Y=cx[L−x], The value of the constant c for a perfect circle

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Homework Statement


For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters.
What would be the value of the constant c for a perfect circle.

3. Attempt at the Solution:
I can approximate and graph this with different values of c however I'm really interested in what is the precise value of c for a perfect circle. I would have to at this point just plug in "1" and see what comes out which really isn't where I wanted to be after reading:
http://www.engineeringwiki.org/wiki/Arch_Structures

Thank You!
 
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  • #2
berkeman
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Homework Statement


For the equation y=cx[L−x] say for a circle with the value of L at 100 meters and the value of x at 25 meters.
What would be the value of the constant c for a perfect circle.

3. Attempt at the Solution:
I can approximate and graph this with different values of c however I'm really interested in what is the precise value of c for a perfect circle. I would have to at this point just plug in "1" and see what comes out which really isn't where I wanted to be after reading:
http://www.engineeringwiki.org/wiki/Arch_Structures

Thank You!
Are you sure that's the equation? Looks more parabolic to me than a circle...
 
  • #3
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I agree. That isn’t a circle. Also, what could it possibly mean about being a circle at a particular value of x? This problem seems to be nonsense
 
  • #4
member 634857
A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ???
 
  • #5
member 634857
That's OK I can probably figure this out myself without help!
 
  • #6
berkeman
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A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ???
The equations have different forms. Do you see how the powers of the variables are different for the different conic sections?
 
  • #8
member 634857
I apologize but that doesn't answer my question as well I was insulted first and your the insults I'm afraid. I wish to dissolve my account at this point. The services of your members are no longer required by me.
 
  • #9
berkeman
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Thread is closed for a bit...
 
  • #10
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A circle is simply a form then of conic and so is a parabola. They should overlap at some point. ???
As already mentioned, the equations are different. The equation for a parabola is first degree in one variable and second degree in the other variable. For a circle, both variable occur to the second power. I don't know what you mean by "they should overlap at some point."

The equation that @berkeman shows in the table, ##y^2 = 4ax## is of a parabola that opens to the right (if a > 0). The equation ##x^2 = 4ay## is that of a parabola that opens upward.

Your equation, ##y = cx(L - x)## is a parabola that opens downward, assuming that both c and L are positive constants. There is no value of c that makes this the equation of a circle.
 
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  • #11
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I was insulted first and your the insults I'm afraid
No, you weren't insulted. Members here were questioning the validity of the question you asked -- these were not insults, nor were they directed to you.
 

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