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Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
 one year ago
 one year ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
 one year ago
 one year ago

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Brent0423Best ResponseYou've already chosen the best response.0
Is it just me or is this problem pretty complex?
 one year ago

Brent0423Best ResponseYou've already chosen the best response.0
this is what all of my problems are like... FML
 one year ago

ChmEBest ResponseYou've already chosen the best response.0
I don't understand squares is a minimum... hmmm
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
x+y=100 x^2+y^2= something x^2 + (100x)^2 = something differentiate set equal to zero
 one year ago

Brent0423Best ResponseYou've already chosen the best response.0
i know how to do the problem now.. i just feel like these problems are really complex
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
x+y=100 > y=100x k=x^2+y^2 k=x^2+(100x)^2 k=x^2+10,000200x+x^2 k=2x^2200x+10,000 u can use derivative like @Algebraic! said
 one year ago

Brent0423Best ResponseYou've already chosen the best response.0
A rancher with 750ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. a. Find a function that models the total area of the four pens. b. Find the largest possible total area of the four pens.
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
dw:1359869626673:dw from the figure we can maka a models the total area of the four pens : 6x+4y=750 or 3x+2y=375 2y=3753x y=(3753x)/2 ...(1) the total area (A) = 4xy ....(2) subt (1) to (2) we get a function : A=4x(3753x)/2 A=6x^2+750x
 one year ago

Brent0423Best ResponseYou've already chosen the best response.0
and your trying to tell me that this is easy....... _
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
ups, sorry mistake from m the total area (A) = 3xy A=3x(3753x)/2 A=562.5x4.5x^2
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
it just a model only :) for solution u can use like the first problem
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
btw, the first has solved ?
 one year ago

akash_809Best ResponseYou've already chosen the best response.2
the correct way is to diffentiate and equate it to zero ...But i think there is an easier method , since \[(x+y)^2=x^2+y^2+2xy\] so \[10000=x^2+y^2+2xy\] now from A.M \[\ge\] GM , so \[(x^2+y^2)/2 \ge \sqrt{x^2.y^2}\] and for \[x^2+y^2\] to be minimum A.M=G.M i.e x=y , so the numbers would be 50,50 ....
 one year ago

akash_809Best ResponseYou've already chosen the best response.2
@Brent0423 do u get it
 one year ago

akash_809Best ResponseYou've already chosen the best response.2
and do you have theanswer , is it 50,50 i gave
 one year ago

akash_809Best ResponseYou've already chosen the best response.2
you gave me the medal so i assume the answer is 50, 50 right ?
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
waw, AMGM is one of the math olympiads material, but i like it i think for basic, we just do it by use simple method... any way, may be u can use this formula : dw:1359871521108:dw
 one year ago
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