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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.

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  1. anonymous
    • 5 years ago
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    set up a couple equations. x+y=30 \[10x+\sqrt{y}\]=f(x,y) What math is this for?

  2. anonymous
    • 5 years ago
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    algebra

  3. anonymous
    • 5 years ago
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    first off, I read that wrong.

  4. anonymous
    • 5 years ago
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    sorry about that. Anyway, the equation should really be 10x+y^2->minimum

  5. anonymous
    • 5 years ago
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    so how do you find the two numbers?

  6. anonymous
    • 5 years ago
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    Sorry, 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 30-y=x and can substitute that in.

  7. anonymous
    • 5 years ago
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    yes I see so far

  8. anonymous
    • 5 years ago
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    so 10(30-y)+y^2 needs to be minimized.

  9. anonymous
    • 5 years ago
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    which means that 300-10y+y^2 needs to be minimized.

  10. anonymous
    • 5 years ago
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    ok so the next step would be setting it to zero?

  11. anonymous
    • 5 years ago
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    I guess. Sorry, I don't remember how to do this the algebra way.

  12. anonymous
    • 5 years ago
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    well I don't really get anywhere doing that anyway. How would you do it?

  13. anonymous
    • 5 years ago
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    do 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.

  14. anonymous
    • 5 years ago
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    i believe integers

  15. anonymous
    • 5 years ago
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    well 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.

  16. anonymous
    • 5 years ago
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    10 and 20?

  17. anonymous
    • 5 years ago
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    I don't know. Try asking the question again to see if anyone can do it better.

  18. anonymous
    • 5 years ago
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    ok thank u

  19. anonymous
    • 5 years ago
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    actually, 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

  20. anonymous
    • 5 years ago
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    where 25 is the one you multiply by 10.

  21. anonymous
    • 5 years ago
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    25 and 5? ok thank you!

  22. anonymous
    • 5 years ago
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    yeah, 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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