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Home » But area 504 may not yield integer. - Upplift

But area 504 may not yield integer. - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Question:** A bioinformatician is analyzing a genomic dataset containing 2^20 sequences. Each day, she processes half of the remaining sequences. How many sequences are left unprocessed after 5 days?

📌 Solution:** Total sequences: \( 2^{20} = 1,048,576 \).

📌 Each day she processes half:

📌 After Day 1: \( 1,048,576 / 2 = 524,288 \) remaining.

📌 After Day 2: \( 524,288 / 2 = 262,144 \).

📌 After Day 3: \( 262,144 / 2 = 131,072 \).

📌 After Day 4: \( 131,072 / 2 = 65,536 \).

📌 After Day 5: \( 65,536 / 2 = 32,768 \).

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Thus, the remainder is \( \boxed{9} \).
Question:** How many lattice points lie on the ellipse \( \frac{x^2}{2...
Solution:** We seek integer solutions \( (x, y) \) to \( \frac{x^2}{25...
9x^2 + 25y^2 = 225
We test integer values of \( x \) from \( -5 \) to \( 5 \), since \( x...
For each \( x \), check if \( 225 - 9x^2 \) is divisible by 25 and the...
\( x = 0 \): \( 9(0) + 25y^2 = 225 \Rightarrow y^2 = 9 \Rightarrow y =...
\( x = \pm 1 \): \( 9(1) = 9 \Rightarrow 25y^2 = 216 \Rightarrow y^2 =...
\( x = \pm 2 \): \( 9(4) = 36 \Rightarrow 25y^2 = 189 \Rightarrow y^2...
\( x = \pm 3 \): \( 9(9) = 81 \Rightarrow 25y^2 = 144 \Rightarrow y^2...

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