Smile 發問於 科學及數學數學 · 4 月 前

Maths problem, thanks?

How to do, thanks

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1 個解答

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  • SC147
    Lv 6
    4 月 前
    最佳解答

    (a) f(x) = x²-36x+648

       = x²-(2)18x+18²-18²+648

       = (x-18)²+324

    ∴ vertex of graph = (18,324)

    (b) (i) length of the other piece = 36-x cm

    sum of areas of 2 squares, A

    = (x/4)² + [(36-x)/4]²

    = (x²+36²-72x+x²) /16

    = (2x²-72x+1296) /16

    = (x²-36x+648) / 8 , or

    = [(x-18)²+324] / 8  --- from (a)

    (ii) From (i) :

    When sum of areas (A) of 2 squares is minimum, x = 18

    ∴ corresponding sum of areas = 324/8 = 40.5 cm²

    • SC147
      Lv 6
      4 月 前舉報

      1) CHECKING: Putting x=18 into A = (x/4)² + [(36-x)/4]² , you will get sum of areas = 40.5
      2) From x=18, get both; x/4 = 9/2 & (36-x)/4 = 9/2. ∴ sum of areas (A) is min. when : the 2 squares have the same length, which means "same area"!

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