Thread: delta!!

hi to all members i am new here hehe tuesday my school started and i have homework to do for tommorow plz help

soit s un nombre reel donne.parmi tous lescouples(alfa,beta) de nb reels dont la somme est s,quel est celui dont le produit p=alfa.beta maximum ??
it's french but plz help!!!

Originally Posted by iceman1

soit s a real number give??.parmi all the couples(alpha,beta) of real numbers dont sum?? is s,which is celui dont the maximum product when p=alfa.beta??

You're going to have to clarify...

Originally Posted by iceman1

hi to all members i am new here hehe tuesday my school started and i have homework to do for tommorow plz help

soit s un nombre reel donne.parmi tous lescouples(alfa,beta) de nb reels dont la somme est s,quel est celui dont le produit p=alfa.beta maximum ??
it's french but plz help!!!

Why did you not translate it for us?

My translation is:

Let S be the set of all pairs of reals (alpha, beta), such that alpha+beta=s.
What is the maximum of p=alpha.beta?

RonL

Originally Posted by iceman1

soit s un nombre reel donne.parmi tous lescouples(alfa,beta) de nb reels dont la somme est s,quel est celui dont le produit p=alfa.beta maximum ??

Originally Posted by Free Online Translator

or s a reel number gives among all couples (alfa, beta) of nb reels whose sum is s, which is the one maximum of which produces it p=alfa.beta

you should always translate before asking the question (even if it's as botchy as the internet translators)...

Originally Posted by CaptainBlack

Why did you not translate it for us?

My translation is:

Let S be the set of all pairs of reals (alpha, beta), such that alpha+beta=s.
What is the maximum of p=alpha.beta?

RonL

beta=s-alpha,

so

p=alpha(s-alpha)=-alpha^2+s.alpha

this has a maximum when ds/d(alpha)=0 (you will have to show this is a maximum rather
than a minimum), or:

-2.alpha + s=0,

or

alpha=s/2.

RonL

lol tnx mate for the traslation and for this results tnx alot

my second probleme??

we have 4 carres de cote respective a,a+1,a+2,a+3...u can choose a pour l'air du plus grand=somme des autres??

and tnx

lol tnx mate for the traslation and for this results tnx alot

my second probleme??

One has access to four carees of respective a,a+1,a+2,a+3. quotations can one to choose has for that the air of the biggest one be
egale has the sum of the others

plz help now


P a number reel donne.parmi all the couples (esparto, beta) of number reels of which produced it is p,quel the one of which the sum s = esparto + beta is minimum?


help me 2 hours and my class started

Originally Posted by iceman1

lol tnx mate for the traslation and for this results tnx alot

my second probleme??

One has access to four carees of respective a,a+1,a+2,a+3. quotations can one to choose has for that the air of the biggest one be
egale has the sum of the others

Lets assume that this is telling us that we have four crates of similar form
with charateristic dimensions a, a+1, a+2, a+3. The largest has a volume
equal to the sum of the volumes of the other three, find a.

The volumes are proportional to the cube of the charateristic dimension, so:

(a+3)^3=a^3 + (a+1)^3 + (a+2)^3.

This simplifies after expanding the cubes to:

2a^3 - 12a -18 = 0.

Which has a single real solution of a=3.

RonL

Originally Posted by iceman1

P a number reel donne.parmi all the couples (esparto, beta) of number reels of which produced it is p,quel the one of which the sum s = esparto + beta is minimum?

Of all pairs of real numbers (alpha, beta) with product equal to p (best
assume p>0 here), find that pair for which their sum s is a minimum.

alpha.beta=p,

so

beta=p/alpha.

Hence:

s=alpha+beta=alpha+p/alpha.

The minimum (if it exists) of s occurs when ds/d(alpha)=0

ds/d(alpha)=1 - p/alpha^2

So the alpha we are interested in is a root of:

alpha^2 - p=0,

or alpha=+/- sqrt(p)

You probably want alpha and beta to be >=0, in which case the positive root is
what you want, also you should justify that this is in fact a minimum.

RonL