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標題:

ratio

發問:

y partly varies directly as x and partly varies inversely as x , when x=9 , y=44 and when x =1 over 5 , y = -44 . a) find the equation connecting x and y. b)Do x and y have the same value when (i) x=3 over 2 ? (ii) x = -3 over 2 ? ans:(a) y=5x-9 over x (b)(i)yes (ii)yes

最佳解答:

y = kx + k1 / x ( k , k1≠0 ) 44 = 9k + k1/ 9 396 = 81k + k1 --- ( 1 ) - 44 = k / 5 + k1 / ( 1 / 5 ) -44 = k / 5 + 5k1 -220 = k + 25 k1 k = - 220 - 25 k1 --- ( 2 ) Put ( 2 ) into ( 1 ). 396 = 81 ( - 220 - 25 k1 ) + k1 396 = -17820 - 2025 k1 + k1 -2024 k1 = 18216 k1 = -9 So k = -220 - 25 ( - 9 ) = 5 Therefore y = 5x - 9/x bi ) When x = 3 / 2, y = 5 ( 3 / 2 ) - 9 / ( 3 / 2 ) = 3 / 2 So the values of x and y are the same. ii ) When x = -3 / 2, y = 5 ( - 3 / 2 ) - 9 / ( - 3 /2 ) = - 3 /2 So the values of x and y are the same.

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