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anonymous
 5 years ago
Can someone help with this?:
Find two numbers whose sum is 30, such that the sum of the square of one number plus ten times the other number is a minimum.
anonymous
 5 years ago
Can someone help with this?: Find two numbers whose sum is 30, such that the sum of the square of one number plus ten times the other number is a minimum.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0set up a couple equations. x+y=30 \[10x+\sqrt{y}\]=f(x,y) What math is this for?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first off, I read that wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry about that. Anyway, the equation should really be 10x+y^2>minimum

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so how do you find the two numbers?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, I forget how to do it with what you know in algebra, but let's see if I can figure it out as I go along. Using those equations, you also know that 30y=x and can substitute that in.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 10(30y)+y^2 needs to be minimized.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which means that 30010y+y^2 needs to be minimized.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so the next step would be setting it to zero?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I guess. Sorry, I don't remember how to do this the algebra way.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well I don't really get anywhere doing that anyway. How would you do it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do the numbers have to be integers? I would use lagrange multipliers, which I'm pretty sure you haven't learned about, and you don't need for the problem.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well to minimize them, 10x would have to be as close to y^2 as possible, so you can just guess and check if they have to be integers to see what gets you the closest.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't know. Try asking the question again to see if anyone can do it better.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually, using my way, which I'm not going to explain because it's not the way you're supposed to do it, I got 25 and 5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0where 25 is the one you multiply by 10.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.025 and 5? ok thank you!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, and you can check that by seeing that no other numbers get you a higher number when you multiply one by 10 and square the other, but I'm almost positive that the answer is 25 and 5.
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