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Home » You Won’t Believe How Ounces to Liters Transforms Your Cooking Recipes! - Portal da AcÃºstica

You Won’t Believe How Ounces to Liters Transforms Your Cooking Recipes! - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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 $.

📌 We know $ a + b = 4 $, and

📌 a^2 + b^2 = (a + b)^2 - 2ab = 16 - 2ab = 10 \Rightarrow 2ab = 6 \Rightarrow ab = 3

📌 a^3 + b^3 = 4^3 - 3 \cdot 3 \cdot 4 = 64 - 36 = \boxed{28}

📌 Question: Let $ x, y, z $ be positive real numbers such that $ x + y + z = 1 $. Find the minimum value of $ \frac{1}{x} + \frac{4}{y} + \frac{9}{z} $.

🔥 Popular Posts

Volume \( V \) of a cone is \( \frac{1}{3}\pi r^2 h \).
Set \( \frac{1}{3}\pi r^2 \times 12 = 100\pi \).
Simplify: \( 4\pi r^2 = 100\pi \).
Divide by \( 4\pi \): \( r^2 = 25 \).
Take the square root: \( r = 5 \) cm.
The sum of the first \( n \) terms of an arithmetic sequence is given...
Substitute into the formula: \( \frac{n}{2}(2 \times 3 + (n-1) \times...
Simplify: \( \frac{n}{2}(6 + 2n - 2) = 110 \).
Further simplify: \( \frac{n}{2}(4 + 2n) = 110 \).
Multiply through by 2: \( n(4 + 2n) = 220 \).

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Area: \( w(2w + 4) = 104 \)
Expand: \( 2w^2 + 4w = 104 \)
Divide by 2: \( w^2 + 2w = 52 \)
Bring to standard form: \( w^2 + 2w - 52 = 0 \)
\( w = \frac{-2 \pm \sqrt{2^2 - 4(1)(-52)}}{2} = \frac{-2 \pm \sqrt{4...
\( \sqrt{212} = \sqrt{4 \times 53} = 2\sqrt{53} \approx 2 \times 7.28...
\( w = \frac{-2 + 14.56}{2} = \frac{12.56}{2} = 6.28 \)
Width ≈ 6.28 meters.
The population of a town grows by 5% annually. If it was 8,000 in 2020...
Growth factor = 1.05 per year.

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