Question

The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of a roller coaster is 30 feet above the ground.

1. Write the equation that models the height of the roller coaster.

a. Start by writing the equation of the circle. (Remember that the general form of a circle with the center at the origin is x^2 + y^2 = r^2

b. Now solve this equation for y. (Remember the roller coaster is above ground, so you are only interested in the positive root.

2. Graph the model of the roller coaster using the graphing calculator. Either sketch by hand or take a picture and paste the image below.

Answer 1

Explanation:

Part A

x^2 + y^2 = 30^2

I don't know if this is right or not. That would mean that the roller coaster has no clearance and at the lowest point, it would scrape the ground (although not enough to dig a hole).

Part B

y^2 = 900 - x^2

y = sqrt(900 - x^2)

Part C

The graph is actually y = - sqrt(900 - x^2)

That's the only model I can come up with

The wording of the question does not allow for the condition that you want. (0,0) is not the center of the graph the way they want it. See the second graph).

Perhaps it means graph15b. I can't really tell.