Pre-Calc

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The cable in the center portion of a bridge is supported by five pillars to form a parabola. The center support is 10 ft high, the tallest supports are 210 feet high, and the distance between the two tallest supports is 400 ft. Find the height of the two supports equally spaced between the center support and the tallest supports.

Please help and show work :) Thank you in advance!

  • Pre-Calc -

    well, do right 200 foot half of it from the 10 ft level up and add 10 feet at the end
    (0,0) , (100,y middle right) , (200,200)

    y = k x^2
    200 = k (200)^2
    k = 1/200

    at x = 100
    y = (1/200)(100)^2
    = (1/2)(100)
    = 50
    add that ten feet to compensate for moving the origin up at the beginning
    height at 100 feet right of center = 60 feet

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