective, what is the probability that it is manufactured by machine B?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #398 2006-02-15 06:12:39

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Problems and Solutions

igloo myrtilles fourmis

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## #399 2006-02-15 09:10:32

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Problems and Solutions

ganesh wrote:

I made a mistake while posting problem # k + 87.
The problem should have read 'Prove that there exists atleast one power of 5 between 10^k and 10^k+1 where k is a Natural number.

Ah. That makes more sense. I thought there was a mistake somewhere because as it was, the proof was really obvious, so it didn't seem sensible.

I've got a vague idea for k+88, but I'll wait for it to mature a bit more before posting it.

Why did the vector cross the road?
It wanted to be normal.

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## #400 2006-02-15 11:45:49

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Problems and Solutions

Last edited by irspow (2006-02-15 11:49:14)

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