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In 2008, the Singapore Flyer opened up as the world's largest Ferris wheel. It has a maximum height of 165 meters and a diameter of 150 meters, with one full rotation taking about 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis also known as the x = 0 line.
Let's see what I can do here.
If x = o, then the center is (0, y) = (h, k).
The height of the wheel is 165 meters which is the diameter.
I say the value of y is halfway up the wheel.
So, y = 165/2 = 82.5 meters.
This leads to the center point being (0, 82.5).
The radius is r.
r = (1/2)(150) = 75 meters.
I now have the radius and center point.
I think the next step is to plug this information into the standard form of an equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Is this correct so far?
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
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You haven't allowed for any clearance at the bottom with the ground.
The maximum height is 165; subtract the diameter and the lowest point must be 15m off the ground.
So the centre is at 15 + 75 up the y axis.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
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You haven't allowed for any clearance at the bottom with the ground.
The maximum height is 165; subtract the diameter and the lowest point must be 15m off the ground.
So the centre is at 15 + 75 up the y axis.
Bob
So the center is located at (0, 90).
r = 75
(x - h)^2 + (y - k)^2 = r^2
(x - 0)^2 + (y - 90)^2 = (75)^2
x^2 + (y - 90)^2 = 5625
Yes?
Last edited by mathxyz (2024-03-02 18:19:34)
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
Offline
Yes!
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
Yes!
Bob
Good. This is a tough application. To go through it slowly and carefully reaching the right answer is a satisfying feeling of accomplishment.
The greatest truth about the Rapture is not its timing but it's reality.
Dr. David Jeremiah
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