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Home » This absolute value equation splits into two cases: - Appfinity Technologies

This absolute value equation splits into two cases: - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The circumference $ C $ of the circle is given by $ C = 2\pi r $. Substituting the value of $ r $:

📌 C = 2\pi (4\sqrt{2}) = 8\sqrt{2}\pi.

📌 Thus, the circumference of the circle is $ oxed{8\sqrt{2}\pi} $.

📌 Question: A science fair judge is evaluating a student's model of a planet, shaped like a sphere with radius $ 2r $, and a supporting half-sphere with radius $ r $. What is the ratio of the volume of the planet to the volume of the half-sphere?

📌 Solution: The volume of a sphere with radius $ 2r $ is:

📌 V_{ ext{sphere}} = rac{4}{3}\pi (2r)^3 = rac{4}{3}\pi (8r^3) = rac{32}{3}\pi r^3.

📌 The volume of a hemisphere with radius $ r $ is half the volume of a full sphere:

📌 V_{ ext{hemisphere}} = rac{1}{2} \cdot rac{4}{3}\pi r^3 = rac{2}{3}\pi r^3.

🔥 Popular Posts

2y + 4 + 3y = 6
5y + 4 = 6
5y = 2
y = \frac{2}{5}
Substituez de nouveau pour trouver \( x \):
x = \frac{2}{5} + 2 = \frac{2}{5} + \frac{10}{5} = \frac{12}{5}
#### \(\frac{12}{5}, \frac{2}{5}\)
Question:** Trouvez la valeur de \( x \) si \( \log_2(x) + \log_2(8) =...
Solution:** Utilisez la propriété \(\log_b(a) + \log_b(c) = \log_b(ac)...
\log_2(8x) = 5

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