Find the y-coordinate
2014-05-13 10:39 pm
A curve has slope y^2 / x^3 at any point (x, y) on the curve. Given that (1, 1) is a point on the curve, find the y-coordinate of another point (4, y) on the curve. [Answer: 32/17]
回答 (1)
2014-05-14 3:31 am
✔ 最佳答案
dy/dx = y^2/x^3dy/y^2 = dx/x^3
J dy/y^2 = J dx/x^3
- 1/y = -1/2x^2 + C
when x = 1, y = 1
so -1/1 = -1/2 + C, C = - 1/2
that is
- 1/y = - 1/2x^2 - 1/2
1/y = 1/2x^2 + 1/2
when x = 4
1/y = 1/32 + 1/2 = (1 + 16)/32 = 17/32
so y = 32/17.
2014-05-13 19:32:24 補充：
Remark : J stands for the integration sign ∫ .
收錄日期: 2021-04-25 22:39:34
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140513000051KK00064