SOLUTION: I need to figure the following out. I have tried it but I get confused, I can't seem to get anywhere with it x varies directly as the square of s and inversely as t. How does

Algebra ->  Systems-of-equations -> SOLUTION: I need to figure the following out. I have tried it but I get confused, I can't seem to get anywhere with it x varies directly as the square of s and inversely as t. How does       Log On


   

Question 7839: I need to figure the following out. I have tried it but I get confused, I can't seem to get anywhere with it
x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can write the relationship between x and s & t as follows:
x+=+k%28s%5E2%2Ft%29 k is known as the constant of proportionality.
If you want to see the effect on x when s is doubled, just replace s with 2s.
x+=+k%28%282s%29%5E2%29%2Ft = k%284s%5E2%29%2Ft = 4k%28s%5E2%29%2Ft which is 4 times the original equation for x. So x is quadrupled when s is doubled.
Now let's double both s and t by substituting 2s and 2t into the original equation.
x+=+k%282s%29%5E2%2F2t = k%284s%5E2%29%2F2t = k%282s%5E2%2Ft%29 = 2k%28s%5E2%29%2Ft and here, you can see that the effect on x is to double it when you double both s and t.