Mathematics High School

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) Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root. (10 points)

Answers

Answer 1

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

1. Write The Equation That Models The Height Of The Roller Coaster. Start By Writing The Equation Of
Answer 2

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

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