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Home » Is This Mysterious Hobgoblin Spiderman Ruining Your Favorite Comics?! - AMAZONAWS

Is This Mysterious Hobgoblin Spiderman Ruining Your Favorite Comics?! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Solution: The triangle with sides 9, 12, 15 is right-angled (since $9^2 + 12^2 = 15^2$). The area is $\frac{1}{2} \cdot 9 \cdot 12 = 54$. The altitudes correspond to $\frac{2 \cdot \text{Area}}{\text{side}}$, so:

📌 Altitude to hypotenuse (15): $\frac{108}{15} = 7.2$

📌 Altitude to 12: $\frac{108}{12} = 9$

📌 Altitude to 9: $\frac{108}{9} = 12$

📌 The shortest altitude is $\boxed{7.2}$.

📌 Question: A micropaleontologist studies a microfossil shaped like a hemisphere with radius $3x$ and a spherical fossil with radius $x$. What is the ratio of their volumes?

📌 Solution: Volume of hemisphere: $\frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi \cdot 27x^3 = 18\pi x^3$.

📌 Volume of sphere: $\frac{4}{3}\pi x^3$.

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