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Home » infer geologic history from a new mexico outcrop - RTA

infer geologic history from a new mexico outcrop - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Recall that $ \tan x = \frac{\sin x}{\cos x} $, $ \cot x = \frac{\cos x}{\sin x} $, so:

📌 \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \frac{1}{\sin x \cos x}.

📌 \frac{1}{\sin x \cos x} = 2\sqrt{2}.

📌 Use the double-angle identity: $ \sin(2x) = 2\sin x \cos x $, so:

📌 \sin x \cos x = \frac{1}{2} \sin(2x).

📌 \frac{1}{\frac{1}{2} \sin(2x)} = 2\sqrt{2} \Rightarrow \frac{2}{\sin(2x)} = 2\sqrt{2} \Rightarrow \frac{1}{\sin(2x)} = \sqrt{2} \Rightarrow \sin(2x) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}.

📌 Now solve $ \sin(2x) = \frac{\sqrt{2}}{2} $ for $ x \in (0, \pi) $. Then $ 2x \in (0, 2\pi) $.

📌 The solutions to $ \sin \theta = \frac{\sqrt{2}}{2} $ in $ (0, 2\pi) $ are:

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Average speed = 270 / 3.5 ≈ 77.14 km/h.
#### 77.14### 高等045：计算题
如果一个机器人在仓库中搬运箱子，每次携带3个箱子，需要搬运一定数量的箱...
每次搬运3个箱子，总共进行15次搬运，
\times 15 = 45 \text{ 个箱子（用以确认，无需直接计算）}
行驶总距离为900米，
在15次往返中，每次包含一次前行与回返，因此
行进次数为 $2 \times 15 = 30$ 次（前后两次/搬运一次），
所以总共只走900米，分为15段，每段距离为：
\frac{900}{15} = 60 \text{ 米/段}

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