A fountain on a lake sprays water in a parabolic arch modeled by the equation y= -0.3x^2 +3x. A beam of light modeled by the equ
ation -2x+5.5y=19.5 passes through the fountain to create a rainbow effect. f the beam cuts the water spray at points A and B, such that point B is higher than point A, what distance from the ground level is point A?
1 answer:
ANSWER
4.1 units to the nearest tenth.
EXPLANATION
The graph of the two functions are shown in the attachment.
The coordinates of point A is (1.6,4.1).
The coordinates of point B is (7.1,6.1)
The x-axis represents the ground level.
The distance of point A from the ground level is how far the y-coordinate of this point is from the x-axis.
Which is |4.1-0|=4.1
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Step-by-step explanation:
This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a
The formula for the foci of the vertical ellipse is
(h,k+c) and (h,k-c).
where c is
Our center (h,k) is (2, -5)
Here a^2 is 9, b^2 is 4.
So our foci is
and