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3 August, 11:18

A sheet of metal that is 30cm wide and 6m long is used to make a rectangular eavestrough by bending the sheet along the dotted lines. what values of x maximizes the capacity of the eavestrough

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  1. 3 August, 11:36
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    The volume of the rectangular eavestrough would be:

    V = (x) (30 - 2x) (600)

    V = (30x - 2x^2) (600)

    V = 18000x - 1200x^2

    to maximize the capacity of the rectangular eavestrough, get the first derivative and equate it to zero

    dV / dx = 18000 - 2400x

    equate to zero

    18000 - 2400x = 0

    2400x = 18000

    x = 7.5 cm is the value of x that would maximize its capacity
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