SOLUTION: Please Help!!! Thanks 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?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please Help!!! Thanks 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?      Log On


   

Question 203246This question is from textbook
: Please Help!!! Thanks
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? This question is from textbook

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given x%5Bs%5D+=+Ks%5E2%2Ft So you can see that x varies directly with s^2 and inversely with t.
How does x change when s is doubled?
x%5Bs%5D+=+Ks%5E2%2Ft doubling s means "the new value for s is now 2 times the original s ... so use 2s
x%5B2s%5D+=+K%282s%29%5E2%2Ft
x%5B2s%5D+=+4ks%5E2%2Ft
compare x%5Bs%5D to x%5B2s%5D and see that x%5B2s%5D%2Fx%5Bs%5D =
%28+4Ks%5E2%2Ft%29+%2F+%28Ks%5E2%2Ft%29
4 thus doubling s, makes x 4 times larger (makes sense since 2^2 = 4)

When both s and t are doubled?
x%5B2s2t%5D+=+K%282s%29%5E2%2F%282t%29
x%5B2s2t%5D+=+4Ks%5E2%2F%282t%29
x%5B2s2t%5D+=+2Ks%5E2%2Ft
compare x%5Bs%5D to x%5B2s2t%5D and see that x%5B2s2t%5D%2Fx%5Bs%5D =
%28+2Ks%5E2%2Ft%29+%2F+%28Ks%5E2%2Ft%29
2 thus doubling both s and t, doubles x