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17 March, 05:09

An engineer designs a satellite dish with a parabolic cross section. The dish is 16 ft wide at the opening, and the focus is placed 6 ft from the vertex.

a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola's axis of symmetry and find an equation of the parabola.

b) Find the depth of the satellite dish at the vertex.

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  1. 17 March, 05:19
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    We are given

    width = 16 ft

    focus = 6 ft from the vertex

    The equation of the parabola is

    y = 4ax^2

    a = 6

    y = 4 (6) x^2

    y = 24 x^2

    The depth of the satellite dish is

    y = 24 (16/2) ^2

    y = 1536 ft
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