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標題:
Variation questions
發問:
Y is the sum of two parts. One part varies directly as x, while the other part varies directly as x^2. Y= -33 when x=3 and Y= -48 when x=6 (a) Express Y in terms of x. (b) Find the minimum possible value of Y when x varies.
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最佳解答:
a)Let Y = k1 x + k2 x^2 -33 = k1 *3 + k2 *3^2......(1) -48 = k1 *6 + k2 *6^2......(2) (2) - (1)*2 : -48 + 66 = 36k2 - 18k2 k2 = 1 , sub it to (1) : -33 = k1 *3 + 3^2 k1 = - 14 So Y = -14x + x^2 b)Y = -14x + x^2 = x^2 - 2(7)x + 7^2 - 7^2 = (x - 7)^2 - 49 When x = 7 The minimum possible value of Y = - 49
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