Answer:
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)
