Question

A fountain on a lake sprays water in a parabolic arch modeled by the equation y = -0.3x2 + 3x. A beam of light modeled by the equation -2x + 5.5y = 19.5 passes through the fountain to create a rainbow effect. If the beam cuts the water spray at points A and B, such that point B is at a higher level than point A, what distance from the ground level is point A?

1.66 units
4.15 units
5.44 units
6.14 units
7.13 units

Answer 1

Hello,

Answer A

y=-0.3x²+3x ==>y=-3/10x²+3x ==>11y=-33/10x²+33x
-2x+5.5y=19.5==>11y=4x+39
==>-33/10x²+33x=4x+39
==>33x²-290x+390=0
Δ=32620
x=(290-√32620)/66=1.657723214....≈1.66