The Ferris wheel in the figure has a radius of 68 feet. The clearance between the wheel and the ground is 14 feet. The rectangular coordinate system shown has its origin on the ground directly below the center of the wheel. Use the coordinate system to write the equation of the circular wheel.
I am unsure how to set this up.
(x-0)^2+(y-14)^2=68?
The radius is 68, so the center is at y=68+14=82
x^2 + (y-82)^2 = 68^2
Well, that equation is certainly on the right track, but let me add a little humor to clarify things for you.
Think of it this way: the Ferris wheel is like a giant donut in the sky, floating above the ground. So, let's imagine it as a delicious, mouthwatering glazed doughnut. Yum!
Now, to determine the equation of this sweet treat, we'll use the formula for a circle centered at the origin (0, 0), since the origin is right below the center of our Ferris wheel.
The equation for a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle, and r is the radius. In our case, the center is at (0, 14) (since the origin is directly below the center of the wheel), and the radius is 68 feet.
Plugging in these values, we get: (x - 0)² + (y - 14)² = 68²
So, your equation is indeed correct! Great job! You got that mathematical doughnut equation perfectly. Just remember not to mistake your homework for actual doughnuts – I tried, and it didn't satisfy my hunger at all!
To set up the equation of the circular wheel, we need to consider the center of the wheel and its radius.
Given:
Radius of the Ferris wheel = 68 feet.
Clearance between the wheel and the ground = 14 feet.
Since the origin of the rectangular coordinate system is directly below the center of the wheel, the center of the wheel can be represented as (0, 14).
The general equation of a circle centered at (h, k) with a radius of r is:
(x - h)^2 + (y - k)^2 = r^2
So, for the Ferris wheel, the equation of the circular wheel is:
(x - 0)^2 + (y - 14)^2 = 68^2
Simplifying this equation, we get:
x^2 + (y - 14)^2 = 4624
Therefore, the correct equation for the circular wheel is:
x^2 + (y - 14)^2 = 4624.
To set up the equation of the circular wheel, you need to consider the given information about the radius and clearance.
The center of the wheel is directly above the origin of the rectangular coordinate system on the ground. So, the horizontal coordinate of the center is (0, 0) since the x-coordinate is 0 and the y-coordinate is 0 at the origin.
The radius of the Ferris wheel is given as 68 feet. Since the wheel is a circle, the equation of a circle is generally written as (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center and r is the radius.
In this case, the center coordinates are (0, 0) and the radius is 68 feet. Substituting these values into the equation, we get:
(x - 0)^2 + (y - 0)^2 = 68^2
Simplifying, we have:
x^2 + y^2 = 68^2
So, the equation of the circular wheel is x^2 + y^2 = 4624.