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Home » Day 2 = x + 0.2x = 1.2x. - Silent Sales Machine

Day 2 = x + 0.2x = 1.2x. - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Set up the equation: \( rac{n(n + 1)}{2} = 5050 \).

📌 Multiply both sides by 2: \( n(n + 1) = 10100 \).

📌 Solve the quadratic equation \( n^2 + n - 10100 = 0 \) using the quadratic formula \( n = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

📌 Here, \( a = 1, b = 1, c = -10100 \).

📌 Calculate the discriminant: \( 1^2 - 4 imes 1 imes (-10100) = 1 + 40400 = 40401 \).

📌 The square root of 40401 is 201.

📌 Calculate \( n \): \( n = rac{-1 \pm 201}{2} \).

📌 Choose the positive solution: \( n = rac{200}{2} = 100 \).

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angle\), \(ec{OB} = \langle -1 - \sqrt{7}, 1 - \sqrt{7}
Dot product:
ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})...
= [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -...
Magnitudes:
|ec{OA}| = \sqrt{(-1 + \sqrt{7})^2 + (1 + \sqrt{7})^2} = \sqrt{(1 - 2...
|ec{OB}| = \sqrt{(-1 - \sqrt{7})^2 + (1 - \sqrt{7})^2} = \sqrt{(1 + 2...
\cos heta = rac{-12}{(2\sqrt{6})(2\sqrt{6})} = rac{-12}{24} = -rac...
The area of the circular sector is:
A_{ ext{sector}} = rac{1}{2} r^2 heta = rac{1}{2} \cdot 16 \cdot r...

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