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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

That's right, very good!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

If some polynomial is divided by ( x- 9 ) the remainder is 10. When it is divided by ( x+ 6 ) the remainder is 4. When it is divided by ( 3 x - 4 ) it has a remainder of 12. What is the polynomial?

When you divide your answer by (x-9) what do you get for a remainder? Is it 10?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

bobbym wrote:

When you divide your answer by (x-9) what do you get for a remainder? Is it 10?

I think so

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi;

That is not the correct way to divide the 2 polys. MIF has a good page on it. Take a look and I will help you if you get stuck. Work your way to this answer.

(x^2 + 27x + 22) / (x - 9 ) = x + 36 with a remainder of 346

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Aah, I see.

I never learnt about dividing polynomials. Anyway, I worked my way to your answer with MIF's help.

Looks like I didn't interpret "remainder" correctly as applied to polynomial division...although I think it stands up mathematically when applying x = 30 to my polynomial and the divisors.

MIF says: "just put the remainder divided by the bottom polynomial as part of the answer", and so my answer becomes x + 36 + 346/(x-9).

For x = 30, 346/(x-9) is 16 remainder 10, and so still agrees with my misinterpreted understanding of "remainder".

That puts a whole new light onto your problem. Not sure if I can manage to solve it now.

*Last edited by phrontister (2010-04-26 11:09:30)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi phrontister;

Here is the solution to the polynomial problem. You will see that it requires no more math than you already know. I will steer clear of fancy jargon and leave only the barebones.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Thanks for that solution. I'd thought of applying those divisors to the same dividend, but couldn't progress beyond that thought.

I haven't grasped it fully yet, but will try to do that later.

I came home from work early to try to catch up on some paperwork, but the lure of MIF is eating into my productivity time!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi phrontister;

Glad to help.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

bobbym wrote:

You will see that it requires no more math than you already know.

That should read, "You will see that it requires no more math than you once knew"...although I don't recall ever learning about the Division Algorithm.

Is there a page about the D.A. on MIF? I couldn't find it. Wikipedia covers it, so I'm looking at it over there. But I prefer MIF's explanations as they're more suited to know-nothings like me.

So I haven't got terribly far with your solution just yet...stuck already after just four words into it!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi phrontister;

Try this:

http://www.mathsisfun.com/algebra/polyn … actor.html

Post where you are having a problem, I will try to help. If I can't there are others here who are stronger than I on this subject, they will help.

Hint: Don't let a little piece of wording stop you. Skip over it if necessary, but learn the method. This way you can solve a similiar problem. Later on you can come back and pound out the definitions. You don't have to totally understand something to use it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Thanks, Bobby. Looks like that page will help. I wasn't totally daunted by not understanding the D.A. and would have skipped it and tracked back if there was no choice, but I thought I'd at least have a bit of a go at tackling this from the ground up if it wasn't going to make life too difficult.

Bed...early start in the morning.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi phrontister;

Okay, Wikipedia is either good or terrible. It is typically only for people that already understand the particular material. We will pick it up when you get back.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

bobbym wrote:

and try to get it into this form:

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi ZHero;

First 2 steps are fine; Since the question wants the moves rather than the answer to the integral can you please expand line 2 to 3 and the next one a little bit more.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi;

prob 45

Borrowed this from another site.

This one should get 3913 replies to it all of them correct.

A survey asked 650 runners which marathons they had run in the past year. The results were:

340 NY Marathon

400 Boston Marathon

300 SS Marathon

140 NY and Boston

90 NY and SS

240 Boston and SS

50 Boston and NY and SS

How many of the runners surveyed didn't run in any of these three marathons?

If you get the same answer I did you better recheck you work.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

*Last edited by ZHero (2010-05-01 01:59:18)*

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

That's Correct! Good, but please hide your answer, I am expecting hundreds of replies. Okay, dozens of replies...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

prob 46

A factory is determining how much to charge for a dinner. Each month it produces 78 dinners for sale. The factory figures that charging x pounds for the dinners, the sales will be 78-3x dinners. At the months end, unsold dinners will be bought back at regular price by the factory.What price x should the factory charge for the dinners so they can maximize profit?

B says)

I am assuming regular price is x.

Factory profit is:

P = x ( 78 - 3x ) - 3 x^2

Which gives a maximum at 6.5. Since they cannot sell 6.5 dinners the maximum occurs when x = 6 or x = 7 then their profit will be 252 pounds.

A says) B is wrong, the answer is x = 13.

What do you like?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi;

prob 47

A number is picked randomly from the Fibonacci numbers. What is the probability that it is divisible by 63 and not by 17?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

Hey bobbym!

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi ZHero;

That's why I phrased it like that. I think as it stands the question is ambiguous as to what the cost function is. But I prefer B's answer. I think the original question is somewhat clearer than my rendition and favors B's viewpoint.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

Hey.. bobbym!!

bobbym wrote:

At the months end, unsold dinners

will be bought backat regular price by the factory.

so the factory **must have first sold it** for x. I mean, u cannot buy back without selling it first.. right?

and thus B is wrong in subtracting 3x[sup]2[/sup]?

If two or more thoughts intersect with each other, then there has to be a point.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,459

Hi;

Nope.

At the months end, unsold dinners will be bought back at regular price by the factory

Since the factory manufactured them this implies a loss of some amount when they don't sell the product. B assumes a loss of x dollars as he states, his solution is based on that assumption. If their is no loss on each product then there is no maximum. Since the question does not indicate what the loss is, it is not possible to determine a maximum price.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

bobbym wrote:

Since the factory manufactured them this implies a loss of some amount when they don't sell the product. B assumes a loss of x dollars as he states, his solution is based on that assumption.

If their is no loss on each product then there is no maximum.Since the question does not indicate what the loss is, it is not possible to determine a maximum price.

The profit is "Maximized or Minimized" depending upon the "No. of Dinners sold" which is "Dependent upon the price x".

If you sell dinner at price 2, then the profit is P[sub]2[/sub] = 2*(78-3*2)=144.

If you sell it at 10, then the profit is P[sub]10[/sub] = 10*(78-3*10)=480. (P

If you sell it at price 5, then the profit is P[sub]5[/sub] = 5*(78-3*5)=315.

If you sell it at price 15, then the profit is P[sub]16[/sub] = 16*(78-3*16)=480.

hence.. P[sub]2[/sub]<P[sub]10[/sub], P[sub]5[/sub]<P[sub]10[/sub], P[sub]10[/sub]=P[sub]16[/sub] and so on.

thus... Different prices offer different profits to the factory **(even though there is no loss on the products)**!

this is coz **the profit decreases with an increase in the price!!!**

B is wrong if he thinks that the unsold dinners are a loss...

Its a typical case where there's no question of loss but of profit only!

Q: You and I buy a slice of Cheese each at $10. I sell it for $100 and you sell it for $50 only.

Wud you say you made a profit of $(50-10)=$40 or a loss of $(100-50)=$50 (had you sold it for $100)??

see the difference.....?

If two or more thoughts intersect with each other, then there has to be a point.

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