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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

Respuesta :

caylus
Hello,

Answer B (2.0017868263...feet)

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

[tex]- \dfrac{4}{10} x^2+3x= \dfrac{22}{49}x+ \dfrac{818}{490}\\ ...\\ 196x^2-1250x+818=0\\ x= \dfrac{1250- \sqrt{921188} }{392}\approx0.7403433860\\ y=-0.4*0.74034...^2+3*0.74034...\approx2.0017868263... [/tex]

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