Finding the area of a disk divided by a parabola function.

In summary, the parabola y=1/2 x^2 divides the disk x^2+y^2 <or= to 8 into two equal parts. The area of both parts can be found by calculating the area under the curve of the parabola and subtracting it from the area of the disk. It is suggested to draw a picture and find the points of intersection for a better understanding of the problem. There may be a transcription error in the question, as it seems one of the parts is significantly larger than the other.
  • #1
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Homework Statement


The parabola y=1/2 x^2 divides the disk x^2+y^2 <or= to 8 into two equal parts. Find the area of both parts.


Homework Equations





The Attempt at a Solution


I have no idea of how to go about solving this. We haven't done any application problems until now and when I transferred colleges they were several chapters ahead so I'm struggling as it is. If someone could give me a system to go about solving these and point me in the right direction I'd be very grateful.
 
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  • #2
Do you know how to calculate an area under a curve?
Do you know how to calculate an area between two functions?

Those two parts don't look equal to me.
 
  • #3
Drawing a picture seems like a good start. In particular, at what points do the two curves intersect?
 
  • #4
mfb said:
Those two parts don't look equal to me.
Agree, this question seems wrong as stated. One of the two "halves" will contain the entire bottom half of the disk and then some.
 
  • #5
I suspect a transcription error. Maybe the original says "unequal".
 

1. What is the formula for finding the area of a disk divided by a parabola function?

The formula for finding the area of a disk divided by a parabola function is A = πr2 / (2a), where r is the radius of the disk and a is the coefficient of the parabola function.

2. How do you determine the radius of the disk in this equation?

The radius of the disk is the distance from the center of the disk to the edge, and can be determined by finding the midpoint of the parabola's focus and vertex, and taking the distance from that point to the vertex.

3. Can this formula be used for any parabola function?

Yes, this formula can be used for any parabola function as long as the function is in the form y = ax2 + bx + c, where a is not equal to 0.

4. What is the significance of dividing the area of a disk by a parabola function?

Dividing the area of a disk by a parabola function allows us to determine the portion of the disk that is covered by the parabola, which can have various real-world applications in fields such as engineering and physics.

5. Are there other methods for finding the area of a disk divided by a parabola function?

Yes, there are other methods such as using integral calculus or approximating the area using numerical methods. However, the formula A = πr2 / (2a) is the most straightforward and commonly used method for finding the area of a disk divided by a parabola function.

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