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標題:
F.4 variations~
發問:
y varies directly as x+9 and inversely as √z where z＞0, y=13 when x=17 and z=16. (a) Express y in terms of x and z (b) Find the value of x when y=3 and z=64(c) If x is fixed and z decreases by 75%, find the percentage change in y.
(a) y = k(x+9)/√z where k is a constant 13 = k(17+9)/√16 13 = 26k/4 k = 2 Hence, y = 2(x+9)/√z (b) when y = 3, z = 64, 3 = 2(x+9)/√64 24 = 2(x + 9) 12 = x + 9 x = 3 (c) y = 2(x+9)/√z If z is decreased by 75%, new value of z = (1-0.75)z = 0.25z New value of y = 2(x+9)/ √(0.25z) = 2(x+9)/[0.5√z] = 2y = 2 * 2(x+9)/√z = 2y Hence y is increased by (2y – y)/y * 100% = 100%
其他解答:
F.4 variations~
發問:
y varies directly as x+9 and inversely as √z where z＞0, y=13 when x=17 and z=16. (a) Express y in terms of x and z (b) Find the value of x when y=3 and z=64(c) If x is fixed and z decreases by 75%, find the percentage change in y.
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最佳解答:(a) y = k(x+9)/√z where k is a constant 13 = k(17+9)/√16 13 = 26k/4 k = 2 Hence, y = 2(x+9)/√z (b) when y = 3, z = 64, 3 = 2(x+9)/√64 24 = 2(x + 9) 12 = x + 9 x = 3 (c) y = 2(x+9)/√z If z is decreased by 75%, new value of z = (1-0.75)z = 0.25z New value of y = 2(x+9)/ √(0.25z) = 2(x+9)/[0.5√z] = 2y = 2 * 2(x+9)/√z = 2y Hence y is increased by (2y – y)/y * 100% = 100%
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