Samantha and Isaac are playing racquetballSamantha 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 = 1/3 * x + 4 When does his racquet hit the ball? (1 point ) after 1.5 milliseconds after 6.8 milliseconds after 8.4 milliseconds after 3.5 milliseconds

Question

Samantha and Isaac are playing racquetballSamantha 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 = 1/3 * x + 4 When does his racquet hit the ball? (1 point ) after 1.5 milliseconds after 6.8 milliseconds after 8.4 milliseconds after 3.5 milliseconds

Answer 1

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

-3|x - 4| + 20 = 1/3 * x + 4

Simplify the equation:

-3|x - 4| = 1/3 * x - 16

Multiply by -3 to get rid of the absolute value:

|x - 4| = -1/9 * x + 48

Now we can solve for x:

Case 1: x - 4 = -1/9 * x + 48
9x - 36 = -x + 432
10x = 468
x = 46.8

Case 2: x - 4 = 1/9 * x - 48
9x - 36 = x - 432
8x = -396
x = -49.5

Since time cannot be negative, we discard the second solution.

Therefore, Isaac's racquet hits the ball after approximately 46.8 milliseconds, which is not one of the provided options. So, the answer is none of the above.