Arranging & Combining Equations (problem)

  • Thread starter drsponge
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In summary, the two given equations, P = aR2T4 and E = p/bd2, can be combined and rearranged to derive an expression for a/b, which is a/b = Ed2/R2T4. To solve for a/b, the first equation can be divided by the corresponding side of the second equation, giving the solution bd2 = aR2T4/p/bd2.
  • #1
drsponge
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0
Figured it out!
 
Last edited:
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  • #2
drsponge said:

Homework Statement



P = aR2T4
and
E = p / bd2

(a and b are constants.)


Homework Equations



If these two equations are combined and rearranged an expression can be derived for a/b:
a / b = Ed2 / R2T4

Show how this has been done, step by step.

The Attempt at a Solution



I have no idea where to begin & I can't find good instruction anywhere on how to handle this.
An obvious first step would be to divide each side of the first equation by the corresponding side of the second equation.
 
  • #3
drsponge said:

Homework Statement



P = aR2T4
and
E = p / bd2

(a and b are constants.)


Homework Equations



If these two equations are combined and rearranged an expression can be derived for a/b:
a / b = Ed2 / R2T4

Show how this has been done, step by step.

The Attempt at a Solution



I have no idea where to begin & I can't find good instruction anywhere on how to handle this.

Are little p and big P the same variable? In the final equation they don't appear so I would assume you solve for P in one equation and plug it into the other equation for P.
 
  • #4
scurty said:
Are little p and big P the same variable? In the final equation they don't appear so I would assume you solve for P in one equation and plug it into the other equation for P.


Sorry they're the same variable.
 
  • #5
Mark44 said:
An obvious first step would be to divide each side of the first equation by the corresponding side of the second equation.

I don't know how this would go though? Divide both sides by P / bd2 to give bd2 = aR2T4 / p / bd2?
 

1. What is the purpose of arranging and combining equations?

The purpose of arranging and combining equations is to simplify and solve complex mathematical problems. By rearranging and combining equations, we can manipulate the given information to make it easier to solve for a particular variable or to find a specific solution.

2. What are some common methods for arranging and combining equations?

Some common methods for arranging and combining equations include substitution, elimination, and graphing. These methods involve manipulating the equations in different ways, such as substituting one equation into another or adding/subtracting equations to eliminate variables.

3. How can I know when to use each method for arranging and combining equations?

The method you choose will depend on the specific problem and the given equations. It is important to carefully analyze the problem and determine which method will be most effective in solving it. Some methods may be more suitable for certain types of equations or variables.

4. Can I use arranging and combining equations in real-world situations?

Yes, arranging and combining equations can be applied to real-world problems, such as calculating distances, rates, and proportions. Many scientific and engineering fields use these methods to solve practical problems and make predictions based on data.

5. Are there any tips for effectively arranging and combining equations?

Some helpful tips for arranging and combining equations include keeping your work organized, carefully checking your calculations, and practicing with different types of problems. It is also important to understand the basic rules of algebra, such as the properties of equality and the order of operations.

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