Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Ok,
We can get very close answers using that formula, cool!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hopefully, it depends on how well the numerical quadrature approximated the area under the curve.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

For CCP, it may be sufficiently accurate since the curve lies in the same quadrant and uniform from 0 to infinity.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

For any curve to be well approximated by numerical integration.

1) It must have no singularities in the first or second or greater derivatives.

2) It must be well approximated by a polynomial. If the curve goes vertical or horizontal then a polynomial fit will not be accurate and numerical integration will struggle.

3) The function must not oscillate.

4) The function must be numerically stable.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

Thanks for the points.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

New problem!

B and E are out for their daily runs. There is a tree that is 2100 feet directly ahead of B, and another tree that is 4200 feet directly ahead of B at point A. E is at point J and is x feet directly ahead of B, but E has not yet reached either tree. They both run at a constant rate of an integral number of feet per minute. When running at their constant rates, each can run a mile in more than 5 minutes but less than 5.5 minutes. E's constant rate is 50 feet more per minute than B's constant rate. If both are travelling at their constant rates, E will reach point A at exactly the same time that B will reach point J. Find the number of feet in E's constant rate of feet per minute.

And one more thing x is an integer.

A says) Quite impossible. That x is an integer kills the whole problem. That just can not have a soultion.

B says) I can not say. I was one of the runners so I know the answer.

C says) A is right of course!

D says) I got it!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: What do you think?

This page was very helpful - http://www.mathsisfun.com/numbers/factors-all-tool.html

Last edited by 123ronnie321 (2011-04-17 04:46:18)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi 123ronnie321;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hello gAr;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Thank you!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

New problem!

E has a problem. She knows that there is at least one expert on generating functions among our experts. She wants to stump him. She asks the following question.

How many ways can I make 1 000 000 using an unlimited supply of 1's, 5's, 10's, 100's and 1000's ? I will accept the best answer.

A says) ≈ 8451977304243061 ways
B says) ≈ 8351911304663031 ways
C says) ≈ 8306381904125731 ways
D says) ≈ 8656883517002232 ways

After looking at the answers E was forced to accept one. Which one?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

The Graham, Patashnik, Knuth book? What pages?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Yes.
2nd edition, page 358, example 4.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Your answer is not exactly what B has because B's is an asymptotic approximation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Yeah, saw that approximation sign.
But how did B get that?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi gAr;

It will take a little time for me to catch up I am still looking at your solution.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Okay.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Hi;

That page is badly damaged on mine so I am looking around.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Hi bobbym,

That's bad. I'll try to explain if you can't get a copy.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

I am looking at my brothers copy and I can at least read this one but I have to ask a question.

How the heck did you get those coefficients?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Well, I followed those clever authors. Answering that means explaining the whole stuff!
Is your brother's copy good?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What do you think?

Yes, but I still do not get it. I think you used A(z)?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: What do you think?

Yes, from A(z).

Did you expand A(z)?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."