Express t and s as functions of x and y given

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In summary, the problem is to express t and s as functions of x and y given the equations x = -(2t+1)*s/(t^2-1) and y = e^(t + ln|s|). The suggested solution is to use substitution, resulting in t = sqrt(1-s/x) and s = e^(-t)y. However, this leads to a loop and it is not possible to find a clear expression for T(x,y) and S(x,y). The question arises whether this is necessary or if there is another way to approach the problem.
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Homework Statement

How do I express t and s as functions of x and y given

x = -(2t+1)*s/(t^2-1)
y = e^(t + ln|s|)
I keep getting stuck in a loop.


Homework Equations



substitution

The Attempt at a Solution



x= -(2t+1)*s/(t^2-1) I get t = sqrt(1-s/x)

t = sqrt(1-s/x)

s = e^(-t)y

substituting the terms in either expression gets me stuck in a loop. What am I doing wrong?

what I need is t = T(x,y) and s = S(x,y). The other important part is that s needs to stay any real number.

Thanks!
 
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I don't think you have a prayer of finding a nice expression for T and S. Why do you want to do this? Ask yourself if you really have to.
 

FAQ: Express t and s as functions of x and y given

1. What does the term "express t and s as functions of x and y given" mean?

The phrase "express t and s as functions of x and y given" refers to the process of finding mathematical equations that represent the variables t and s in terms of the variables x and y. This means that the values of t and s can be determined using the values of x and y, according to the given equations.

2. How is the process of expressing t and s as functions of x and y given useful in science?

Expressing t and s as functions of x and y given is useful in science because it allows for the understanding and prediction of relationships between different variables. These equations can be used to make calculations, create models, and make predictions about the behavior of a system.

3. What are some common techniques used to express t and s as functions of x and y given?

Some common techniques used to express t and s as functions of x and y given include algebraic manipulation, substitution, and elimination. These techniques involve using mathematical operations to rearrange equations and solve for the desired variables.

4. Are there any limitations to expressing t and s as functions of x and y given?

Yes, there can be limitations to expressing t and s as functions of x and y given. In some cases, it may not be possible to find a single equation that represents t and s in terms of x and y. Additionally, the accuracy of the equations may also be limited by the accuracy of the data used to create them.

5. Can we express t and s as functions of x and y given in any coordinate system?

Yes, t and s can be expressed as functions of x and y given in any coordinate system. However, the specific equations and techniques used may vary depending on the coordinate system being used. It is important to use the appropriate coordinate system for the given problem or situation.

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