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?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.
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.
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!
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?