A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−125x(x−45), where h(x) is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole? 0=−125x(x−45) (1 point) Responses 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. 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. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole. The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole. The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole.
The function h(x)=−125x(x−45) represents the height of the golf ball at any given horizontal distance x. To determine when the ball hits the ground, we need to find the values of x when h(x)=0.
Setting h(x)=0, we have −125x(x−45)=0.
This equation is true when either −125x=0 or x−45=0.
-125x=0 implies that x=0. However, we are given that the ball is already 55 yards away, so x=0 is not a valid solution.
x−45=0 implies that x=45.
Therefore, the ball will hit the ground after it has traveled 45 yards.
To determine how far the ball needs to roll to reach the hole, we need to find the total distance traveled by the ball. Since the ball has already traveled 45 yards in the air, we need to find the additional distance it needs to roll to reach the hole, which is 55 yards.
Hence, the ball will need to roll an additional 10 yards to reach the hole.
Therefore, 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.
To find out how far the ball will have traveled when it hits the ground, we need to solve the equation:
0 = −125x(x−45)
Let's solve it step by step:
1. Expand the equation:
0 = −125x^2 + 5625x
2. Move all terms to one side of the equation:
125x^2 - 5625x = 0
3. Factor out the common term of 125x:
125x(x - 45) = 0
4. Set each factor equal to zero and solve for x:
125x = 0
x = 0
x - 45 = 0
x = 45
So, the ball will hit the ground after it has traveled 45 yards.
To determine how far the ball will need to roll to make it to the hole, we need to subtract the distance it has traveled already (45 yards) from the total distance to the hole (55 yards):
55 - 45 = 10
Therefore, 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.
To determine how far the ball will have traveled when it hits the ground and how far it needs to roll to make it to the hole, we need to solve the equation 0 = -125x(x - 45).
To solve this quadratic equation, we can set it equal to zero and then factor it:
-125x(x - 45) = 0
Now we have two factors, -125x = 0 and (x - 45) = 0. Solving each equation separately gives us:
-125x = 0
x = 0
(x - 45) = 0
x = 45
So, the ball will hit the ground after it has traveled 45 yards.
To determine the distance it needs to roll to make it to the hole, we subtract 45 from the total distance of 55 yards:
55 - 45 = 10
Therefore, the ball will need to roll an additional 10 yards to reach the hole.
So the correct answer 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.