Question

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?

Answer 1

can someone please help me

Answer 2

you need to solve a system of equations
y =-0.3x^2 + 3x
and
-2x + 5.5y = 19.5

make x the subject in the second equation
then substitute for x in the first to get a quadratic in y
solve for y The lowest root will give you the height of the point A

Answer 3

on second thoughts it would be easier to make y the subject of second equation and plug in the value for y in to the first eqaution and find values of x
then you can use these values by substituting in the original equation to get y

Answer 4

5.5y = 2x + 19.5
y = 0.3636x + 3.5455
0.3636x + 3.5455 = -0.3x^2 + 3x
0.3x^2 - 2.6364x + 3.5455 = 0

Answer 5

you can solve this using the quadratic formula

Answer 6

yes thank you

Answer 7

yw