設 y 一部分為常數及一部分隨 x 的平方而正變。
若當 x = 3 時， y = 30 及當 x = 4 時，y = 44，則
A. y = 12 + x。
B. y = 8 + x 2 。
C. y = 8 + 2x 2 。
D. y = 12 + 2x 2 。
MATHS??部分變??選擇題
2009-03-26 12:30 am
回答 (2)
2009-03-26 1:38 am
✔ 最佳答案
y = C + kx^230 = C + k(3)^2...(1)
44 = C + k(4)^2...(2)
(2)-(1) :
16k - 9k = 44-30
7k = 14
k = 2,代入(1)以求C:
30 = C + 2 (3)^2
C = 12
所以 y = 12 + 2x^2 ,答案(D)
2009-03-25 17:43:52 補充：
由於是選擇題,可以逐個選項代x = 3 ， y = 30 或 x = 4 ，y = 44 入各備選答案中,可很快排除錯誤選項。
2009-03-26 1:40 am
y = k + k1x^2 where k and k1 are non - zero constants
When x = 3, y = 30,
30 = k + k1(3)^2
k = 30 - 9k1 --- ( 1 )
When x = 4, y = 44,
44 = k + k1(4)^2
k = 44 - 16k1 --- ( 2 )
Put ( 1 ) into ( 2 ),
44 - 16k1 = 30 - 9k1
14 = 7k1
k1 = 2
k = 44 - 16(2) = 12
Hence y = 12 + 2x2 [ Ans : D ]
When x = 3, y = 30,
30 = k + k1(3)^2
k = 30 - 9k1 --- ( 1 )
When x = 4, y = 44,
44 = k + k1(4)^2
k = 44 - 16k1 --- ( 2 )
Put ( 1 ) into ( 2 ),
44 - 16k1 = 30 - 9k1
14 = 7k1
k1 = 2
k = 44 - 16(2) = 12
Hence y = 12 + 2x2 [ Ans : D ]
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