A community for students.
Here's the question you clicked on:
 0 viewing
Brent0423
 3 years ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
Brent0423
 3 years ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

This Question is Closed

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

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

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

Algebraic!
 3 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
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0and your trying to tell me that this is easy....... _

RadEn
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0btw, the first has solved ?

akash_809
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2@Brent0423 do u get it

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

akash_809
 3 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
 3 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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.