1. ## variation help

h is inversely proportional to the third power of t and h=3/16 when t=4.

Do you divide the #'s? Multipy? I am completely confused.

2. h is inversely proportional to the third power of t and h=3/16 when t=4.

Do you divide the #'s? Multipy? I am completely confused.
I assume the aim of this exercise is to find h in terms of t then?

So you know that h is inversely proportional to the third power of t.

What does that mean? Let's turn it from maths-speak into real words.

Well, it means that 1/h (the "inversely" bit) equals some number (call it k) times (the "proportional" bit) t^3 (the "third power of t" bit).

(By the way, if a is PROPORTIONAL to b, then a = some number times b.)

Now let's turn the real words back into maths again ;-)

In maths,

1/h = k * t^3

Fantastic. Oh wait. We still need to know what k is. But we know that when t is 4, h is 3/16.

So

16/3 = k * (4)^3

You can use that to find k.

Then voila, you've got a relationship between h and t.

I hope this helps.

3. ok maybe this will help you explain it the way they are wanting it. I have been given the answer to the question now.
so again the question states
h is inversely proportional to the third power of t and h = 3/16 when t= 4.

the answer I have here in the key is.....
h= 12/t^3

I am guessing that 12 would be the k that you were referring to earlier.

I do have a question about the equations you set up. When you plugged in the h value of 3/16 I noticed that you flipped it when you put it in the equation. you put it as 16/3. Why is that?

thanks for the help so far!

4. I see. I did guess what the question was properly.

We got as far as this earlier:

1/h = k * t^3

And we know that when t = 4, h = 3/16

So let's substitute them

I flipped h because we need 1/h in that equation, not h.

1/ (3/16) = k * (4)^3

So

16/3 = k * 64

16 = 3*64*k
Work that out and you'll get k = 1/12

So we've got our k. Putting it all together gives:

1/h = 1/12 * t^3

Now, they wrote the answer as h =, not 1/h =

So we'll just rearrange it a little. There's nothing clever here - it's just rearranging it.

h = 12 / (t^3)

Sorted?

5. ok let me try the next probelm and see how I do. thanks!

6. You're welcome.

Good luck.

7. i got the next problem right. thanks so much! hopefully i can do the rest with no help!