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#1 2016-06-06 09:24:07

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

Quickies #4, Mathematics.

1. If x and y are real numbers,and x^2 = (y^2-x^2), find all possible values of x and y.

2. What is 2^2 + 2^-3 + 2^4 + 2^-5........
3. Bobbym is stranded on a desert island. To cure his boredom, he plays the game of Bobbymcoin. He flips a fair coin 10 times.
He gets 2 points for every head and -2 points for every tail. However, he gets +10 points for 1 PAIR of heads. What is bobbym's average score?
4. 1/2 + 1/3 + 1/4 + 1/5..... =
5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?
6. f(x) = 2x^2-log(2x^2). What is f(1)-f(2)+f(3)-f(4)..... If it diverges, r\write DIVE as your answer.

Last edited by Mathegocart (2016-06-07 08:02:25)


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#2 2016-06-06 09:44:07

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

Re: Quickies #4, Mathematics.

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.

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#3 2016-06-06 13:28:49

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

Re: Quickies #4, Mathematics.

bobbym wrote:

Hi;

Duh


The integral of hope is reality.

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#4 2016-06-06 14:18:00

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

Re: Quickies #4, Mathematics.

You are adding increasing large powers of 2 with some small numbers. There can be no convergence because the terms of this series do not get smaller.

I also will need a bit more to solve #3. I can make assumptions but they may not be what you want.

For instance, supposing we get this for 10 coin flips:

H, T, T, H, H, H, H, T, H, T

That H, H, H, H, do you call it 3 groups of H, H and add 30?


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.

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#5 2016-06-06 22:02:50

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

Re: Quickies #4, Mathematics.

bobbym wrote:

You are adding increasing large powers of 2 with some small numbers. There can be no convergence because the terms of this series do not get smaller.

I also will need a bit more to solve #3. I can make assumptions but they may not be what you want.

For instance, supposing we get this for 10 coin flips:

H, T, T, H, H, H, H, T, H, T

That H, H, H, H, do you call it 3 groups of H, H and add 30?

Yes and I knew it would not converge.
however h h h h h would be 2 pairs.

Last edited by Mathegocart (2016-06-06 22:03:21)


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#6 2016-06-07 03:00:47

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

Re: Quickies #4, Mathematics.

however h h h h h would be 2 pairs.

2 pairs? How do you get that?


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.

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#7 2016-06-07 08:01:10

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

Re: Quickies #4, Mathematics.

bobbym wrote:

however h h h h h would be 2 pairs.

2 pairs? How do you get that?

because there are only two COMPLETE pairs of h.


The integral of hope is reality.

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#8 2016-06-07 12:00:33

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

Re: Quickies #4, Mathematics.

sorry for misunderstandings bobbym


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#9 2016-06-07 12:33:27

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

Re: Quickies #4, Mathematics.

Hi;

No problem.


On the pattern  h h h h h do we say that h h h h h = 20 or h h h h h = 20 with an h left over which we would then say is 2?


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.

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#10 2016-06-08 19:01:09

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

Re: Quickies #4, Mathematics.

Last edited by thickhead (2016-06-08 19:04:57)


{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.}

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#11 2016-06-08 19:21:12

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

Re: Quickies #4, Mathematics.

(6) divergent.


{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.}

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#12 2016-06-08 19:26:31

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

Re: Quickies #4, Mathematics.

mathgogocart wrote:

1. If x and y are real numbers,and x^2 = (y^2-x^2), find all possible values of x and y.

Why are the terms on R.H.S.  within  brackets? Is something missing?

Last edited by thickhead (2016-06-08 19:26:57)


{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.}

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#13 2016-06-08 20:06:31

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

Re: Quickies #4, Mathematics.

Howdy;


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.

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#14 2016-06-08 22:28:37

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

Re: Quickies #4, Mathematics.

bobbym wrote:

Howdy;

He has 10 hp.


The integral of hope is reality.

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#15 2016-06-09 04:41:34

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

Re: Quickies #4, Mathematics.


{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.}

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#16 2016-06-09 11:04:52

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

Re: Quickies #4, Mathematics.

Hi;

We are almost ready to solve this:

5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?

40% + 20%+ 20% = 80%

What happens the remaining 20% ?

Perhaps you would like to change the percentages to 40%, 30% and 30%.


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.

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#17 2016-06-09 22:51:59

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

Re: Quickies #4, Mathematics.

bobbym wrote:

Hi;

We are almost ready to solve this:

5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?

40% + 20%+ 20% = 80%

What happens the remaining 20% ?

Perhaps you would like to change the percentages to 40%, 30% and 30%.

Change it to what you say.


The integral of hope is reality.

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#18 2016-06-10 03:44:30

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

Re: Quickies #4, Mathematics.

Do not take any step before consulting Agnishom. He knows the proper values of course if not already killed by slime.


{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.}

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#19 2016-06-11 04:48:16

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

Re: Quickies #4, Mathematics.

I have not seen Agnishom, so the slime guy may have gotten him. I will remember him forever.

mathgogocart wrote:

Change it to what you say.

I posted an answer here but the model I used was incorrect as pointed out to me by EVW. I am working on a better 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.

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#20 2016-06-12 05:16:45

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

Re: Quickies #4, Mathematics.

I can't make head or tail of the problem. I do not understand what are the health points and what it has to do with the fight.


{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.}

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#21 2016-06-12 22:34:40

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

Re: Quickies #4, Mathematics.

clarification: Slime guy starts the fight.


The integral of hope is reality.

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#22 2016-06-13 10:48:23

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

Re: Quickies #4, Mathematics.

Hi;

I wished you would have told me that earlier because I just spent 2 days solving the problem with neither side starting first. That condition makes it a whole different problem.


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.

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