SOLUTION: three quantities t,x, and y such that t varies directly as x and inversely as the square root of y. find the percentafe decrease in t , if x decreases by 4% , when y increases by 4

Algebra ->  Finance -> SOLUTION: three quantities t,x, and y such that t varies directly as x and inversely as the square root of y. find the percentafe decrease in t , if x decreases by 4% , when y increases by 4      Log On


   

Question 1100487: three quantities t,x, and y such that t varies directly as x and inversely as the square root of y. find the percentafe decrease in t , if x decreases by 4% , when y increases by 44%
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
t=kx%2F%28sqrt%28y%29%29

k=t%2Asqrt%28y%29%2Fx


Change x to 0.96x and y to 1.44y.
Change in t:
k%2A0.96x%2Fsqrt%281.44y%29-kx%2F%28sqrt%28y%29%29
kx%280.96%2Fsqrt%281.44y%29-1%2Fsqrt%28y%29%29
%28kx%2Fsqrt%28y%29%29%280.96%2Fsqrt%281.44%29-1%29
%28kx%2Fsqrt%28y%29%29%280.96%2F1.2-1%29
t%2A%28-0.2%29
Decrease in t by 2/10 or 20%.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

The variation equation is
t+=+%28kx%29%2Fsqrt%28y%29

x decreased by 4% is 0.96x
sqrt%28y%29 with y increased by 44% is sqrt%281.44y%29+=+1.2%2Asqrt%28y%29

Then the "new" value of t is %280.96kx%29%2F%281.2%2Asqrt%28y%29%29+=+0.8%2A%28%28kx%29%2Fsqrt%28y%29%29

The new value of t is 0.8, or 0.80, times the original value; its value has decreased by 20%.