Answer: 42.25 feet
Step-by-step explanation:
We know that after "t" seconds, its height "h" in feet is given by this function:
The maximum height is the y-coordinate of the vertex of the parabola. Then, we can use the following formula to find the corresponding value of "t" (which is the x-coordinate of the vertex):
In this case:
Substituting values, we get :
Substituting this value into the function to find the maximum height the ball will reach, we get:
Answer:
Here is the full question:
Another plan to secure the roller coaster involves placing two concrete struts on either side of the center of the leg of the roller coaster to add reinforcement against southerly winds in the region. Again, using the center of the half-circle as the origin, the struts are modeled by the equations and . A vertical reinforcement beam will extend from one strut to the other when the two cables are 2 feet apart.
Graph the two struts on the model of the roller coaster. Take a screenshot of your graph and paste the image below, or sketch a graph by hand.
Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.
(a) Algebraically determine the x -value of where the beam should be placed.
(b) Explain where to place the beam
Step-by-step explanation:
Find attached the graphing calculator.
(a) The x-value where the beam should be placed is x = -4
(b) The beam should be placed directly above 4 feet from the center.
