1. ## Writing a formula...

Write a formula representing the following function. Use k as the proportionality constant.
The strength, S, of a beam is proportional to the cube of its thickness, h.

S(h) = ?

I'm not even 100% sure what this problem means. Can someone direct me towards how I'm suppose to solve this?

2. Originally Posted by JAMESveeder
Write a formula representing the following function. Use k as the proportionality constant.
The strength, S, of a beam is proportional to the cube of its thickness, h.

S(h) = ?

I'm not even 100% sure what this problem means. Can someone direct me towards how I'm suppose to solve this?

This problem is deceptive in its simplicity:

$S(h)=k\cdot h^3$

Something that is proportional to another thing simply means that the two things will have a constant ratio. The k is the proportionality constant because its magnitude determines this ratio. If they had a ratio of 1:1, k would = 1, such that the strength of the beam is exactly the same as its cube of thickness. If it was 0.5, the strength would be half of its cube of thickness...and so on.

3. Ah, but I'm still not exactly sure how you got that. How do the words match up to make the formula?

is k proportional to S?

Here's another question that I'm having trouble with...

Write a formula representing the following function.
The number of animal species, N, of a certain body length, L, is inversely proportional to the square of L. Use k as the proportionality constant.
I said N(L) = k*-L^2... But this is wrong. I'm not exactly sure what everything in the question means.

Edit: Nevermind, I got it right. N(L) = k/L^2

4. Originally Posted by JAMESveeder
I'm not even 100% sure what this problem means. Can someone direct me towards how I'm suppose to solve this?
To learn how to "translate", set up, and solve "variation" type exercises, try here.

5. Originally Posted by JAMESveeder
Ah, but I'm still not exactly sure how you got that. How do the words match up to make the formula?

is k proportional to S?

Here's another question that I'm having trouble with...

Write a formula representing the following function.
The number of animal species, N, of a certain body length, L, is inversely proportional to the square of L. Use k as the proportionality constant.
I said N(L) = k*-L^2... But this is wrong. I'm not exactly sure what everything in the question means.

Edit: Nevermind, I got it right. N(L) = k/L^2
Let's take a simpler example:

Say that y was proportionately related to x:

$y=k \cdot x$

If k=1, then the equation is simply $y=x$. So in this case, y simply equals x. But what if say...y is five times larger than x? Then y is still porportional to x, but it isn't equal.

It would look like this:

$y=5x$, so in this case, k= 5. The ratio of y to x will be 5:1. So the two values will always have a constant ratio to each other, and that defines the fact that they're proportional.

k is not proportional to S. S is proportional to h, and the magnitude of the resulting constant ratio between S and h is defined by k.