Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Is this you?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Hmmm

It also has a sharpened head.

*Last edited by Agnishom (2014-05-04 01:39:48)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

That is not me.

**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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

4. Use Lagrange Multipliers to find the minimum value of

that lie on the hyperbola .Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Agnishom wrote:

What does the notation E ∘ O mean?

The composition of f(x) and g(x) is f(g(x)). In other words, compositions are evaluated by plugging the second function listed into the first function listed. Note as well that order is important here. Interchanging the order will usually result in a different answer.

*Last edited by ShivamS (2014-05-05 23:28:58)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,376

Hi;

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi ShivamS

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

"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."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

bobbym wrote:

Hi;

anonimnystefy wrote:

Hi ShivamS

gAr wrote:

Hi,

All are correct!

This was a nice problem when I first solved it a couple of years/months ago, but I remember that when I drew the picture I had the wrong answer.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

5. Let the curve C be given by

between . Calculate*Last edited by ShivamS (2014-05-23 11:33:31)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi ShivamS

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**zetafunc****Member**- Registered: 2014-05-21
- Posts: 87

*Last edited by zetafunc (2014-05-21 21:20:46)*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Hi zetafunc;

That is correct!

Hi Stefy;

I think you perhaps didn't understand the problem, because we are getting different answers and mine agrees with zetafunc's.

I'm searching for a good problem from my database, but I am mostly finding routine ones (I forgot to sort routine and difficult problems on the set of problems I am looking at).

Here is a problem with OK difficulty:

6. A right circular cone is inscribed inside a larger right circular cone with a volume of 180 cm^3. The axes of the cones coincide and the vertex of the inner cone touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the inner cone volume.

*Last edited by ShivamS (2014-05-23 11:32:49)*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Reposting question 6 from last post with new problem.

6. A right circular cone is inscribed inside a larger right circular cone with a volume of 180 cm^3. The axes of the cones coincide and the vertex of the inner cone touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the inner cone volume.

7. Prove or disprove the following statement

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi Shivam

Here lies the reader who will never open this book. He is forever dead.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

anonimnystefy wrote:

Hi Shivam

Great!

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**Olinguito****Member**- Registered: 2014-08-12
- Posts: 320

ShivamS wrote:

7. Prove or disprove the following statement

*Last edited by Olinguito (2014-08-25 23:09:13)*

*Bassaricyon neblina*

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

8.

*Last edited by ShivamS (2014-08-26 03:03:48)*

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