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#51 2009-01-07 18:02:58

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Answer to #24:-
You're right, JaneFairfax!
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Character is who you are when no one is looking.

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#52 2009-01-07 18:14:48

ganesh
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Registered: 2005-06-28
Posts: 14,462

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

?


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#53 2009-01-07 20:05:23

ganesh
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Posts: 14,462

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.


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#54 2009-01-08 01:51:47

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#55 2009-01-08 02:22:14

ganesh
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Posts: 14,462

Re: 5 Star Questions

Answer to #30:-
Excellent, JaneFairfax! You're right again!


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#56 2009-01-08 02:26:23

ganesh
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Registered: 2005-06-28
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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?


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#57 2009-01-08 02:42:31

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

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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Registered: 2005-06-28
Posts: 14,462

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!
ty8001.gif


Character is who you are when no one is looking.

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#59 2009-01-08 03:14:00

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#60 2009-01-08 17:03:25

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Answer to #27:-
Absolutely right, JaneFairfax!
fantastic3.jpg


Character is who you are when no one is looking.

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#61 2009-01-09 01:41:17

ganesh
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Posts: 14,462

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?


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#62 2009-01-09 08:50:00

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions

Last edited by JaneFairfax (2009-01-09 08:52:38)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#63 2009-01-09 17:59:25

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Answer to #31:-
You are correct, JaneFairfax!
outstanding1201.gif


Character is who you are when no one is looking.

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#64 2009-01-10 03:30:40

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

#32. Find the value of

.

#33. Find the value of x if

.


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#65 2009-01-10 03:46:16

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#66 2009-01-10 17:22:17

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Answer to #33:-
You are correct, JaneFairfax!
nicewrk1.jpg


Character is who you are when no one is looking.

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#67 2009-01-10 18:06:55

ganesh
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Registered: 2005-06-28
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Re: 5 Star Questions

#34. Which is the largest number each number of the sequence is divisible by?

?
Why?


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#68 2009-01-10 23:35:09

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#69 2009-01-11 00:12:32

ganesh
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Registered: 2005-06-28
Posts: 14,462

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

is divisible by 30.
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!


Character is who you are when no one is looking.

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#70 2009-01-11 01:03:03

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions

ganesh wrote:

For proving that

is always divisible by 5


NO!! If
is divisible by 5 then
is NOT difvisible by 5. shame

You do it this way.

Either

or
.

If

then clearly
.

If

, then
by Fermat’s little theorem.

In that case,

.

Hence

in every case.


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#71 2009-01-11 01:10:35

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Thanks, JaneFairfax!
That has made things a lot more clearer to me! smile


Character is who you are when no one is looking.

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#72 2009-01-11 01:49:33

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

#35. What is the value of xyz if

?

#36. What is the value of z if

and
.


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#73 2009-01-11 12:24:18

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: 5 Star Questions


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#74 2009-01-11 20:52:19

ganesh
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Registered: 2005-06-28
Posts: 14,462

Re: 5 Star Questions

Answer to #35:-
You are correct, JaneFairfax!
Your point is fully acceptable.

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Character is who you are when no one is looking.

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#75 2009-01-11 20:59:57

ganesh
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Registered: 2005-06-28
Posts: 14,462

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,

would not be divisible by 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? dunno


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