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2 April, 21:04

An open box is made from a square piece of cardboard 30 inches on a side by cutting identical squares and turning up the sides. A) express the volume of the box as V, as a function of the length of the side of the square cut from each corner, x. B) Find and interpert V (3), V (4), V (5), V (6), V (7). What is happening to the volume of the box as th elength of the side of the square cut from each corner increases? C) Find the domain of V

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  1. 2 April, 21:15
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    Step-by-step explanation:

    A)

    The length of the box is 30 - 2x inches.

    The width of the box is 30 - 2x inches.

    The height of the box is x inches.

    So the volume is:

    V = x (30 - 2x) ²

    B)

    V (3) = 3 (30 - 6) ² = 1728

    V (4) = 4 (30 - 8) ² = 1936

    V (5) = 5 (30 - 10) ² = 2000

    V (6) = 6 (30 - 12) ² = 1944

    V (7) = 7 (30 - 14) ² = 1792

    As x increases, the volume of the box increases to a maximum and then decreases.

    C)

    The ends of the domain occur when V = 0.

    0 = x (30 - 2x) ²

    x = 0 or 15

    So the domain is (0, 15).
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