hi,
i need the proof of the following equation:
y = (4Rx(L-2x)) / L^2
I shall be very thankful to you.

Relevant page
<a href="/applications-differentiation/applications-of-differentiation-intro.php">Applications of Differentiation</a>
What I've done so far
Tried to work out the proof, but couldn't

Like all mathematics equations, you need to state the situation and the meaning of each of the variables.

What does `y` represent here? What are `R` and `L`?

Let me know these and I may be able to help you.

X

Hi again Hasham
Like all mathematics equations, you need to state the situation and the meaning of each of the variables.
What does `y` represent here? What are `R` and `L`?
Let me know these and I may be able to help you.

y= length of parabola of a structure
R = vertical distance b/w highest point if parabola and supports
L = length of span lets say of a bridge
x= x coordinate of any point

basicaly the equation is to find out the length of a parabola lets say of a bridge or something.

X

hi, here is the information:
y= length of parabola of a structure
R = vertical distance b/w highest point if parabola and supports
L = length of span lets say of a bridge
x= x coordinate of any point
basicaly the equation is to find out the length of a parabola lets say of a bridge or something.

Ah, I see. "Length of parabola" possibly means the curve length, for which you need integration, not differentiation. See the last example on this page:

I think it best if you draw a diagram then we'll both be talking about the same thing.

Another point: "y= length of parabola of a structure" is not quite correct here - actually, `y` will be the height of the parabola `x` units from the origin.

X

Hello Hasham
Ah, I see. "Length of parabola" possibly means the curve length, for which you need integration, not differentiation. See the last example on this page:
<a href="/methods-integration/5-integration-other-trigonometric-forms.php">5. Integration: Other Trigonometric Forms</a>
Is that what you mean?
I think it best if you draw a diagram then we'll both be talking about the same thing.
Another point: "y= length of parabola of a structure" is not quite correct here - actually, `y` will be the height of the parabola `x` units from the origin.

hi,
now i attached the fig. i have to explain the things as posible to me.
w8ing for the solution.

X

hi,
now i attached the fig. i have to explain the things as posible to me.
w8ing for the solution.
<img src="/forum/uploads/parabola310.png" width="310" height"145" alt="parabola" />

Hmmm - your diagram is fine (it represents the parabola you were talking about at the beginning), but you now have `dy/dx` at the beginning, which is a bit confused.

To find the arc length of a parabola, you need integration, not differentiation.

So let's clarify - is your question asking for the arc length of this parabola?

X

Hmmm - your diagram is fine (it represents the parabola you were talking about at the beginning), but you now have `dy/dx` at the beginning, which is a bit confused.
To find the arc length of a parabola, you need integration, not differentiation.
So let's clarify - is your question asking for the arc length of this parabola?

OK, please post your actual question (which is not asking for a proof, nor for differentiating the expression) in the Applications of Integration forum.

X

OK, please post your actual question (which is not asking for a proof, nor for differentiating the expression) in the <a href="/forum/applications-of-integration-30/">Applications of Integration</a> forum.