Direct/Inverse proportion

[_Muddy_]

hello

we have been covering direct and inverse proportion at school. Are there any other types of proprtion?

We've been coming across questions like:

x is directly proportion to Y

Then I've been told to write

X (the proportion sign, which is like 8 on its side) Y

X=ky

We are then given a value for x and a value for y and asked to work out k. I'm fine with that but I'm wondering why we have to put "k"? Why does that proportion sign turn into "K"?

Also i was looking at the friedmann equation and i saw it had a "k" in it. When i see a physics equation like that will the K usually mean "constant" and will it have something to do with proportion?

thanks _Muddy_

 

[symbolipoint]

Any proportionality constant, if consistantly applied in the situation can be used; whether k, or c, or R, or K, or C, or anything which you can accept as a constant. Just understand that case-level really matters, so that k is a different number than K. x is a different number than X. Be consistant with your use of variables.

 

[symbolipoint]

In case it helps, direct variation means that the RATIO between two numbers is a constant. When you express that x=ky, and that k is the proportionality constant, then we equivalently mean x/y is a constant, and that this constant is k.

 

[maverick_starstrider]

k is just a constant (it is a number). The fact that you use k is entirely arbitrary, you could have used a,b,c,d,e,f,g,h,i,a happy face, the peace sign whatever (although usually it is convention to use the beginning of the alphabet (a,b,c) to represent constants and the end to represent variables (x,y,z). The reason the proportional sign turn into a constant is because when you say something is PROPORTIONAL it doesn't mean 1 to 1 (i.e. if I have one person standing in a room I have (assuming they are properly attired) 2 shoes in the room (they have one on each foot). If another person enters the room you then have FOUR shoes. Therefore, the number of shoes in the room is PROPORTIONAL to the number of people but it is in fact TWICE the number of people therefore (# of people) time 2 = # of shoes. So in that case the porportionality 'constant' is 2. What if I considered limbs (2 arms, 2 legs) then, for each person in the room I have 4 times as many limbs so the proportionality constant is 4. And so on.

And yes there are more then just direct and inverse. For example, in physics the force that two charged particles feel towards each other is proportional to the inverse of the SQUARE of their distances (i.e. Force is proportional to 1/(distance)^2 so it's F = c/(distance)^2 where c is just a constant)