Silly question about exact equations.

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In summary, exact equations are mathematical expressions with a precise and unambiguous meaning that are used in scientific fields to describe relationships between variables and can be solved to find specific values. They differ from other types of equations in that they have a specific meaning and can be solved for precise values. Examples of exact equations include the ideal gas law, Newton's second law of motion, and the Pythagorean theorem. They are used in scientific research to describe and analyze relationships, make predictions, and test hypotheses. While they can be applied to many scientific fields, their specific applications may vary.
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Paintjunkie
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Can you manipulate any exact equation to be a first order linear equation? if you are not concerned with which variable is the dependant one and which is the independant one. i.e. dx/dy or dy/dx?
 
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Certainly not. For example [itex]cos(x)dy- sin(x)dx= 0[/itex] is an exact equation but we cannot get rid of those trig functions.
 

FAQ: Silly question about exact equations.

1. What are exact equations?

Exact equations are mathematical expressions that have a precise and unambiguous meaning. They are typically used in scientific fields to describe the relationship between different variables and can be solved to find specific values.

2. How are exact equations different from other types of equations?

Exact equations are different from other types of equations because they have a specific and unambiguous meaning, whereas other types of equations may be more general or open to interpretation. Additionally, exact equations can be solved to find specific values, while other types of equations may only be used to describe a relationship between variables.

3. What are some examples of exact equations?

Examples of exact equations include the ideal gas law, Newton's second law of motion, and the Pythagorean theorem. These equations have a specific meaning and can be solved to find precise values.

4. How are exact equations used in scientific research?

Exact equations are used in scientific research to describe and analyze relationships between different variables. They can also be used to make predictions and test hypotheses. Scientists often use exact equations to model real-world situations and make calculations based on the known values of variables.

5. Can exact equations be applied to all scientific fields?

Exact equations can be applied to many different scientific fields, including physics, chemistry, biology, and engineering. However, their specific applications may vary depending on the field and the specific variables being studied. Some fields may also have their own unique set of exact equations that are commonly used in research and calculations.

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