Intercept of Two Equations: y^2.5=1-x^1.5 and y=(a/b)*x

[yriverahernande]

Hello,

I have 2 equations and I have to find the intercept. The equations are:

y^2.5=1-x^1.5

y=(Rs/Rt)*x

In this equation Rs and Rt are constants and we need the solutions that will make x and y to be in between 0 and 1.

I have been trying but I get a warning message that I dont understand. Attach is a picture of what my code looks like. Any help will be appreciated.

[RichardJ]

Since the picture doesn't show the error message, it would be helpful if you told us what it is. Even better, post the worksheet (in the edit dialog, click on "Use advanced editor" at the top right).

[AlanStevens]

Why not just use a numerical solution

Alan

[yriverahernande]

Hello,

I need the euqations because I need to develop an equation.... If use values then I am not going to be able to develop the equation. here is a code. Any help will be appreciated!

[RichardJ]

Why do you need the equation? Like lturek, I don't think you will find a closed form solution. I also tried the Maple symbolic engine used in earlier versions of Mathcad, and it does not give anything useful either.

[lturek]

At the end you demand Mathcad to solve an equation like R*u^5+u^3-1=0 symbolically, which it can't do - like many other math packages, including On-line Wolfram Alpha. (u=x^0.5 and R=ratio^2.5).

I don't think that you will be able to get a closed solution to this equation.

There is no closed formula to solve an algebraic equation of fifth order.

But as Alan pointed out Mathcad can provide a numerical solution for any given ratio.

And you will get a pair (x,y) where both are in the range (0,1) for any positive ratio Rs/Rt.

I am not sure what you would need a closed expression for, but I guess the best you will be able to achieve is the creation of a lookup table for the values of x with respect to the value of the Ratio Rs/Rt which can be used by another (embedded?) program to provide the values.

[yriverahernande]

Hello,

We are trying to prove or disprove and provide an equation.

According to several sources the ratio from OB/OA=1/sqrt(y^2.5+x^1.5)

in the chart you see 2 examples: Example 1 and Example 2

The ratio is been calculated based on the distances for example:

OA=sqrt(x^2+y^2)

OB=sqrt (x^2+y^2)

But we need to get what will be x and y for point B....

we know the equations for the 2 curves and that they intersecpt....

y=(Rs/Rt)x

y^2.5+x^1.5=1

x and y will always be <=1

Looks to me that the ratio provided is wrong....

OB/OA=1/sqrt(Y^2.5+x^1.5).... WRONG!!!!!

So I am trying to provide a real equation....

[RichardJ]

It's not clear to me what defines the distance OA. The distance OB is the distance from the origin to the intersection of the curves y=(Rs/Rt)*x and y^2.5+x^1.5=1, but what is OA?

[StuartBruff]

YAIXA RIVERA HERNANDEZ wrote:

Hello,

We are trying to prove or disprove and provide an equation.

According to several sources the ratio from OB/OA=1/sqrt(y^2.5+x^1.5)

in the chart you see 2 examples: Example 1 and Example 2

The ratio is been calculated based on the distances for example:

OA=sqrt(x^2+y^2)

OB=sqrt (x^2+y^2)

But we need to get what will be x and y for point B....

we know the equations for the 2 curves and that they intersecpt....

y=(Rs/Rt)x

y^2.5+x^1.5=1

x and y will always be <=1

Looks to me that the ratio provided is wrong....

OB/OA=1/sqrt(Y^2.5+x^1.5).... WRONG!!!!!

So I am trying to provide a real equation....

I'm puzzled. Your equation relating x and y is the same as the expression in the sqrt in the ratio formula. By definition, this would appear to be 1? Furthermore, by inspection, there is only one value of B for each of the infinite number of A points lying along an arbitrary Rs/Rt line, which implies the ratio OB/OA has an infinite number of values ... and we're not just talking aleph-null here!

As there are several texts claiming that that the ratio formula is correct, I've clearly misunderstood the problem, am getting confused as to which x and y are meant (although if the x and y specify A, the ratio should always be <= 1) or there are some other constraints on the allowed values for A, or ...? Could you please clarify?

Stuart

[yriverahernande]

A is the actual point... is where we actually are... we are looking for a equation that will define the ratio betwwen the allowable to the actual...

the y^2.5+x^1.5=1 define the limit... the allowable.... thats why point B is there... it extend from A hope this make sense

[RichardJ]

I do not believe there is any closed form expression for the ratio OA/OB.

Do you actually need such an expression, or just a proof that the expression you have been given is wrong?

[yriverahernande]

Today I know that equation is wrong... Looks to me that is been used as an approximation. I am planning on doing it graphically.. and see if I find a pattern that will help find simplify my equation. Yep I agree there is no way this equation can be easily solve the way it is.

You guys are awesome!!!