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Home » Question: Find the minimum value of $(\csc x + \cot x)^2 + (\sec x - an x)^2 - Silent Sales Machine

Question: Find the minimum value of $(\csc x + \cot x)^2 + (\sec x - an x)^2 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A pyramid-shaped container has a square base with side length 10 meters and a height of 15 meters. If the container is filled with sand, and the sand is then evenly spread into a rectangular box measuring 5 meters by 10 meters by 3 meters, how high will the sand fill the box?

📌 Volume of the pyramid = \( \frac{1}{3} \times \text{base area} \times \text{height} \)

📌 Base area = \( 10 \times 10 = 100 \) square meters

📌 Volume = \( \frac{1}{3} \times 100 \times 15 = 500 \) cubic meters

📌 Volume of the box = \( 5 \times 10 \times 3 = 150 \) cubic meters

📌 Height of sand in the box = \( \frac{500}{150} \approx 3.33 \) meters

📌 #### 3.33 meters

📌 An athlete runs a 100-meter dash in 10.5 seconds. If he runs at a constant speed, what is his average speed in kilometers per hour?

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\frac{3\sqrt{3}}{2}s^2 = 54\sqrt{3}
Dividing both sides by \(\sqrt{3}\), we get:
\frac{3}{2}s^2 = 54
Multiplying both sides by \(\frac{2}{3}\) gives:
s^2 = 36
s = 6

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