calculus homework problem?

2018-07-30 11:36 pm

回答 (2)

2018-07-31 12:36 am
(a)
F = K / [a(a + l)]
F = K (a² + al)⁻¹

When l is constant:
dF/da = (d/da)[ K (a² + al)⁻¹]
dF/da = K * d(a² + al)⁻¹/d(a² + al) * d(a² + al)/dt
dF/dt = K * [-1/(a² + al)²] * [2a(da/dt) + l(da/dt)]

When da/dt = 3, a = 15 and l = 5:
dF/dt = K * [-1/(15² + 15*5)²] * [2*15*3 + 5*3]
dF/dt = K * [-1/90000] * [105]
dF/dt = -0.00117K

F is decreasing at a rate of 0.00117K newtons per min.

====
(b)
When a is constant:
dF/da = (d/da)[ K (a² + al)⁻¹]
dF/da = K * d(a² + al)⁻¹/d(a² + al) * d(a² + al)/dt
dF/dt = K * [-1/(a² + al)²] * [a*(dl/dt)]

When dl/dt = -3, a = 15 and l = 5:
dF/dt = K * [-1/(15² + 15*5)²] * [15*(-3)]
dF/dt = K * [-1/90000] * [-45]
dF/dt = 0.00050K

F is increasing at a rate of 0.00050K newtons per min.
2018-07-30 11:38 pm
unreadable, sorry


收錄日期: 2021-04-24 01:07:31
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20180730153602AAbOxFp

檢視 Wayback Machine 備份