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Home » \( 95,000 imes 0.95 = 90,250 \) - Groen Casting

\( 95,000 imes 0.95 = 90,250 \) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Sum: \( 0 + 2 + 4 + 6 + 8 = 20 \), and \( 20 \mod 11 = 9 \).

📌 Thus, the remainder is \( \boxed{9} \).

📌 Question:** How many lattice points lie on the ellipse \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \)?

📌 Solution:** We seek integer solutions \( (x, y) \) to \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \), or equivalently:

📌 9x^2 + 25y^2 = 225

📌 We test integer values of \( x \) from \( -5 \) to \( 5 \), since \( x^2 \leq 25 \Rightarrow |x| \leq 5 \).

📌 For each \( x \), check if \( 225 - 9x^2 \) is divisible by 25 and the result for \( y^2 \) is a perfect square.

📌 \( x = 0 \): \( 9(0) + 25y^2 = 225 \Rightarrow y^2 = 9 \Rightarrow y = \pm 3 \) → 2 points

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