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Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −3x2 + 24x + 3 and y = −4x2 + 25x + 15, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?

Respuesta :

semsee45

Answer:

4s

Step-by-step explanation:

Equate the equations and solve for x:

[tex]-3x^2 + 24x + 3=-4x^2 + 25x + 15[/tex]

[tex]\implies x^2 -x -12=0[/tex]

[tex]\implies x^2 -4x+3x -12=0[/tex]

[tex]\implies x(x-4)+3(x-4)=0[/tex]

[tex]\implies (x+3)(x-4)=0[/tex]

[tex]\implies x=-3, x=4[/tex]

As time is positive, x = 4

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