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

You are not logged in.

#1 2016-07-19 07:20:45

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Exponent Slash, #1

1.Express 8f3344ddc83b6ba70f7ea2524dfa8e916e464fae.png
as the product of 2 factors, where neither of them is 1.

2. Express d99cf3151cf8b5fd07dacb5a1e81c28dd0c22613.png as the product of 2 factors, where neither of them is 1. Do not express these 2 factors explicitly.

3. What does4270153977b88c146f9cdfb3155db286e02ea467.png equal?

4. Find all integers where n! is a multiple of n^2.

5. If 3 numbers are chosen at random from first 1000 natural numbers,what is the probability that the three numbers are in G.P.? All numbers are distinct.

6. prove that 7aa736fda62b8cc084a32d1c3f0130a101b1fd30.png is true for all non negative integers.

Last edited by Mathegocart (2016-07-21 02:09:08)


The integral of hope is reality.

Offline

#2 2016-07-19 09:27:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Exponent Slash, #1

Hi;


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.

Offline

#3 2016-07-19 09:55:12

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Exponent Slash, #1

bobbym wrote:

Hi;

Correct.


The integral of hope is reality.

Offline

#4 2016-07-19 12:59:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Exponent Slash, #1

Hi;


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.

Offline

#5 2016-07-19 16:14:30

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1


The answer is not unique. There are 63 different ways.

Last edited by thickhead (2016-07-20 04:05:57)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#6 2016-07-19 16:22:11

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#7 2016-07-21 02:07:08

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Exponent Slash, #1

thickhead wrote:

Thickhead, could you explain the process on the inequality? I used a bit of Cauchy Schwarz on this.

Last edited by Mathegocart (2016-07-21 02:08:44)


The integral of hope is reality.

Offline

#8 2016-07-21 02:10:10

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Exponent Slash, #1

bobbym wrote:

Hi;

Both answers are reasonable solutions, also thickhead has a good soultion as well.


The integral of hope is reality.

Offline

#9 2016-07-21 02:12:24

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Exponent Slash, #1

thickhead wrote:

6 also is a solution, and 6 is not a cube. gif.latex?%5Cfrac%7B6%21%7D%7B6%5E%7B2%7D%7D = 20

Last edited by Mathegocart (2016-07-21 02:12:49)


The integral of hope is reality.

Offline

#10 2016-07-21 02:46:10

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1

Mathegocart wrote:
thickhead wrote:

6 also is a solution, and 6 is not a cube. http://latex.codecogs.com/gif.latex?%5Cfrac%7B6%21%7D%7B6%5E%7B2%7D%7D = 20

I just wrote offhand. I had an obvious flash about cubes.Unless n is specified it becomes difficult to make exhaustive list.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#11 2016-07-21 02:52:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Exponent Slash, #1

Hi;


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.

Offline

#12 2016-07-21 03:47:12

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1

bobbym is right. I had not thought properly.After knowing it it looks very simple. A composite number means at least two factors which make up for one "n" the other n being provided by the number itself. Perhaps I tried 4 and seeing it not correct went for 8 and made it a cube. Very unscientific thinking on my part.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#13 2016-07-24 22:41:11

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1

Last edited by thickhead (2016-07-24 23:20:14)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#14 2016-07-25 04:51:22

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1

Last edited by thickhead (2016-07-25 15:28:10)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#15 2016-07-26 23:57:50

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1

Why is Mathegocart  silent ?Is he too busy with other problems? One more thing instead of G.P. if the 3 numbers are in A.P. what is the probability for first 1000 natural  numbers or even first n natural  numbers?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#16 2016-07-27 01:40:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Exponent Slash, #1

Hi;

f the 3 numbers are in A.P. what is the probability for first n natural  numbers?


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.

Offline

#17 2016-07-27 03:27:15

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,108
Website

Re: Exponent Slash, #1

Last edited by zetafunc (2016-07-27 05:02:26)

Offline

#18 2016-07-27 04:02:20

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Exponent Slash, #1


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

#19 2016-07-27 06:05:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Exponent Slash, #1

You are correct, further simplification is possible. Normally, I do not automatically simplify all the way. There are good reasons for this but in this case they do not apply, further simplification was called for.


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.

Offline

Board footer

Powered by FluxBB