<p>Simple questions, but I get confused each time I think of it.
Question:
IF *Y is directly proportional to the square of X
and..
*Z is inversely proportional to Y
Then..
The only answer I remember and chose is: 'Z is inversely proportional to the square of X.'</p>
<p>My proof: I assumed the constant K, in the equation Y=KX for direct variation, to be 1. I also assumed X to be, for example, 2. Therefore, Y=1<em>(2^2).. Y=4....... and since we now know Y, we can figure out Z. Z, being inversely proportional to Y, means Z= K/Y, and by using the same constant, yields Z=1/4. Therefore, (almost done), if Z is inversely proportional to the square of X, that means Z=K/X^2... which is 1/4=1/2^2. Correct?
Another way to do it:
if Y=K</em>X^2 then Z=K/K*X^2 which is Z=1/x^2, which also makes sense for Z to be proportional to the square of X</p>
<p>Where I got confused:
Plug in a different value for K, for example 2, and lets say X is 3, therefore Y=2*3^2.. Y=18
Then Z=K/Y which is 2/18. And thus, if Z equals 1/9 then (1/9)=2/3^2, which is not correct? :)</p>
<p>That’s what I did too! I hope its correct it makes sense…</p>
<p>y = kx^2
z = a / y ----> z = a / kx^2 translated to words: z is inversely proportional to the square of x
(constants may be different between the two equations)</p>
<p>What about the logarithm question with w, b,c, and x?</p>
<p>I chose the same answer as you did. I hope its correct lol</p>
<p>Im so nervous about results!</p>
<p>Was this experimental? Did not have this Q</p>
<p>No way of knowing which section number is experimental. </p>
<h2>I`m answering your question:
"Plug in a different value for K, for example 2, and lets say X is 3, therefore Y=2*3^2.. Y=18
Then Z=K/Y which is 2/18. And thus, if Z equals 1/9 then (1/9)=2/3^2, which is not correct?"
Your calculation made an assumption: Y=kx², Z=k/y;
Here is the problem-- you were assuming that two k (constant) were the same value, but actually it`s not definitely true.
Now that the assumption is problematic, the inducement followed is not reliable.</p>
<p>To fix the problem, you can use different letter for each constant.</p>
<p>I did not have this question, maybe this was an experimental section?</p>