# Thread: Direct and inverse proportions

1. ## Direct and inverse proportions

If x is directly proportional to the square root of y, then y is inversely proportional to...?

2. Originally Posted by jpp
If x is directly proportional to the square root of y, then y is inversely proportional to...?

lets begin with definitions. what does it mean for x to be proportional to y?

3. x = ky

in this problem..

x = k * sqrt(y)

is that correct?

4. Originally Posted by jpp
x = ky

in this problem..

x = k * sqrt(y)

is that correct?
yes, correct! now what does it mean to be inversely proportional? Lets say i said "a is inversely proportional to b", what equation would go along with that?

5. Originally Posted by Jhevon
yes, correct! now what does it mean to be inversely proportional? Lets say i said "a is inversely proportional to b", what equation would go along with that?
a = k / b, right?

6. Originally Posted by jpp
a = k / b, right?

Correct.

so according to your question: $\displaystyle x = {k}{\sqrt{y}}$

can you complete it now by finding what y is inversely proportional to?

7. Originally Posted by jpp
a = k / b, right?
right. so you know $\displaystyle \displaystyle x = k \sqrt y$ and you want to get to $\displaystyle \displaystyle y = \frac C{f(x)}$ (by solving for y and, perhaps, rearranging)

where $\displaystyle \displaystyle C$ is a constant and $\displaystyle \displaystyle f(x)$ is some function of $\displaystyle \displaystyle x$. That $\displaystyle \displaystyle f(x)$ is the answer to your question. can you find it?

8. I rearranged x = k * sqrt(y) to get y = x^2/k^2

y = C/f(x) -> x^2/k^2 = C/f(x)

does C = k?

9. Originally Posted by jpp
I rearranged x = k * sqrt(y) to get y = x^2/k^2

y = C/f(x) -> x^2/k^2 = C/f(x)

does C = k?
C is just a constant. and you do not yet have the form you need to get to. you need to write it as a constant over a function of x.

10. Originally Posted by jpp
I rearranged x = k * sqrt(y) to get y = x^2/k^2

y = C/f(x) -> x^2/k^2 = C/f(x)

does C = k?
the crucial point is not "C", but f(x). What is f(x) here?