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Home » \cos 180^\circ + \cot 30^\circ = -1 + \sqrt3 - Silent Sales Machine

\cos 180^\circ + \cot 30^\circ = -1 + \sqrt3 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \frac{d}{80} + \frac{d}{100} = 9

📌 Finding a common denominator and solving:

📌 \frac{5d + 4d}{400} = 9 \quad \Rightarrow \quad \frac{9d}{400} = 9

📌 9d = 3600 \quad \Rightarrow \quad d = 400

📌 The side length of the square is:

📌 \sqrt{64} = 8

📌 The diameter of the circle is equal to the side of the square, so:

📌 \text{Diameter} = 8

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Find all real solutions to the inequality \( x^3 - 4x^2 + x + 6 < 0 \)...
To solve the inequality \( x^3 - 4x^2 + x + 6 < 0 \), we first find th...
Using the Rational Root Theorem, we test possible rational roots: \( \...
\[ 1^3 - 4(1)^2 + 1 + 6 = 1 - 4 + 1 + 6 = 4
eq 0 \]
\[ (-1)^3 - 4(-1)^2 + (-1) + 6 = -1 - 4 - 1 + 6 = 0 \]
Thus, \( x = -1 \) is a root.
We perform synthetic division of \( x^3 - 4x^2 + x + 6 \) by \( x + 1...
egin{array}{r|rrrr}
& 1 & -4 & 1 & 6 \

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