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The shape of this particular section of the rollercoaster 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. 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)

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timofay14 timofay14 · Answer 1 · 2017-12-05T19:19:35+01:00

Best Answer: 1.)
x^2 + y^2 = 30^2 since the radius is 30 ft
x^2 + y^2 = 900

2.)
Solving for y
y = √(900 - x^2)

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swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-04-06T11:48:22+02:00

The equation that models the height of the roller is y = root (900-x^2).

We have given that the,

Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

[tex]x^2+y^2=r^2[/tex]

Where r is the radius

From given we can say that the radius =30

[tex]x^2 + y^2 = 30^2[/tex]

since the radius is 30 ft

[tex]x^2 + y^2 = 900[/tex]

We have to find the equation that can be represent the height of the roller coaster so find the value of y

Solving for y

[tex]x^2 + y^2 = 900[/tex]

Subtract x^2 from both side we get,

[tex]y = \sqrt{(900 - x^2) }[/tex]

Therefore the models the height of the roller coaster y equal to square root of 900-x square

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