Question
During a water balloon fight Louise uses a slingshot to fire water balloon over the fortified wall of opponent when fired from the slingshot the balloon will follow the path h * X = at -x + 12x were 8X is the height of the balloon in feet and X is a horizontal distance it will travel could it come how far the balloon will travel before it reaches the ground where we set the height equation to zero and solves the quadratic equations 0 equals negative x squared plus 12x how far will the balloon travel before it reaches the ground
Answers
GPT-4o mini
To determine how far the water balloon travels before it hits the ground, we will set the height equation \( h(x) = -x^2 + 12x \) to zero and solve for \( x \).
The equation is:
\[
0 = -x^2 + 12x
\]
Rearranging the equation gives:
\[
x^2 - 12x = 0
\]
We can factor this equation:
\[
x(x - 12) = 0
\]
Setting each factor to zero gives us the potential solutions:
1. \( x = 0 \) (the point where the balloon was launched)
2. \( x - 12 = 0 \) or \( x = 12 \)
From our calculations, \( x = 12 \) feet represents the distance the water balloon travels horizontally before it hits the ground.
Therefore, the balloon will travel **12 feet** before it reaches the ground.
The equation is:
\[
0 = -x^2 + 12x
\]
Rearranging the equation gives:
\[
x^2 - 12x = 0
\]
We can factor this equation:
\[
x(x - 12) = 0
\]
Setting each factor to zero gives us the potential solutions:
1. \( x = 0 \) (the point where the balloon was launched)
2. \( x - 12 = 0 \) or \( x = 12 \)
From our calculations, \( x = 12 \) feet represents the distance the water balloon travels horizontally before it hits the ground.
Therefore, the balloon will travel **12 feet** before it reaches the ground.