Question 125838
You can express "x varies as the square of s and inversely as t" like this:
{{{x = ks^2/t}}} k is the constant of variation.
To see how x changes when s is doubled (2s), simply substitute 2s for s in the above formula and simplify.
{{{x = k(2s)^2/t}}}
{{{x = k(4s^2)/t}}} 
{{{x = 4(ks^2/t)}}} but, as you can see, the factor in parentheses ({{{ks^2/t}}}) is the original x, so...
{{{x = 4x}}} or, in words, x is quadrupled when s is doubled.
Now, when both s and t are doubled, substitute 2s and 2t for s and t respectively in the first formula:
{{{x = ks^2/t}}}
{{{x = k(2s)^2/2t}}} Simplify.
{{{x = k(4s^2)/2t}}} Cancel 2's in the top and bottom.
{{{x = 2(ks^2/t)}}} or...
{{{ x = 2x}}} so you see that x is doubled when both s and t are doubled.