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Home » Determine the limit $ \lim_n \to \infty b_n $. - Tacotoon

Determine the limit $ \lim_n \to \infty b_n $. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A triangle has sides of lengths 7, 24, and 25 units. Is it a right triangle, and if so, what is its area?

📌 Check using Pythagoras' theorem: \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\).

📌 It is a right triangle. The area is \(\frac{1}{2} \times 7 \times 24 = 84\) square units.

📌 Solve for \(x\) in the equation \(2x^2 - 8x + 6 = 0\).

📌 Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

📌 Here, \(a = 2\), \(b = -8\), \(c = 6\).

📌 \(x = \frac{8 \pm \sqrt{(-8)^2 - 4 \times 2 \times 6}}{4} = \frac{8 \pm \sqrt{64 - 48}}{4} = \frac{8 \pm \sqrt{16}}{4}\).

📌 \(x = \frac{8 \pm 4}{4}\), so \(x = 3\) or \(x = 1\).

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