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 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 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 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 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. Skip to navigation
To determine how far the ball will have traveled when it hits the ground, we need to solve the equation 0 = -125x(x - 45).
Step 1: Set the equation equal to zero:
0 = -125x(x - 45)
Step 2: Factor out the common factor, x:
0 = -125x^2 + 5625x
Step 3: Set each factor equal to zero and solve for x:
-125x^2 + 5625x = 0
Factor out -125x:
-125x(x - 45) = 0
Set each factor equal to zero:
-125x = 0 or x - 45 = 0
Solve for x in each equation:
x = 0 or x = 45
Step 4: Determine the valid solution:
Since the distance cannot be negative, we can disregard the solution x = 0.
Therefore, the ball will hit the ground after it has traveled 45 yards.
To determine how far the ball will need to roll to reach the hole, we need to find the remaining distance from the ground to the hole, which is 55 yards - 45 yards = 10 yards.
Therefore, the ball will need to roll an additional 10 yards to reach the hole.
To find how far the ball will have traveled when it hits the ground, we need to solve the equation:
0 = -125x(x-45)
To do this, we can set each factor equal to zero and solve:
-125x = 0
x = 0
or
x - 45 = 0
x = 45
So the ball will hit the ground after it has traveled 45 yards.
To find how far the ball will need to roll to make it to the hole, we need to find the horizontal distance the ball has traveled when the height is zero.
So, we set h(x) = 0 and solve:
-125x(x - 45) = 0
Setting each factor equal to zero:
-125x = 0
x = 0
or
x - 45 = 0
x = 45
So the ball will need to roll an additional 45 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 45 yards to reach the hole.
To determine how far the ball will have traveled when it hits the ground, we need to solve the equation h(x) = 0.
Given the equation h(x) = -125x(x-45), we set it equal to zero:
0 = -125x(x-45)
To solve this quadratic equation, we can either factorize it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -125, b = 0, and c = -125 * 45.
Plugging these values into the formula, we have:
x = (0 ± √(0^2 - 4*(-125)*(-125*45))) / (2*(-125))
Simplifying the formula, we have:
x = ± √(0 + 250 * 125 * 45) / -250
x = ± √(562500) / -250
Since distance cannot be negative in this context, we take the positive root and simplify further:
x = 750 / -250
x = -3
So, the ball will hit the ground after it has traveled 3 yards.
Now, to determine how far the ball needs to roll to make it to the hole, we need to subtract the distance traveled in the air from the total distance of 55 yards.
Distance rolled = Total distance - Distance traveled in the air
Distance rolled = 55 - 3
Distance rolled = 52
Therefore, the ball needs to roll an additional 52 yards to reach the hole.