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Brent0423
 2 years ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
Brent0423
 2 years ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

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Brent0423
 2 years ago
Best ResponseYou've already chosen the best response.0Is it just me or is this problem pretty complex?

Brent0423
 2 years ago
Best ResponseYou've already chosen the best response.0this is what all of my problems are like... FML

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand squares is a minimum... hmmm

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

Brent0423
 2 years ago
Best ResponseYou've already chosen the best response.0i know how to do the problem now.. i just feel like these problems are really complex

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0x+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

Brent0423
 2 years ago
Best ResponseYou've already chosen the best response.0A 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.

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0dw: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

Brent0423
 2 years ago
Best ResponseYou've already chosen the best response.0and your trying to tell me that this is easy....... _

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

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0it just a model only :) for solution u can use like the first problem

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0btw, the first has solved ?

akash_809
 2 years ago
Best ResponseYou've already chosen the best response.2the 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 ....

akash_809
 2 years ago
Best ResponseYou've already chosen the best response.2@Brent0423 do u get it

akash_809
 2 years ago
Best ResponseYou've already chosen the best response.2and do you have theanswer , is it 50,50 i gave

akash_809
 2 years ago
Best ResponseYou've already chosen the best response.2you gave me the medal so i assume the answer is 50, 50 right ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0waw, 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
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