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#51 2009-01-07 18:02:58
- ganesh
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Re: 5 Star Questions
Answer to #24:-
You're right, JaneFairfax!
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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#52 2009-01-07 18:14:48
- 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 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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#53 2009-01-07 20:05:23
- 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 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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#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
- ganesh
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Re: 5 Star Questions
Answer to #30:-
Excellent, JaneFairfax! You're right again!
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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#56 2009-01-08 02:26:23
- 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 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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#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
- 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 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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#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
- ganesh
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Re: 5 Star Questions
Answer to #27:-
Absolutely right, JaneFairfax!
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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#61 2009-01-09 01:41:17
- 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 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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#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
- ganesh
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Re: 5 Star Questions
Answer to #31:-
You are correct, JaneFairfax!
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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#64 2009-01-10 03:30:40
- ganesh
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Re: 5 Star Questions
#32. Find the value of
#33. Find the value of x if
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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#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
- ganesh
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Re: 5 Star Questions
Answer to #33:-
You are correct, JaneFairfax!
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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#67 2009-01-10 18:06:55
- 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 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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#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
- 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 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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#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
- ganesh
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Re: 5 Star Questions
Thanks, JaneFairfax!
That has made things a lot more clearer to me! 
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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#72 2009-01-11 01:49:33
- 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 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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#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
- ganesh
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Re: 5 Star Questions
Answer to #35:-
You are correct, JaneFairfax!
Your point is fully acceptable.
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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#75 2009-01-11 20:59:57
- 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 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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