Question

At the circus, a down throws a melon off a platform. The height of the melon above the groundin feetafter seconds can be modeled by the equation y = - (x - 2) ^ 2 + 9 Another clown tries to shoot the melon in midair using a bow and arrow. The height reached by the arrow, in feet, after x seconds can be modeled by the equation y = 7/3 * x + 1 At what height will the arrow hit the melon? (1 point)

Answer 1

To find the height where the arrow hit the melon, we need to set the two equations equal to each other and solve for x:

- (x - 2) ^ 2 + 9 = 7/3 * x + 1
- x^2 - 4x + 4 + 9 = 7/3 * x + 1
- x^2 - 4x + 13 = 7/3 * x + 1
- 3x^2 - 12x + 39 = 7x + 3
- 3x^2 - 19x + 36 = 0

Now we can solve this quadratic equation for x. By factoring or using the quadratic formula, we find that x = 3 or x = 4.

Substitute x = 3 into either equation to find the height where the arrow hit the melon:

y = 7/3 * 3 + 1
y = 7 + 1
y = 8

Therefore, the arrow will hit the melon at a height of 8 feet.