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

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

*Last edited by ShivamS (2014-08-26 03:00:45)*

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1.

'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: 86,481

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

bobbym wrote:

Hi;

That is correct.

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By the way, the constants are not unique.

Is the solution for 1 wrong?

'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: 86,481

Can you show another pair?

**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

Agnishom wrote:

By the way, the constants are not unique.

Is the solution for 1 wrong?

Your first equation is correct, but not the second one.

The constants are unique, as bobbym showed.

*Last edited by ShivamS (2014-05-01 01:29:40)*

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

*Last edited by ShivamS (2014-05-01 01:48:21)*

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You are correct. Sorry

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

anonimnystefy wrote:

Hi ShivamS

Both are correct.

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

3. Let E be an even function and O be an odd function. Determine the symmetry, if any, of E ∘ O.

*Last edited by ShivamS (2014-05-01 07:39:06)*

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

Full Solutions with explanation:

1. Find the general formula for all solutions of 2 cos x + 1 = 0

2. Find the constants b and c in the polynomial p(x) = x^2 + bx + c such that

. Are the constants unique?I'll add all the problems and full solutions in the first post too.

*Last edited by ShivamS (2014-05-01 07:52:09)*

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ShivamS wrote:

3. Let E be an even function and O be an odd function. Determine the symmetry, if any, of E ∘ O.

What does That mean?

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

Hi ShivamS

*Last edited by anonimnystefy (2014-05-01 22:14:09)*

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

Agnishom wrote:

ShivamS wrote:3. Let E be an even function and O be an odd function. Determine the symmetry, if any, of E ∘ O.

What does That mean?

Which part do you not understand?

anonimnystefy wrote:

Hi ShivamS

That is correct.

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What does the notation E ∘ O mean?

'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: 86,481

That is a composition of functions.

**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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Is it Kaboobly Doo?

'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: 86,481

Heavens no! It is quite useful. There are practical applications for it.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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The URL contains the string 'sets'

'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: 86,481

Have you been there yet?

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

Set theory is introduced in India in grade 11 and the Indian government controlling education is smart, so they introduce functions (and therefore inverse functions, composition etc) after set theory in grade 11. I believe it is the first unit in grade 11, so Agnishom will be able to solve that problem soon.

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Yes, bobbym has taken up the math teacher post in our school.

'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: 86,481

Yes, I have and I am a tough marker.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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