作业帮求解美国微积分应用题!
来源：学生作业帮 编辑：作业帮 分类：英语作业 时间：2024/05/25 17:55:55
求解美国微积分应用题!
the hand of a clock in some tower are approxiately 3m and 2.5m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: use the law of cosine)
question: the rate is ____m/hr at 9:00
the hand of a clock in some tower are approxiately 3m and 2.5m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: use the law of cosine)
question: the rate is ____m/hr at 9:00
根据余弦定理,两表针尖端的距离L的平方为
L^2 = 3.0^2 + 2.5^2 - 2*3.0*2.5*cosθ = 15.25 - 15*cosθ
其中 θ = t*(2π - 2π/12)
两端对 t 求导
2 L dL/dt = 15*sinθ * (2π - 2π/12)
v = dL/dt ,将 t = 9.00 代入,得
v(9.00) = 11.0616 m/h
L^2 = 3.0^2 + 2.5^2 - 2*3.0*2.5*cosθ = 15.25 - 15*cosθ
其中 θ = t*(2π - 2π/12)
两端对 t 求导
2 L dL/dt = 15*sinθ * (2π - 2π/12)
v = dL/dt ,将 t = 9.00 代入,得
v(9.00) = 11.0616 m/h