calculus homework problem?
回答 (2)
(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.
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(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.
收錄日期: 2021-04-24 01:07:31
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