deposits have formed a coating 3mm thick uniformly on the inside of a pipe.
as a result,the cross-section area through which the fluid can flow is 4/9 that of the original.
find the original inner diameter of the pipe.
可否譯中文??尤其中間那句不明!
這題是Quadratic Equation.怎樣用Quadratic Equation.的方法去計
?? 圖是圓中圓.求內徑.過程和ans!!thank!!
Quadratic Equation?
2015-09-29 5:58 am
回答 (2)
2015-09-29 1:09 pm
✔ 最佳答案
題目的中譯版本：管道內已均勻地被 3mm厚的沉澱物覆蓋著，因此，液體能流過橫切面只有原來的 4/9。
求管道內圓的原來直徑。
Solution ：
Let r - original inner radius of the pipe ( in mm ),
then inner radius of the pipe with coating = r-3
π ( r - 3) ^2 / π r^2 = 4/9
( r^2 - 6r + 9 ) / r^2 = 4/9
9 r^2 - 54r + 81 = 4 r^2
5 r^2 - 54r + 81 = 0
(r - 9 )(5r - 9) = 0
r = 9 or r = 9/5 = 1 4/5 (rejected - ∵ original r cannot be < 3)
∴ diameter = 18 mm
2015-09-29 9:32 am
請參考 qid=20150926051258AAGOKbo
該篇已加上中譯, 並提供兩種解法.
該篇已加上中譯, 並提供兩種解法.
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