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Math Help - Minimise A= 1/2(1-x+qx^2)

  1. #1
    Kai
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    Minimise A= 1/2(1-x+qx^2)

    Hey, got a question, my sis has exams tomorrow and she cant solve this,...its been 7 years ive done this lvl of maths, and dont remember enough to help her...any help ?

    Its part of the question

    Show A= 1/2(1-x+qx^2)

    Given that x can vay, show that Qy=Yr when A is a min and express the min of A in terms of q

    First part she did, now 2nd part Minimise A= 1/2(1-x+qx^2)-neh.jpg

    I forgot, PQRS is a square
    Last edited by mr fantastic; November 10th 2010 at 01:18 PM. Reason: Re-titled.
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  2. #2
    Kai
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    A is the area of triangle sxy, and q is a constant...

    Still dont get it

    Btw, its an o level question for may 02
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  3. #3
    Kai
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    Minimise A= 1/2(1-x+qx^2)-neh.jpg

    sorry, some info was missing in the first diagram
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  4. #4
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    (1/2)(qx^2- x+ 1) is quadratic. You can rewrite it as (q/2)(x^2- (1/q)x+ 1/q) and complete the square: (q/2)(x^2- (1/q)x+ (1/4q^2)- (1/4q^2)+ 1/q= (q/2)(x- 1/2q)^2+ (4q-1)/4q^2. Since a square is never negative, this will be a minimum (assuming q is positive) when x= 1/(2q) and that minimum will be (4q-1)/(4q^2).
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  5. #5
    Kai
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    Thanks, have been able to solve it
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