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Home » Final Price with Tax:** \( 200 \times 1.08 = 216 \) dollars - Dyverse

Final Price with Tax:** \( 200 \times 1.08 = 216 \) dollars - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5Question: Compute \(\cos 45^\circ\) and use it to find the length of the diagonal of a square with side length \(7\) units.

📌 Solution: The cosine of \(45^\circ\) is given by \(\cos 45^\circ = \frac{\sqrt{2}}{2}\). For a square with side length \(s = 7\) units, the length of the diagonal \(d\) can be calculated using the Pythagorean theorem: \(d = s\sqrt{2}\). Substituting the value of \(s\), we get \(d = 7\sqrt{2}\). Therefore, the length of the diagonal is \(\boxed{7\sqrt{2}}\).

📌 Question: The area of a regular hexagon is \(54\sqrt{3}\) square units. Find the length of each side of the hexagon.

📌 Solution: The area \(A\) of a regular hexagon with side length \(s\) is given by the formula \(A = \frac{3\sqrt{3}}{2}s^2\). Setting this equal to \(54\sqrt{3}\), we have:

📌 \frac{3\sqrt{3}}{2}s^2 = 54\sqrt{3}

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