Anonymous
Anonymous asked in 科學及數學數學 · 5 years ago

math help

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    Suppose x and h are numbers

    a)

    Method1:

    Perimeter of base triangle=x+x+x=3x (m)

    Area of the base triangle

    =√[3x/2 (3x/2 - x)(3x/2 - x)(3x/2 - x)]

    =√(3x⁴/16)

    =(√3)x²/4 (m²)

    Method2:

    In the base triangle

    Since 3 sides are also equal,

    then 3 angles are also equal(=60°) (property of equil Δ)

    Area of the base triangle

    =(x)(x)(sin60°)/2

    =(√3)x²/4 (m²)

    b)

    The volume of the prism

    =Area of the base triangle * hight

    =(√3)x²h/4 (m³)

    c)

    Area of a rectangle

    =xh (m²)

    C

    =12*2*(√3)x²/4 + 8*3*xh

    =(6√3)x² + 24xh

    d)

    Since the prism volume=100 (m³)

    (√3)x²h/4=100

    h=400/[(√3)x²]

    C=(6√3)x² + 24xh

    C=(6√3)x² + 24x{400/[(√3)x²]}

    C=(6√3)x² + (3200√3)/x

    dC/dx

    =d[(6√3)x² + (3200√3)/x]/dx

    =d[(6√3)x²]/dx + d[(3200√3)/x]/dx

    =(12√3)x - (3200√3)/x²

    d²C/dx²

    =d[(12√3)x - (3200√3)/x²]/dx

    =d[(12√3)x]/dx - d[(3200√3)/x²]/dx

    =12√3 + (6400√3)/x³

    e)

    dC/dx=0

    (12√3)x - (3200√3)/x²=0

    12x=3200/x²

    x=(800/3)^(1/3)

    Sub x=(800/3)^(1/3) into d²C/dx²

    d²C/dx²>0

    ∴If x=(800/3)^(1/3), the cost is the minimum.

    f)

    The minimum cost

    =(6√3) (800/3)^(2/3) + (3200√3)/[(800/3)^(1/3)]

    =240 * 3^(5/6) * 10^(1/3)

    =$ 1292 (corr to the nearest dollar)

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  • 5 years ago

    請不要把帖子刪掉,謝謝你的合作。

    你看看答題者其實很用心地幫你解答。

    如果你就這樣刪了帖子,他們幫助你的心機和時間就白費了,也不能在這數學版留下有用的參考資料。

    2015-07-06 22:05:52 補充:

    無救啦~ 你剛剛刪了我的帖子啦~

    看來你一定會刪本帖...

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