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)

y = √(900 - x²)

Step-by-step explanation:

The equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where (h,k) is the coordinate of the circle center, r is the radius of the circle.

Since the circle is at the origin, the equation of the circle is given by:

(x - 0)² + (y - 0)² = r²

x² + y² = r²

the highest point on this leg of the roller coaster is 30 feet above the ground, therefore the radius of the circle is 30 ft.

x² + y² = 30²

x² + y² = 900

we need to make y the subject of formula. First, subtract x² from both sides:

x² + y² - x² = 900 - x²

y² = 900 - x²

taking square root of both sides:

y = √(900 - x²)

The equation that models the height of the roller coaster is given by:

y = √(900 - x²)