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Home » Total pollinating only one: \( 80 + 60 = 140 \) - AMAZONAWS

Total pollinating only one: \( 80 + 60 = 140 \) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 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} $.

📌 Solution: We apply the **Cauchy-Schwarz inequality** in the Engel form (also known as Titu’s Lemma):

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However, reconsider: maybe the problem assumes integer? But no.
Final precise answer:
x = \sqrt[3]{18}
But wait — perhaps mistake. Let’s double-check.
Volume = \( l \cdot w \cdot h = 3x \cdot x \cdot 2x = 6x^3 = 108 \Righ...
But this is irrational. Accept it.
#### \(\sqrt[3]{18}\)
A train travels from City A to City B at 60 km/h and returns at 90 km/...
Let the distance between cities be \( d \) km.
Time from B to A: \( \frac{d}{90} \) hours

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