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Home » Subtract: \( 2,400,000 < 120,000t \) - Veritas Home Health

Subtract: \( 2,400,000 < 120,000t \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 n = 20 → 360° → 360 ÷ 90 = 4 → invalid.

📌 But 45° is target, and no integer n gives 18n = 45 → so 45° is unreachable in 18° steps?

📌 Wait — the arm rotates incrementally, so position must be exact. But 45 and 18 have LCM:

📌 Find smallest θ such that θ = 18n, θ = 45k, and θ mod 90 ≠ 0.

📌 So 18n = 45k → 2n = 5k → n = 5m, k = 2m → θ = 18×5m = 90m° → always multiple of 90!

📌 So every multiple of 18° that is also multiple of 45 must be multiple of LCM(18,45).

📌 LCM(18,45) = (18×45)/gcd(18,45) = 810 / 9 = 90.

📌 So the only positions that are multiples of both 18 and 45 are multiples of 90°.

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Question: Let $ a $ and $ b $ be complex numbers such that
\frac{a}{b} + \frac{b}{a} = 3.
Find the value of $ \frac{a^3}{b^3} + \frac{b^3}{a^3} $.
Let $ x = \frac{a}{b} \Rightarrow \frac{b}{a} = \frac{1}{x} $, so:
x + \frac{1}{x} = 3
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