F.4 Variations,,QUICK!!!

1)

y varies inversely as the square root of x:
y = k/√x

When x = xo, y = yo:
yo = k/√xo

When x = (1 - 36%)xo = 0.64xo
y = k/√(0.64xo) = 1.25(k/√xo) = 1.25yo

% change in y = [(1.25yo - yo)/yo] x100% = +25%


2)
y ∞1/x^3:
y = k/x^3
x^3 = k/y
x = (k/y)^1/3

When x = xo, y = yo:
xo = (k/yo)^1/3

(a)
When y = (1 - 27.1%)yo = 0.729yo :
xo = (k/0.729y)^1/3 = (1/0.9) (k/yo)^1/3 = 10yo/9
% changes in x = {[(10yo/9) - yo]/yo} x100% = +(11 and 1/9)%

(b)
When y = (1 + 33.1%)yo = 1.331yo :
xo = (k/1.331y)^1/3 = (1/1.1) (k/yo)^1/3 = 10yo/11
% changes in x = {[(10yo/11) - yo]/yo} x 100% = -(9 and 1/11)%