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Home » Distance traveled: 6 ÷ 0.08 = 75 km - Blask

Distance traveled: 6 ÷ 0.08 = <<6 ÷ 0.08 = 75>>75 km - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Set \( 50 \times 2^{t/3} \geq 800,000 \)

📌 Divide both sides by 50: \( 2^{t/3} \geq 16,000 \)

📌 Take log base 2: \( \frac{t}{3} \geq \log_2(16,000) \)

📌 \( \log_2(16,000) = \log_2(16 \times 1000) = \log_2(16) + \log_2(1000) = 4 + \log_2(10^3) \)

📌 \( \log_2(10^3) = 3 \log_2(10) \approx 3 \times 3.3219 = 9.9657 \)

📌 So \( \log_2(16,000) \approx 4 + 9.9657 = 13.9657 \)

📌 \( \frac{t}{3} \geq 13.9657 \Rightarrow t \geq 41.897 \)

📌 Since days are discrete, round up to 42 days.

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Solution: Observe that the right-hand side is $ (x^3 + 1)^2 + 2 $. How...
h(x^3 + 1) = (x^3 + 1)^2 + 2 \Rightarrow h(u) = u^2 + 2
Then, substitute $ u = x^3 - 1 $:
h(x^3 - 1) = (x^3 - 1)^2 + 2 = x^6 - 2x^3 + 1 + 2 = x^6 - 2x^3 + 3
oxed{x^6 - 2x^3 + 3}
Question: Find the remainder when $ (x^2 + x + 1)^3 $ is divided by $...
Solution: Let us compute $ (x^2 + x + 1)^3 \mod (x^2 - x + 1) $.
Note that $ x^2 + x + 1 $ and $ x^2 - x + 1 $ are related via complex...
Let $ \omega $ be a primitive cube root of unity, satisfying $ \omega^...
e 1 $, and $ \omega^2 + \omega + 1 = 0 $.

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