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Home » Here, $ n = 12 $, $ k = 4 $, so: - SUpost

Here, $ n = 12 $, $ k = 4 $, so: - SUpost

📅 July 5, 2026 👤 scraface

Jul 05, 2026

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📌 But in real context, rounding not done. However, educational math problems use exact arithmetic.

📌 Assume the problem allows exact computation: but answer must be integer.

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We solve:
rac{2x - 1}{x + 3} > 1
Subtract 1 from both sides:
rac{2x - 1}{x + 3} - 1 > 0 \Rightarrow rac{2x - 1 - (x + 3)}{x + 3} >...
Now analyze the sign of \( rac{x - 4}{x + 3} \)
Critical points: \( x = -3 \) (excluded), \( x = 4 \)
Sign chart:
For \( x < -3 \), say \( x = -4 \): \( rac{-4 - 4}{-4 + 3} = rac{-8}...
For \( -3 < x < 4 \), say \( x = 0 \): \( rac{-4}{3} < 0 \) â negat...
For \( x > 4 \), say \( x = 5 \): \( rac{1}{8} > 0 \) â positive

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From first set: \( \theta = \frac{2\pi(3k+1)}{9} \), \( k=0,1,2 \) → \...
From second set: \( \theta = \frac{2\pi(3k+2)}{9} \), \( k=0,1,2 \) →...
List the real parts: \( \cos\theta \) for each:
\( \cos\left(\frac{2\pi}{9}\right) \approx \cos(40^\circ) \approx 0.76...
\( \cos\left(\frac{4\pi}{9}\right) = \cos(80^\circ) \approx 0.1736 \)
\( \cos\left(\frac{8\pi}{9}\right) = \cos(160^\circ) \approx -0.9397 \...
\( \cos\left(\frac{10\pi}{9}\right) = \cos(200^\circ) \approx -0.9397...
\( \cos\left(\frac{14\pi}{9}\right) = \cos(280^\circ) = \cos(-80^\circ...
\( \cos\left(\frac{16\pi}{9}\right) = \cos(320^\circ) = \cos(-40^\circ...
Maximum real part is \( \cos\left(\frac{2\pi}{9}\right) \approx 0.766...

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