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Math Help - What to do?

  1. #1
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    Question What to do?

    Hi
    i got this question and not sure what its about:

    Find the value of x that minimises
    y = 8X^2 (400/X)
    for positive x.

    Give the required x both exactly (i.e. as a surd).

    What do i do?
    This is what i started doing but no idea what else:
    => y=8x^2+(400/x)
    => 16x-400x^(-2)
    ==> 16x-400x^(-2) = 0


    Thanks
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  2. #2
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    Quote Originally Posted by taurus View Post
    Hi
    i got this question and not sure what its about:

    Find the value of x that minimises
    y = 8X^2 (400/X) Mr F says: So there's meant to be a + between these two terms?

    for positive x.

    Give the required x both exactly (i.e. as a surd).

    What do i do?
    This is what i started doing but no idea what else:
    => y=8x^2+(400/x)
    => 16x-400x^(-2)
    ==> 16x-400x^(-2) = 0


    Thanks
    So solve the equation by multiplying through by x^2 to end up with x^3 = 25 => x = (25)^(1/3)....... Now use the sign test to check the nature of the solution.
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  3. #3
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    kind of confused still


    and yes theres meant to be a plus
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  4. #4
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    Quote Originally Posted by taurus View Post
    kind of confused still


    and yes theres meant to be a plus
    Did you multiply 16x-400x^(-2) = 0 through by x^2?? Show me what you get.
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  5. #5
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    ok so gives:

    16x^2 + 400x^(-4)
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  6. #6
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    Quote Originally Posted by taurus View Post
    ok so gives:

    16x^2 + 400x^(-4)
    Wrong for several reasons, including the fact that there's no = sign and therefore you have not given an equation.

    16x-400x^(-2) = 0 multiplied through by x^2 gives 16x^3 - 400 = 0.

    Do you understand that x^(-2) times x^2 = x^0 = 1? You need to revise your basic algebraic skills.
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  7. #7
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    oh ya sorry, i was not thinking correctly

    what do i do after that?
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  8. #8
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    Quote Originally Posted by taurus View Post
    oh ya sorry, i was not thinking correctly

    what do i do after that?
    I can't see Mr. Fantastic beeing around so I'll take over:

    Separate variable and constant:

    16x^3-400=0~\implies~16x^3=400~\implies~x^3=25 ~\implies~x=\sqrt[3]{25} \approx 2.924...
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