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)

Answer 1

Answer:

$y = \sqrt{900 - x^2$

Step-by-step explanation:

Given

From the complete question, we have:

$r=30$ --- radius

Required

Expression for the height of the roller coaster

We have:

$x^2 + y^2 = r^2$ --- equation of circle

Substitute 30 for r

$x^2 + y^2 = 30^2$

$x^2 + y^2 = 900$

Since the roller coaster is half of the circle, the height is defined by y.

So: make y the subject

$y^2 = 900 - x^2$

Take square roots

$y = \sqrt{900 - x^2$

Hence, the height is:

$\sqrt{900 - x^2$