16. Beginning at 8:30 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Cap
itol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time? Every 15 minutes Every 30 minutes Every 45 minutes Every 60 minutes
1. The function H= -16T^2+80T+5 is a parabola of the form , so to find the maximum height of the ball, we are going to find the y-coordinate of the vertex of the parabola. To find the y-coordinate of the vertex we are going to evaluate the function at the point . From our function we can infer that and , so the point \frac{-b}{2a} [/tex]will be . Lets evaluate the function at that point:
We can conclude that the ball reaches a maximum height of 105 feet.
2. Since we now know that the maximum height the ball reaches is 105 feet, we are going to replace with 105 in our function, then we are going to solve for to find how long the ball takes to reach its maximum height:
We can conclude that the ball reaches its maximum height in 2.5 seconds.
3. Just like before, we are going to replace with 5 in our original function, then we are going to solve for to find how long will take for the ball to be caught 5 feet off the ground:
We can conclude that it takes 5 seconds for the ball to be caught 5 feet off the ground.
The picture of the question in the attached figure N 1
we know that
The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)
see the attached figure N 2 to better understand the problem
step 1
Find the area of the two trapezoids (#1 and #2)
simplify
we have
substitute
step 2
Find the area of the two smaller rectangles (#3 and #4)
we have
substitute
step 3
Find the area of the walkway around the rectangular pool