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Thread: Calc Help!!!

  1. #1
    Oct 2007

    Calc Help!!!

    A car is traveling at night along a highway shaped like a parabola with its vertex at the origin. The car starts at a point 100 m west and 100 m north of the origin and travels inan easterly direction. There is a statue located 100 m east and 50 m north of the origin. At what point on the highway will the car's headlights illuminate the statue?

    what i have so far:
    delta x=100-x
    delta y=50-y
    delta y=f(x+deltax)-f(x)

    I dont no how to finish the problem off so and i feel like i am going in circles, so any help would be great! Thanks!!!!
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  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    What you must do is find at what point a line is tangent to the parabola and passes through (100,50).

    You can use $\displaystyle y=a(x-h)^{2}+k$ to find your parabola equation.

    You need to find the derivative of y to get the slope m.

    In doing so, we find the equation is $\displaystyle y=\frac{1}{100}x^{2}$

    Now, you have a 'passes through' point but do not know where it is tangent.

    You can use $\displaystyle y-y_{1}=m(x-x_{1})$

    $\displaystyle \underbrace{\frac{1}{100}x^{2}}_{\text{y}}-\overbrace{50}^{\text{y1}}=\underbrace{\frac{x}{50 }}_{\text{m}}\overbrace{(x-100)}^{\text{x-x1}}$

    Now, solve for x. Only one answer will be within reason.
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