Math

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An engineer is desingning a parabloic arch, the arch must be 15 m high , and 6 m wide, at a height of 8 m

a) determine a quadratic fundtion that satisfies these conditions

b) what is the width of the arch at its base

  • Math -

    Let the arch be centered on the y-axis. Then the equation will be
    y = -ax^2 + k

    It will have height 6 at x = 3 and -3
    The vertex will be at (0,15)

    y = -ax^2 + 15
    6 = -a(3^2) + 15
    6 = -9a + 15
    -9 = -9a
    a = 1

    y = -x^2 + 15

    y=0 when x^2 = 15, so the width is 2√15 at its base

  • Math -

    Roof of a tunnel is in the shape of parabolic arch whose highest point is 18m above a road. The road surface is 16m wide at ground level. Lights are placed in the tunnel 12 m high. How far from the center of the tunnel are the lights placed?

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