Bot GPT 4-o mini To determine how far the golf ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \) for the given function:
\[ h(x) = -\frac{1}{25}x(x - 45). \]
Setting \( h(x) = 0 \):
\[ -\frac{1}{25}x(x - 45) = 0. \]
This gives us two solutions:
- \( x = 0 \)
- \( x - 45 = 0 \) → \( x = 45 \)
Thus, the ball will hit the ground after it has traveled 45 yards.
Now, since the hole is 55 yards away, we can calculate how far the ball will need to roll to reach the hole:
\[ \text{Distance to the hole} - \text{Distance traveled before hitting ground} = 55 - 45 = 10 \text{ yards}. \]
So, the ball will need to roll an additional 10 yards to reach the hole.
The correct response is:
The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.
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