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Home » Since \(x > 4\), \(x = 2 + 2\sqrt3 \approx 5.464\). - Dachbleche24

Since \(x > 4\), \(x = 2 + 2\sqrt3 \approx 5.464\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 So slope \( m = \frac{3}{4} \). The perpendicular slope is \( -\frac{4}{3} \).

📌 The line through \( (1, 2) \) with slope \( -\frac{4}{3} \) is:

📌 y - 2 = -\frac{4}{3}(x - 1)

📌 \Rightarrow y = -\frac{4}{3}x + \frac{4}{3} + 2 = -\frac{4}{3}x + \frac{10}{3}

📌 Now find intersection with original line \( 3x - 4y + 12 = 0 \).

📌 Substitute \( y = -\frac{4}{3}x + \frac{10}{3} \):

📌 3x - 4\left(-\frac{4}{3}x + \frac{10}{3}\right) + 12 = 0

📌 \Rightarrow 3x + \frac{16}{3}x - \frac{40}{3} + 12 = 0

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