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Home » Circumference formula: \( C = 2\pi r \). - AMAZONAWS

Circumference formula: \( C = 2\pi r \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 12a + 3(2 - 3a) = 10 \Rightarrow 12a + 6 - 9a = 10 \Rightarrow 3a = 4 \Rightarrow a = \frac{4}{3}

📌 Then $ b = 2 - 3 \cdot \frac{4}{3} = 2 - 4 = -2 $

📌 From (2): $ \frac{4}{3} - 2 + c = 3 \Rightarrow c = 3 + 2 - \frac{4}{3} = 5 - \frac{4}{3} = \frac{11}{3} $

📌 And $ d = 2 $

📌 p(x) = \frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2

📌 Thus, the remainder when $ p(x) $ is divided by $ x^4 - 1 $ is simply $ p(x) $, since $ \deg p < 4 $. So the remainder is:

📌 \boxed{\frac{4}{3}x^3 - 2x^2 + \frac{11}{3}x + 2}

📌 Question: Let $ a $ and $ b $ be complex numbers such that $ a + b = 4 $ and $ a^2 + b^2 = 10 $. Find $ a^3 + b^3 $.

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\text{Diagonal} = 2R = 10 \text{ cm}
For a square with side $ s $, the diagonal is $ s\sqrt{2} $. Therefore...
s\sqrt{2} = 10 \Rightarrow s = \frac{10}{\sqrt{2}} = 5\sqrt{2}
The area of the square is:
s^2 = (5\sqrt{2})^2 = 25 \cdot 2 = 50
Thus, the area is $ \boxed{50} $.
Question: An equilateral triangle has an area of $ 36\sqrt{3} $ cm². I...
The area $ A $ of an equilateral triangle with side length $ s $ is:
A = \frac{\sqrt{3}}{4} s^2
Given $ \frac{\sqrt{3}}{4} s^2 = 36\sqrt{3} $, divide both sides by $...

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