A. Equation of line l: y = mx + 20 where m = y' = 1- (1/250)x
At the point Q, The equation of the line equals the equation of the parabola.
So (1-x/250)x + 20 = x - x^2/500
20 = x^2/250 - x^2/500 = x^2/500
x = sqrt(20*500) = 100ft
B. m = 1 - 100/250 = 3/5.
<span>Equation of line L is y = 3/5x + 20
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C) If a spotlight is located at the x intercept of line L (-33 1/3,0), its light will go only above line L past the point where line L is tangent to the hill at (100,80) because the hill blocks the light below the tangent line.
<span>The highest point on the equation of y = x - x²/500 is at (250,125), so a tree 50 feet tall at that location would reach up to (250,175). The tangent line goes through (250,170), so the top 5 feet of the tree would be above the tangent line, in the glow of the spotlight.
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