Two water balloons were launched into the air at different moments and collided. the water balloons were modeled by the quadratic functions: y = −7x2 26x 3 and y = −6x2 23x 5, where y represents the height in meters and x represents the time in seconds after the launch. 2.0 seconds is the time, in seconds, that the balloons collided at the highest point
The time in seconds that the balloons collided at the highest point is; B: 2.0 seconds
We are told that the water balloons were modeled by the quadratic functions:
y = -7x² + 26x + 6 and y = -6x² + 25x + 4
where;
y = the height in meters
x = the time in seconds after the launch
The time at which they will collide has to be at the same height.
Thus;
-7x² + 26x + 6 = -6x² + 25x + 4
Rearranging this gives;
x² - x - 2 = 0.
Using an online quadratic equation solver gives us x = 2 or -1. We will take the positive one as x = 2.0 seconds
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