Going from proportional to equals

In summary, to go from proportional to equals, you need to determine the constant of proportionality and then set up an equation to solve for the unknown variable. The constant of proportionality is represented by the letter "k" and remains the same even when the quantities are equal. You can find the constant of proportionality by dividing one quantity by the other. An example of going from proportional to equals is setting up an equation where y = x and solving for x. The main difference between proportional and equals is that proportional means the two quantities are related by a constant, while equals means the two quantities are exactly the same. You can go from equals to proportional by setting up a proportion equation where x/y = k and solving for k.
  • #1
Hazzattack
69
1
Hi guys,

This may well be a very trivial question but it isn't immediately obvious to me..

I know if you have x is proportional to y by adding a constant you can say;

x = cy

However, if we have x is proportional to y + z, is there a similar 'trick' that can be used?

Basically, i have an expression;

J(w) [itex]\propto[/itex] [w-w0]^1/2 + [w0 - w]^1/2

and want to set this equal.

Thanks in advance!
 
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  • #2
x=c*(y+z)
 
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Likes 1 person
  • #3
Ok great, so it is trivial. Thanks Arildno :)
 

1. How do you go from proportional to equals?

To go from proportional to equals, you need to determine the constant of proportionality and then set up an equation to solve for the unknown variable. The constant of proportionality is the number that relates the two proportional quantities, and it remains the same even when the quantities are equal.

2. What is the constant of proportionality?

The constant of proportionality is the number that relates the two proportional quantities. It is represented by the letter "k" and remains the same even when the quantities are equal. You can find the constant of proportionality by dividing one quantity by the other.

3. Can you give an example of going from proportional to equals?

Sure! Let's say you have the proportional relationship y = 3x, where y is proportional to x with a constant of proportionality of 3. To go from proportional to equals, you would set up an equation where y = x and solve for x. In this case, x would equal y/3.

4. What is the difference between proportional and equals?

The main difference between proportional and equals is that proportional means the two quantities are related by a constant, while equals means the two quantities are exactly the same. In other words, proportional quantities vary together, while equal quantities have the same value.

5. Can you go from equals to proportional?

Yes, you can go from equals to proportional by setting up a proportion equation. An example of this would be if you have two equal quantities, x and y, and you want to find the constant of proportionality between them. You would set up the equation x/y = k, where k is the constant of proportionality, and then solve for k.

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