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math grade 12

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A open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Derermine the dimensions of the square that must be cut to create a box with a volume of 100cm3. Widht= 20-2x, length =30-2x, height=x.

  • math grade 12 - ,

    just plug the values into the equation

    100 = x(20-2x)(30-2x)
    4x^3 - 100x^2 + 600x - 100 = 0
    x^3 - 25x^2 + 150x - 25 = 0

    There are 3 real solutions, approximately
    0.17, 9.52, 15.31

    15.31 is out, since the sides aren't long enough.

    Not an easy problem, if you have no tools for solving cubics.

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