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feinicks
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Post: #31

RE: EP Mathematical Challenge,

ZiNgA BuRgA Wrote:What is the 48,574th digit after the decimal point of PI?

easily done, if you know a way to jump to that particular digit.. (I don't.. thinking how). I have obtained the first 2million digits after the decimal. Now I can either sit and count or find a way to jump...

just for those interested, here are the first 4million digits of Pi

Spoiler:

◄◄••• 天使たちの夢か？ •••►►

[Image: ewualizer.gif]

My works!

08/10/2008 08:47 PM

feinicks
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Post: #32

RE: EP Mathematical Challenge,

Spoiler:

◄◄••• 天使たちの夢か？ •••►►

[Image: ewualizer.gif]

My works!

08/10/2008 08:48 PM

feinicks
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Post: #33

RE: EP Mathematical Challenge,

Spoiler:

◄◄••• 天使たちの夢か？ •••►►

[Image: ewualizer.gif]

My works!

08/10/2008 08:48 PM

Kaiser
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Post: #34

RE: EP Mathematical Challenge,

feinicks Wrote:
Kaiser Wrote:10000 cows get a serious illness. they decrease exponentially as they die at a rate that in 60 weeks, only half (1/2) of the cows remain, how much cows will remain after 70 weeks?
i dont really know the answer, this was from a pre calculus quiz and i didn't knew what to do, som if somebody could explain to me i would be grateful enough to give piggies
by the way, im currently taking exponential/quadratic functions... so it should be using that...
my answer: the total no. of cows alive at end of 70 weeks= 4167 cows

how do you do it?

COLEGIOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!
FEEL THE POWER \(m)/ (@_@) \(m)/
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08/10/2008 09:09 PM

feinicks
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Post: #35

RE: EP Mathematical Challenge,

Kaiser Wrote:
feinicks Wrote:
Kaiser Wrote:10000 cows get a serious illness. they decrease exponentially as they die at a rate that in 60 weeks, only half (1/2) of the cows remain, how much cows will remain after 70 weeks?
i dont really know the answer, this was from a pre calculus quiz and i didn't knew what to do, som if somebody could explain to me i would be grateful enough to give piggies
by the way, im currently taking exponential/quadratic functions... so it should be using that...
my answer: the total no. of cows alive at end of 70 weeks= 4167 cows
how do you do it?

can solve it using quadratic equations..

verify if the answer is correct. if so, then I'll solve it here.

◄◄••• 天使たちの夢か？ •••►►

[Image: ewualizer.gif]

My works!

(This post was last modified: 08/10/2008 09:39 PM by feinicks.)

08/10/2008 09:39 PM

Assassinator
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Post: #36

RE: EP Mathematical Challenge,

feinicks Wrote:
Kaiser Wrote:
feinicks Wrote:my answer: the total no. of cows alive at end of 70 weeks= 4167 cows
how do you do it?
can solve it using quadratic equations..

verify if the answer is correct. if so, then I'll solve it here.

That's wrong. (Lolwut? quadratic equations... for an exponential decay problem?)

The correct answer is 4454 cows.

Let t=time.
N(t)=the number of cows alive at time t.
r=rate of decay

Wee are given
N(0)=10000. (That is, there are 10000 at the start).
N(60)=5000. (At 60 weeks, there are 5000 cows).

Wee want to find N(70).

Because the number of cows decreases exponentially, it can be modeled as

N(t)= N(0)*(1-r)^t

Spoiler for What the fudge that means:

Now wee are given n(60)=5000.

Therefore N(60)=N(0)*(1-r)^60
=>  5000=10000*(1-r)^60
=>  1/2=(1-r)^60.
=>  (1-r)=0.5^(1/60)

Now substituting (1-r) into the original equation, wee have

N(t)=10000*(0.5^(1/60))^t
=>  N(70)=10000*(0.5^(1/60))^70

Stick that into a calculator/excel/whatever, and you should get

N(70)=4454.493591...

Ok, that's the simple way of doing it (which is perfectly fine by the way).

But if you want to be/feel hardcore/troublesome/annoying/whatever

The more rigorous way is with the differential equation

dN/dt=-λt

Solve that (don't ask me how) to get N(t)=N(0)*e^(-λt)

And then do the substitutions and stuff on that. If you want to do it that way then figure it out yourself. Will get you the same answer in the end.

(This post was last modified: 09/10/2008 11:15 PM by Assassinator.)

09/10/2008 01:08 AM

Assassinator
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Post: #37

RE: EP Mathematical Challenge,

Ok, slightly better explanation.

(+ shameless bump).

09/10/2008 11:16 PM

Kaiser
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Post: #38

RE: EP Mathematical Challenge,

Thanks!!

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10/10/2008 05:28 AM

diego
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Post: #39

RE: EP Mathematical Challenge,

Haha so that was just to help you!?!>!.

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10/10/2008 05:52 AM

Kaiser
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Post: #40

RE: EP Mathematical Challenge,

diego Wrote:Haha so that was just to help you!?!>!.

well, it was a mathematical challenge thread and i needed help so...

COLEGIOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!
FEEL THE POWER \(m)/ (@_@) \(m)/
Vi Veri Veniversum Vivus Vici

10/10/2008 05:54 AM

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