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
ratio
2007-07-12 4:27 am
回答 (1)
2007-07-12 4:44 am
✔ 最佳答案
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.
參考: My Maths Knowledge
收錄日期: 2021-04-12 20:10:44
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https://hk.answers.yahoo.com/question/index?qid=20070711000051KK04335