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?

Question

anonymous · Answer

options. 
a) 1.66 units b) 4.15 units c) 5.44 units d) 6.14 units e) 7.13 units

anonymous · Answer

do you have to solve this algebraically?

anonymous · Answer

yes

anonymous · Answer

$y=-0.3x^2+3x$
$-2x + 5.5y = 19.5$

Substitute the top equation into the bottom one
$$-2x + 5.5(-0.3x^2+3x) = 19.5$$
Make one side equal to 0 and combine like terms so you can use the quadratic formula to solve for x

anonymous · Answer

I don't get it

anonymous · Answer

@peachpi

anonymous · Answer

where are you stuck?

anonymous · Answer

I solved the equation you gave me and the answer isn't one of my options

anonymous · Answer

You gotta show me what you did so I see if you went wrong somewhere

And not for nothing, but it's not the equation I gave you. It's the equation typed in the problem statement.