The Apollo's chariot, a rollercoaster at Busch gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation h(t)=-16t^2+101t+10. What is the maximum height reached my this ride?

169.39 feet.

Step-by-step explanation:

We have been given that the Apollo's chariot, a roller coaster at Busch gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation . We are asked to find the maximum height that the ride can reach.

To  find the maximum height that the ride can reach, we need to find y-coordinate of vertex of parabola because our given equation is downward opening parabola and its maximum point will be the vertex.

First of all, we will find x-coordinate of vertex using formula .

Now, we will substitute in our equation to find y-coordinate of vertex as:

Therefore, the ride will reach to a maximum height of 169.39 feet.169.39 feet.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3