By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may b

Question

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 15 in. long and 7 in. wide, find the dimensions (in inches) of the box that will yield the maximum volume. (Round your answers to two decimal places if necessary.) smallest value in in largest value in

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Piper 2 months 2021-10-09T01:10:18+00:00 1 Answer 0 views 0

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    2021-10-09T01:11:29+00:00

    Answer:

    Length l = 15 – 2x = 15 – 2(1.5) = 12.00 in

    Breadth b = 7 – 2x = 7 – 2(1.5) = 4.00 in

    Height h = x = 1.50 in

    Step-by-step explanation:

    The volume of a box can be written as;

    V = l×b×h

    Where;

    Length = l

    Breadth = b

    Height = h

    Let x represent the length of the cube cut out of the four edges.

    Using the attached image;

    Length l = 15 – 2x

    Breadth b = 7 – 2x

    Height h = x

    Substituting the values to the volume equation;

    V = (15-2x)(7-2x)(x)

    V = 105x – 30x^2 – 14x^2 + 4x^3

    V = 105x – 44x^2 + 4x^3

    At Maximum volume, V’ = dV/dx = 0

    V’ = 105 – 88x + 12x^2 = 0

    Solving the quadratic equation, we have;

    x = 5.83 or x = 1.50

    x cannot be 5.83 since 2x > 7 (greater than the breadth of cardboard)

    Therefore ;

    Length l = 15 – 2x = 15 – 2(1.5) = 12.00 in

    Breadth b = 7 – 2x = 7 – 2(1.5) = 4.00 in

    Height h = x = 1.50 in

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45:7+7-4:2-5:5*4+35:2 =? ( )