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Home » a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0. - Portal da AcÃºstica

a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0. - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A linguist studies code-switching in bilingual communities. She finds that 70% of conversations involve switching between English and Spanish. Of those, 40% also include fragments of Native American languages. If she analyzes 350 conversations, how many include both English-Spanish switching and Native American language elements?

📌 English-Spanish switch: 0.70 × 350 = <<0.70*350=245>>245 conversations.

📌 Of these, with Native American language: 0.40 × 245 = <<0.40*245=98>>98.

📌 An environmental historian examines soil data from 1880 to 1920. The land had 80% forest cover in 1880. Each decade, 12% of the remaining forest was cleared, but conservation efforts restored 5% of cleared land each decade. Starting with 2,500 acres of forest in 1880, how much remained in 1920?

📌 Decade 1 (1880–1890):

📌 Cleared: 0.12 × 2500 = <<0.12*2500=300>>300 acres.

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Length per turn = \( \sqrt{(\text{circumference})^2 + (\text{pitch})^2...
Number of turns in 10 m: \( \frac{10}{1.895} \approx 5.273 \).
Total path length: \( 5.273 \times 1.895 \approx 10.0 \) m (approximat...
Time = \( \frac{10}{0.4} = 25 \) seconds.
But uses approximation.
To avoid, redefine:
A robotic arm traverses a helical path on a cylindrical component with...
Then total path length = \( 5 \times \sqrt{(2\pi r)^2 + 0.4^2} \), but...
Still missing.
Final decision: use a linear displacement only and ignore path curvatu...

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