Answer:
a.)x² + y² = 900
b.)y = √900 - x²
Step-by-step explanation:
P.S - The exact equation is as follows :
As given,
The shape of the roller coaster is a half of a circle. Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
a.)
Equation of circle be x² + y² = r²
As given , leg of the roller coaster is 30 feet above the ground.
⇒ r = 30
⇒x² + y² = 30²
⇒x² + y² = 900
∴ we get
Equation of height of Roller coaster - x² + y² = 900
b.)
As we have, x² + y² = 900
⇒y² = 900 - x²
⇒y = √900 - x²
The equation that models the height of the roller coaster is [tex]y = \sqrt{900 -x^2[/tex]
The general equation of a circle is:
[tex]x^2 + y^2 = r^2[/tex]
From the complete question, the radius of the circle is 30 units.
This means that:
r = 30
So, we have:
[tex]x^2 + y^2 = 30^2[/tex]
Express 30^2 as 900
[tex]x^2 + y^2 = 900[/tex]
Subtract x^2 from both sides
[tex]y^2 = 900 -x^2[/tex]
Take square roots of both sides
[tex]y = \pm \sqrt{900 -x^2[/tex]
Remove the negative root
This is so because the roller coaster is above the ground, and the height will be positive.
So, we have:
[tex]y = \sqrt{900 -x^2[/tex]
Hence, the required equation is [tex]y = \sqrt{900 -x^2[/tex]
Read more about equations of circle at:
https://brainly.com/question/10244007
