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)
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.