Simplifying the Equation for a Circle: r2 = 20 - 4θ + 10θ2

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In summary, eliminating parameters in scientific research serves to narrow down the focus of a study and improve the accuracy of the results. This can increase the validity of the study by reducing the potential for confounding variables. Common methods for eliminating parameters include randomization, control groups, and statistical techniques. However, there are limitations to this approach, such as limited generalizability and the difficulty of completely eliminating all potential variables. Scientists must carefully consider the parameters to eliminate based on their research question and consult with other experts for guidance.
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Lurid
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Homework Statement



Eliminate the parameter:

x=2-3θ
y= 4+θ

Homework Equations



x2 + y2 = r2

The Attempt at a Solution



[x=2-3θ]2; [y= 4+θ]2

x2= 4-12θ+9θ2
y2= 16+8θ+θ2
-------------------------------------
x2+y2 = 20 - 4θ + 10θ2

r2 = 20 - 4θ + 10θ2

Is there another step that I can take to simplify this expression further?
 
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  • #2
From the statement "eliminate the parameter", and assuming the parameter is θ, I would more expect you would have to establish a direct relation between x and y (that is, eliminate θ from the two equations to form one equation involving only x and y).
 

FAQ: Simplifying the Equation for a Circle: r2 = 20 - 4θ + 10θ2

What is the purpose of eliminating parameters in scientific research?

The purpose of eliminating parameters is to narrow down the focus of a study and reduce the number of variables that could potentially affect the results. This allows for a more precise and accurate analysis of the data.

How does eliminating parameters impact the validity of a study?

Eliminating parameters can increase the validity of a study by reducing the potential for confounding variables, which could skew the results. By controlling for certain factors, researchers can have more confidence in the accuracy of their findings.

What are some common methods for eliminating parameters in scientific experiments?

Some common methods for eliminating parameters include randomization, control groups, and statistical techniques such as regression analysis or ANOVA. These methods help to isolate specific variables and minimize their impact on the results.

What are the potential limitations of eliminating parameters in research?

Eliminating parameters can limit the generalizability of a study, as it may not accurately reflect real-world conditions. Additionally, it may be difficult to completely eliminate all potential variables, which could still impact the results.

How can scientists determine which parameters to eliminate in their research?

The parameters to eliminate will depend on the specific research question and the variables that are most relevant to it. Scientists may conduct pilot studies or consult with other experts in their field to determine which parameters are most important to control for in their research.

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