Question

An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B? 8 units 6 units 5 units 3 units

Answer 1

We need to solve the system

y = -2x^2 + 8x
y = (x + 10.34) / 2.23

-2x^2 + 8x =  0.4484x +  4.637

this gives x = 0.77 and 3

So required height = y when x = 3  =  -2(3)^2 + 8(3) =  6 feet  answer