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On a movie set, an archway is modeled by the equation:

y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?

OPTIONS:

A) 1.5 feet and 3.5 feet
B) 1.5 feet and 4 feet
C) 3.5 feet and 4 feet
D) 4 feet and 4 feet

Respuesta :

you need to solve the two equations simultaneously:-

y = -0.5x^2 + 3x 
-0.5x + 2.42y = 7.65

from second equation  y =  7.65 / 2.42  + 0.5x / 2.42 
                                     y = 3.161 + 0.207x

plug this value of y into the first question

3.161 + 0.207x =  -0.5x^2 + 3x

0.5x^2 -2.793x + 3.161 = 0

giving x = 4.01 , 1.571

To find the heights we need to find the y values

y = -0.5(4)^2 + 12 =  4 feet
and 
y = -0.5*(1.571)^2 + 3*1.571 =  3.5 feet

so C is the correct choice