Math Is Fun Forum

zefir

Member

Registered: 2007-03-27

Posts: 3

weird prove and exercises with 3 unknows

First
There is big yard, on this yard the grass are growing everywhere in the same speed and now, 70 sheeps eat it in 24 days, 30 sheeps eat ir in 60 days, how many sheeps eat the yard in 96 day?

second

a,b,x,y are i can't translate this for example: 1, 3, -238593, i mean total?
and is true for them:

a+b*root2001 = (x+y*root2001)^2000

prove that:

a>=44b

please help me and i'm sorry for my english

Last edited by zefir (2007-03-28 09:17:43)

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: weird prove and exercises with 3 unknows

Assume the growth rate is x , the eating speed of a sheep is y , and the total grass is T , S sheep eat it in 96 days
24*70y-T-24x=0 (1)
60*30y-T-60x=0 (2)
96*Sy-T-96x=0   (3)
Since , y , T , S , x are unknown , then we can use (1)+(2)=(3) to solve it
since 24+60 is not equal to 96
then we have to solve this 24n+60m=96k  & nT+mT=kT , Cuz, n(1)+m(2) = k(3).
Simplified get 2n+5m=8k & n+m=k  => 0=2n+m , let n=1 then m=-2 , then k=-1
multiply (1) by n=1 , get 24*70y-T-24x=0
multiply (2) by m=-2 , get -60*60y+2T+120x=0
multiply (3) by k=-1 , get -S*96y+T+96x=0
Note that n(1)+m(2)=-1920y+T+96x=0
Then -96S=-1920, S=20

Last edited by Stanley_Marsh (2007-03-28 10:08:07)

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Numbers are the essence of the Universe

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: weird prove and exercises with 3 unknows

I'd like to know how long the grass is to start off.
Perhaps in the units of "days of growth" we begin with.

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igloo myrtilles fourmis

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: weird prove and exercises with 3 unknows

Too many unknown , I use trick to eliminate them , I dont know if it's correct tho.

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Numbers are the essence of the Universe

zefir

Member

Registered: 2007-03-27

Posts: 3

Re: weird prove and exercises with 3 unknows

what about prove?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: weird prove and exercises with 3 unknows

For second problem, does root16 equal 4 and root81 equal 9 ??
What is root, is it the square root or the 2000th root, such that
2000 numbers multiplied equal what you start with.
For example, the 12th root of 2 is about 1.059, which has
interesting usages in the 12 note scale in music.
Now the square root of 2 is 1.4142 or so.
Please explain.
Also, 1, 3, -238593, why only three numbers, not four ?

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: weird prove and exercises with 3 unknows

I get that 40/3 sheep can eat the yard in 90 days.

Edit: 96 days, even. My calculation was with 96, I just made a typo there.

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Why did the vector cross the road?
It wanted to be normal.

zefir

Member

Registered: 2007-03-27

Posts: 3

Re: weird prove and exercises with 3 unknows

mathsyperson becouse it could take 96 days not 90:) 

about second

root4 = 2 root9=3
3^2=9 4^3=64

and next
a,b,x,y are numbers without  coma, those three  was only examples:)

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: weird prove and exercises with 3 unknows

Here is what I think about the second
First ,

rearrange it , get

Obviously

Then

And

Then ...Still working on it.

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Numbers are the essence of the Universe

zefir

Member

Registered: 2007-03-27

Posts: 3

Re: weird prove and exercises with 3 unknows

hm maybe someone can do the first one a little easier?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: weird prove and exercises with 3 unknows

Are a, b, x and y rational numbers? If they are, we can use the comparison method.

a is the sum of the terms involving even powers of y√2001 and b√2001 is the sum of the terms involving odd powers of y√2001 in the binomial expansion of (x+y√2001)[sup]2000[/sup], i.e.

Note that a is the sum of products of even powers and positive coefficients; ∴ a ≥ 0.

CASE 1: b ≤ 0

Then a ≥ 0 ≥ 44b.

CASE 2: b > 0

Note also that

Last edited by JaneFairfax (2007-03-29 09:26:30)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: weird prove and exercises with 3 unknows

A note on the second problem:

a+b*root2001 = (x+y*root2001)^2000

prove that:

a>=44b

a, b, x and y must be rational numbers. Otherwise, you could have, e.g.

then a ≥ 44b would no longer be true.

zefir

Member

Registered: 2007-03-27

Posts: 3

Re: weird prove and exercises with 3 unknows

it's too hard for me, it isn't really a easier way, please one more time help me, i have time until tomorrow