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#1 2013-05-22 13:10:18

BarandaMan
Guest

Rearranging Urgent Help!!

Hi,

I have spent SO long on this problem, so much so that it is now 4.04am here in the UK.

I will post the problem, it is not too hard I have been told, I just cannot rearrange it to get the given solution. Please could someone help me?

Here is the picture of the problem that needs to be rearranged (left hand side) and on the right hand side, the eventual answer.

tinypic.com/view.php?pic=bg49hu&s=5

The methods I have tried are:

1. Dividing everything by (Pi/P)^-n
2. Multiplying everything by (Pi/P)^n+1

Please please help me!

#2 2013-05-22 13:13:14

bobbym
Administrator

Offline

Re: Rearranging Urgent Help!!

Hi;

I do remember doing this type problem with you before.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-05-22 13:19:28

BarandaMan
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

I do remember doing this type problem with you before.

Hello!

I still do not understand it and finals are coming up on Thursday so I am trying it again, but I stll have no idea...sad

#4 2013-05-22 13:44:51

BarandaMan
Guest

Re: Rearranging Urgent Help!!

But those two methods are meant to work, or one of them should definitely work, but i always get to a penultimate stage and cannot get further...

#5 2013-05-22 18:31:23

bobbym
Administrator

Offline

Re: Rearranging Urgent Help!!

Hi;

Is that a y after the (Pi - w)? And what is the power of the first term, -n?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-05-22 18:36:34

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

Is that a y after the (Pi - w)? And what is the power of the first term, -n?

Hi bobby!
No that is as n, the same symbol as the power of the first term, which yes is -n,

then the second term is to the power of -n-1.

#7 2013-05-22 18:46:11

bobbym
Administrator

Offline

Re: Rearranging Urgent Help!!

Hi;

This is what we have:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#8 2013-05-22 19:04:20

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

This is what we have:

Yes! That is exactly what we have at this moment.

#9 2013-05-22 19:07:46

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Hi;

There was one mistake in the way my program did the latexing. This is what you want



one more thing, that Pi is π?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10 2013-05-22 19:18:17

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

There was one mistake in the way my program did the latexing. This is what you want



one more thing, that Pi is π?

I do apologise for not stating that. That Pi is not actually the greek symbol, it denotes the price level for individual goods (whereas P alone represents the overall price level). big_smile

#11 2013-05-22 19:41:14

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Hi;

2. Multiplying everything by (Pi/P)^(n+1)

That is the correct move.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#12 2013-05-22 19:51:35

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

2. Multiplying everything by (Pi/P)^(n+1)

That is the correct move.

Thank you,

When I divide the first term by it, it becomes simply (Pi/P).
When I divide the second term by it, it becomes:   -((Pi-w)n)/P
So (Pi/P) -((Pi-w)n)/P = 0
So (Pi/P) = (nPi/P) (nw/P)
This is where I really do not know how to get this into the correct answer:
(Pi/P)sadW/P)*(n/n-1)

Could you please see where I have gone wrong / how I can continue? Thank you so much

#13 2013-05-22 19:58:39

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Hi;

When I divide the first term by it, it becomes simply (Pi/P).
When I divide the second term by it, it becomes:   -((Pi-w)n)/P

You mean multiply instead of divide, and you are correct up to there.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-05-22 20:14:32

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hi;

When I divide the first term by it, it becomes simply (Pi/P).
When I divide the second term by it, it becomes:   -((Pi-w)n)/P

You mean multiply instead of divide, and you are correct up to there.

Yes, sorry again. I do mean multiply.

What have I done wrong after? I really do not know what is going on, I have spent hours here.

Alternatively I try multiplying the P across from this step: So (Pi/P) -((Pi-w)n)/P = 0

To get Pi - (Pi-w)/n = 0. Then it leads to the same thing, as I divide by P later to try to get the Pi/P expression. These two ways seem equivalent.

#15 2013-05-22 20:23:19

bobbym
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Re: Rearranging Urgent Help!!

Hold on you are going to fast. After the multiplication of the two terms you should have:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#16 2013-05-22 20:26:55

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Hold on you are going to fast. After the multiplication of the two terms you should have:

Yes, I have this!

#17 2013-05-22 20:28:54

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Remember that has a zero on the right so it is really:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#18 2013-05-22 20:30:49

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

Remember that has a zero on the right so it is really:

Yes! So we can multiply across to rid the P, but then we need to divide again by P to get the required expressions? So there is no need multiplying across?

#19 2013-05-22 20:35:15

bobbym
Administrator

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Re: Rearranging Urgent Help!!

No,  do not multiply by the P. Instead split the fraction up like this:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#20 2013-05-22 20:41:32

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:

No,  do not multiply by the P. Instead split the fraction up like this:

Ok thank you, I have now done that. The only next step I can see is to write (nw/P) + (Pi(1-n)/P)=0.

Then I am stuck again. I am really sorry I am not getting this faster I do apologise

#21 2013-05-22 20:46:11

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Hi;

Everything is going fine.

These are the two steps so far:



becomes


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#22 2013-05-22 20:47:45

barandaman
Guest

Re: Rearranging Urgent Help!!

Yes, that is where I am at. At the latter stage, I really have no idea what to do. I tried working backwards from the eventual solution but I can still not see a link.

#23 2013-05-22 20:51:56

bobbym
Administrator

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Re: Rearranging Urgent Help!!




In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#24 2013-05-22 20:56:47

barandaman
Guest

Re: Rearranging Urgent Help!!

bobbym wrote:



Oh my  I think we are close.

So from there, I divide by -1 to get

-Pi(n-1)/P = nw/P

So -Pi/P = nw/(n-1)P, but there is a negative on the LHS which we do not want? big_smile

#25 2013-05-22 21:02:39

bobbym
Administrator

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Re: Rearranging Urgent Help!!

Hi;

We are getting there just a few more steps:





Divide both sides by (1-n)





Now you use the identity:







We are done!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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