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

CaptainSavage0 CaptainSavage0

21-06-2016
Mathematics

contestada

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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To answer this question, we are given with two equations y = −0.4x^2 + 3x which decribes the parabolic arched water of the lake and -2.2x + 4.9y = 8.18 which models the direction of the beam. To find the distance from the ground, y which the beam first touch that water spray, we get the expression of the first equation in terms of y and substitute to the second equation. x is equal to 0.743 meters y is equal to 2.0 meters. Answer is 2 meters.