Help me cut the area under a parabola in half

In summary, to cut the area under a parabola in half, you can use the formula A = (1/3) * b * h, where b is the base and h is the height. This can be achieved by changing either the base or the height while keeping the other variable constant. However, this will ultimately change the shape of the parabola. There are multiple methods to cutting the area in half, such as using calculus or geometric principles. Any parabola can be used for this, but the method may differ depending on the parabola's shape and orientation. To visualize cutting the area in half, you can use a ruler or online graphing tools to manipulate the parabola and see the effects
  • #1
Tennisgoalie
4
0
The problem is: Consider the area under the curve f(x)=2x-x2 and above the x axis. Find the equation of the line through the origin that cuts this area into two equal parts.
 
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  • #2
Here is a link to a very similar problem, and from this you may see how to work this problem:

http://mathhelpboards.com/questions-other-sites-52/phyllis-question-yahoo-answers-regarding-finding-line-divides-area-into-equal-parts-7197.html

Now, please feel free to post your progress using the above as a guide if you get stuck, and we will be glad to offer further guidance. :D
 

FAQ: Help me cut the area under a parabola in half

How can I cut the area under a parabola in half?

To cut the area under a parabola in half, you can use the formula for finding the area under a parabola: A = (1/3) * b * h, where b is the base of the parabola and h is the height. To cut the area in half, you can either decrease the base or increase the height, while keeping the other variable constant.

Can I cut the area under a parabola in half without changing the shape of the parabola?

No, cutting the area under a parabola in half will require changing either the base or the height, which will ultimately change the shape of the parabola. However, you can still maintain the general shape of the parabola while cutting the area in half.

Is there a specific method to cutting the area under a parabola in half?

There are multiple methods to cutting the area under a parabola in half. One method is by using calculus to find the area under a specific portion of the parabola. Another method is by using geometric principles, such as finding the mid-point of the parabola's base and drawing a line to the vertex, which will cut the area in half.

Can I use any parabola to cut the area in half?

Yes, you can use any parabola to cut the area in half as long as you have the base and height measurements. However, the method used to cut the area in half may differ depending on the shape and orientation of the parabola.

How can I visualize cutting the area under a parabola in half?

To visualize cutting the area under a parabola in half, you can graph the parabola and use a ruler or straight edge to physically divide the area in half. You can also use online graphing tools or software to manipulate the parabola and see how changing the base or height affects the area.

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