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

You are not logged in.

## #1 2014-04-30 09:45:49

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Easy Problems

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

Offline

## #2 2014-04-30 13:15:41

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #3 2014-04-30 15:46:46

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

Hi;

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

## #4 2014-05-01 00:27:17

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

bobbym wrote:

Hi;

That is correct.

Offline

## #5 2014-05-01 00:48:03

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #6 2014-05-01 01:24:54

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

Can you show another pair?

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

## #7 2014-05-01 01:29:10

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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)

Offline

## #8 2014-05-01 01:46:46

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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

Offline

## #9 2014-05-01 01:57:13

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #10 2014-05-01 06:47:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

### Re: Easy Problems

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
The knowledge of some things as a function of age is a delta function.

Offline

## #11 2014-05-01 07:29:36

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

anonimnystefy wrote:

Hi ShivamS

Both are correct.

Offline

## #12 2014-05-01 07:36:15

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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)

Offline

## #13 2014-05-01 07:49:15

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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)

Offline

## #14 2014-05-01 21:37:23

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

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?

'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #15 2014-05-01 22:13:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

### Re: Easy Problems

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
The knowledge of some things as a function of age is a delta function.

Offline

## #16 2014-05-02 00:26:08

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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.

Offline

## #17 2014-05-02 00:48:23

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

What does the notation  E ∘ O mean?

'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #18 2014-05-02 00:50:46

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

That is a composition of functions.

http://www.mathsisfun.com/sets/function … ition.html

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

## #19 2014-05-03 02:30:48

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

Is it Kaboobly Doo?

'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #20 2014-05-03 02:32:38

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

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

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

## #21 2014-05-03 02:33:52

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

The URL contains the string 'sets'

'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #22 2014-05-03 02:35:35

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

Have you been there yet?

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

## #23 2014-05-03 04:01:53

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### Re: Easy Problems

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.

Offline

## #24 2014-05-03 04:12:06

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,261
Website

### Re: Easy Problems

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

'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

## #25 2014-05-03 07:23:47

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,821

### Re: Easy Problems

Yes, I have and I am a tough marker.

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online