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Home » \mathbfu \cdot \mathbfv = \|\mathbfu\| \|\mathbfv\| \cos \theta - Ready Digital AB

\mathbfu \cdot \mathbfv = \|\mathbfu\| \|\mathbfv\| \cos \theta - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 C = 2\pi r = 2\pi \cdot \frac{13}{2} = 13\pi \text{ cm}

📌 Therefore, the circumference of the circle is \(\boxed{13\pi}\).

📌 An equilateral triangle has an area of \( 36\sqrt{3} \) cm². If each side of the triangle is increased by 2 cm, by how many square centimeters does the area increase?

📌 \frac{1}{4} s^2 = 36 \quad \Rightarrow \quad s^2 = 144 \quad \Rightarrow \quad s = 12 \text{ cm}

📌 The new side length is:

📌 s' = 12 + 2 = 14 \text{ cm}

📌 A' = \frac{\sqrt{3}}{4} (14)^2 = \frac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} \text{ cm}^2

📌 \Delta A = A' - A = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3} \text{ cm}^2

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