Question

A fountain on a lake sprays water in a parabolic arch modeled by the equation

y = −0.4x2 + 3x, where y is the height in feet and x is the horizontal distance. A beam of light is passed through the fountain to create a rainbow effect. If the beam is directed at an angle modeled by the equation -2.2x + 4.9y = 8.18, at what distance from the ground will the beam first touch the water spray?

A. 0.6 feet
B. 2 feet
C. 4.2 feet
D. 5.6 feet

Answer 1

Hello,

Answer B (2.0017868263...feet)

We must foind the intersection of the line and the parabola:


`- (4)/(10) x^2+3x= (22)/(49)x+ (818)/(490)\\ ...\\ 196x^2-1250x+818=0\\ x= (1250- √(921188) )/(392)\approx0.7403433860\\ y=-0.4*0.74034...^2+3*0.74034...\approx2.0017868263...`