Question

1. write the equation that models the height of the roller - coaster.

start by writing the equation of the circle. (recall that the general form of a circle with the center at the origin is x² + y² = r². (10 points))
now solve this equation for y. remember the roller - coaster is above ground, so you are only interested in the positive root. (10 points)

Explanation:

Step1: Write the circle - equation

The general form of a circle with center at the origin is $x^{2}+y^{2}=r^{2}$.

Step2: Solve for y

Starting from $x^{2}+y^{2}=r^{2}$, we can isolate $y^{2}$:
$y^{2}=r^{2}-x^{2}$
Since we are interested in the positive root (roller - coaster is above ground), we get $y = \sqrt{r^{2}-x^{2}}$.

Answer:

$y = \sqrt{r^{2}-x^{2}}$