Samantha and Isaac are playing racquetball. Samantha hits the ball, sending it on a trajectory modeled by y=−3|x−4|+20 , where y is the height reached by the ball, in feet, after x milliseconds. In a desperate attempt to keep the ball in the air, Isaac throws his racquet toward it at a trajectory modeled by y=1/3x+4 . When does his racquet hit the ball?(1 point) Responses after 6.8 milliseconds after 6.8 milliseconds after 3.5 milliseconds after 3.5 milliseconds after 1.5 milliseconds after 1.5 milliseconds after 8.4 milliseconds

Answer 1

To find out when Isaac's racquet hits the ball, we need to set the two equations equal to each other and solve for x:

-3|x-4| + 20 = (1/3)x + 4
-3|x-4| = (1/3)x - 16
|x-4| = -1/9x + 16/3

Now we can solve for x by considering two cases:

1. When x-4 is positive:
x-4 = -1/9x + 16/3
9x + 36 = -x + 48
10x = 12
x = 1.2 milliseconds

2. When x-4 is negative:
-(x-4) = -1/9x + 16/3
-9x + 36 = -x + 48
-8x = 12
x = 1.5 milliseconds

Therefore, Isaac's racquet hits the ball after 1.5 milliseconds.