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Math Help - Calculus optimization-Drainage channel

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    Calculus optimization-Drainage channel

    A drainage channel of trapezoidal cross section is made by welding three flat strips each 6 cm wide, the middle one being horizontal and the other two inclined at equal angles to it. If the area of the cross section is a maximum, how wide is the channel at the top?
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    Quote Originally Posted by Calculus23 View Post
    A drainage channel of trapezoidal cross section is made by welding three flat strips each 6 cm wide, the middle one being horizontal and the other two inclined at equal angles to it. If the area of the cross section is a maximum, how wide is the channel at the top?
    obviously, you've made a sketch, right?

    let \theta = angle of incline for the two sides

    area of a trapezoid ...

    A = \frac{h}{2}\left(b_1 + b_2\right)

    h = 6\sin{\theta}

    b_1 = 6

    b_2 = 6 + 2(6\cos{\theta})

    substitute in the values to get area as a function of \theta ... then do that optimization thing.
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