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?

Question

Mathematics

Cody Houston

13 May, 07:10

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?

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Marley · Answer 1

Hello,

y=-1.4x²+3x

y=2.2/4.9 x + 8.18/4.9

-0.4x²+3x=2.2/4.9 x + 8.18/4.9

==>1.96 x² - 12.5x + 8.18=0

Δ=92.1188 ... = 9.597 ... ²

x = (12.5-9.597 ...) / (2*1.96) = 0.7403433 ...

=>y=-0.4*0.7403 ... ²+3*0.7403 ... = 2.00178682 ...

Answer: 2.001 ... ft