What is the equation of the height of a roller coaster that is 30 feet above the ground, is in a shape of a half circle and the general form of a circle with the center at the origin is x2 +y2 = r2?

Step-by-step explanation:

The general form of a circle is: (x - h)² + (y - k)² = r² ; where

(h, k) is the centerr is the radius

Since the roller coaster is centered at the origin, then (h, k) = (0, 0)

Since the height of the roller coaster is 30, then radius (r) = 0

Equation of the circle is: (x - 0)² + (y - k)² = 30²

⇒ x² + y² = 900

To find the equation of the semicircle, solve for "y"

x² + y² = 900

      y² = 900 - x²

     

     

Since we are looking for the top half of the semicircle (because it is above ground), then use the positive root:  

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12