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#51 2009-01-07 18:02:58
- Jai Ganesh
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Re: 5 Star Questions
Answer to #24:-
You're right, JaneFairfax!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#52 2009-01-07 18:14:48
- Jai Ganesh
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Re: 5 Star Questions
#26. What is the value of
#27. What is the value of log tan1° + log tan2° + log tan3° + log tan4° + ....log tan 89°
#28. What is the value of
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#53 2009-01-07 20:05:23
- Jai Ganesh
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Re: 5 Star Questions
#29. Decompose into partial fractions:-
.#30. If p and q are the roots of the equation x²+8x = -15, form the equation whose roots are (p+q) and 3pq.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#54 2009-01-08 01:51:47
- JaneFairfax
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Re: 5 Star Questions
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#55 2009-01-08 02:22:14
- Jai Ganesh
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Re: 5 Star Questions
Answer to #30:-
Excellent, JaneFairfax! You're right again!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#56 2009-01-08 02:26:23
- Jai Ganesh
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Re: 5 Star Questions
JaneFairfax,
Did you see the solution to Problem #17? (Post #49 on Page 2)
Do you agree with my answer?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#57 2009-01-08 02:42:31
- mathsyperson
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Re: 5 Star Questions
When you worked out the area of the parallelogram, you use its slant height instead of its perpendicular height and so your answer is larger than the actual area.
I get the area of the trapezium to be the same as Jane's 3rd attempt.
Why did the vector cross the road?
It wanted to be normal.
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#58 2009-01-08 02:55:54
- Jai Ganesh
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Re: 5 Star Questions
Oops!
That was a stupid mistake!
Thanks, mathsyperson, for correcting me!
I am sorry Jane, I said your last attempt was wrong too!
I shall be more careful while checking the answers!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#59 2009-01-08 03:14:00
- JaneFairfax
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Re: 5 Star Questions
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#60 2009-01-08 17:03:25
- Jai Ganesh
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Re: 5 Star Questions
Answer to #27:-
Absolutely right, JaneFairfax!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#61 2009-01-09 01:41:17
- Jai Ganesh
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Re: 5 Star Questions
#31. A person covers the distance from P to Q at the speed of 3 kilometers per hour. From Q to P, he covers the distance at 6 kilometers per hour. What is the average speed per hour?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#62 2009-01-09 08:50:00
- JaneFairfax
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Re: 5 Star Questions
Last edited by JaneFairfax (2009-01-09 08:52:38)
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#63 2009-01-09 17:59:25
- Jai Ganesh
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Re: 5 Star Questions
Answer to #31:-
You are correct, JaneFairfax!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#64 2009-01-10 03:30:40
- Jai Ganesh
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Re: 5 Star Questions
#32. Find the value of
#33. Find the value of x if
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#65 2009-01-10 03:46:16
- JaneFairfax
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Re: 5 Star Questions
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#66 2009-01-10 17:22:17
- Jai Ganesh
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Re: 5 Star Questions
Answer to #33:-
You are correct, JaneFairfax!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#67 2009-01-10 18:06:55
- Jai Ganesh
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Re: 5 Star Questions
#34. Which is the largest number each number of the sequence is divisible by?
Why?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#68 2009-01-10 23:35:09
- JaneFairfax
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Re: 5 Star Questions
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#69 2009-01-11 00:12:32
- Jai Ganesh
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Re: 5 Star Questions
Answer to #34:
(1) The question has been modified. I didn't notice what meaning the question conveyed while posting, sorry!
(2) I have a proof that every number of the form
I wanted to know if I am right.
This product is certainly divisible by 6.
For proving that is always divisible by 5, I use this logic.
Last digit of
0 0
1 1
2 6
3 1
4 6
5 5
6 6
7 1
8 6
9 1
It can be seen that the last digit of
is always 0 or 5, which means it is a multiple of 5.I hope my reasoning is acceptable!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#70 2009-01-11 01:03:03
- JaneFairfax
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Re: 5 Star Questions
For proving that
is always divisible by 5
NO!! If is divisible by 5 then is NOT difvisible by 5.
You do it this way.
Either
or .If
then clearly .If
, then by Fermats little theorem.In that case,
.Hence
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#71 2009-01-11 01:10:35
- Jai Ganesh
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Re: 5 Star Questions
Thanks, JaneFairfax!
That has made things a lot more clearer to me! 
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#72 2009-01-11 01:49:33
- Jai Ganesh
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Re: 5 Star Questions
#35. What is the value of xyz if
#36. What is the value of z if
and.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#73 2009-01-11 12:24:18
- JaneFairfax
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Re: 5 Star Questions
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#74 2009-01-11 20:52:19
- Jai Ganesh
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Re: 5 Star Questions
Answer to #35:-
You are correct, JaneFairfax!
Your point is fully acceptable.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#75 2009-01-11 20:59:57
- Jai Ganesh
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Re: 5 Star Questions
To JaneFairfax:
It occured to me that, as mentioned by you in post #70, if n is a multiple of of 5,
That isn't going to affect the proof.
The idea is to prove that is divisible by 30, hence, if isn't divisible by 5, n would be. We already know that
is divisible by 2 and 3 (because (n-1)(n)(n+1) is a factor). Now that is has been shown that it is also divisible by 5, can we say decisively that a number of the form (n>0, n is a Natural number)
is divisible by 30 with the help of posts #69 and #75 alone, without the help of Fermat's little theorem?
Am I right?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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