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Math Help - [SOLVED] How to solve this word problem ?

  1. #1
    Junior Member xterminal01's Avatar
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    [SOLVED] How to solve this word problem ?

    Bridge is build in a shape of a parabolic arch and its span is 140 feet.
    The height of the arch a distance of 50 feet from the center is to be 12 feet.
    Whats the height of the arch at its center.

    * Round to nearest tenth place if necessary.

    #1 * Equation of the parabola in standard form.
    #2 * Height at center.


    How exactly is one suppose to solve this problem?
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  2. #2
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    Standard form: y=a(x-h)^2+k

    Assuming a is negative for the bridge and center of bridge is half the 140 ft span: y=-a(x-70)^2+k

    12=-a(20-70)^2+k 50 ft from center span is 12 ft high
     12=-2500a+k

    And
    0=-a(140-70)^2+k at 140 ft the arch is back on the ground
    0=-4900a+k

    Solving the two equations you find a=\frac{1}{200}~=.005 ~and~ k=\frac{49}{2}~=24.5

    Equation is then:
    #1) y=-\frac{1}{200}(x-70)^2+\frac{49}{2}
    #2) Looking at k, the height at the center, is 24.5 ft.
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  3. #3
    Junior Member xterminal01's Avatar
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    its suppose to be i guess in the p4 form
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by xterminal01 View Post
    its suppose to be i guess in the p4 form
    Who or what is a "p4" form?

    -Dan
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