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Home » Now compute $ 8104 \mod 10 $: - Silent Sales Machine

Now compute $ 8104 \mod 10 $: - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Multiply through by 3:

📌 9x + 16x - 40 + 36 = 0 \Rightarrow 25x - 4 = 0 \Rightarrow x = \frac{4}{25}

📌 Now find \( y \):

📌 y = -\frac{4}{3} \cdot \frac{4}{25} + \frac{10}{3} = -\frac{16}{75} + \frac{250}{75} = \frac{234}{75} = \frac{78}{25}

📌 So the closest point is \( \left( \frac{4}{25}, \frac{78}{25} \right) \).

📌 Alternatively, use the formula for projection. The distance from point \( (x_0, y_0) \) to line \( ax + by + c = 0 \) is not what we want — we want the **point**. But the vector projection method confirms.

📌 answer is the point:

📌 \boxed{\left( \frac{4}{25}, \frac{78}{25} \right)}

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