標題:
F.4 Variations,,QUICK!!!
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1) It is given that y varies inversely as the square root of x. If x is decreased by 36%, find the % change in y. 2) It is given that y ∞1/x^3 . Find the % changes in x if y is : (a) decreased by 27.1% (b) increased by 33.1%
最佳解答:
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)%
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