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Home » But mathematically, the ratio is **infinite** or **undefined**. - go-checkin.com

But mathematically, the ratio is infinite or undefined. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Try n = 7: \( S_7 = \frac{7}{2}(10 + 18) = 3.5 \times 28 = 98 \)

📌 Try n = 10: \( \frac{10}{2}(10 + 27) = 5 \times 37 = 185 \)

📌 No integer n satisfies exactly—recheck:

📌 Use exact: \( n = \frac{-7 + 51.85}{6} \approx 7.475 \) → No integer solution.

📌 But if we accept approximation: closest integer not valid. Recheck setup.

📌 Wait: Try n = 8 gives 124, n = 7 gives 98 — no match.

📌 But if equation is correct, then solve exactly:

📌 Discriminant = \( 49 + 2640 = 2689 \), which is not a perfect square → no integer n.

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Now compute \( 6084 \mod 9 \). Use digit sum or direct division:
Sum of digits of 6084: \( 6 + 0 + 8 + 4 = 18 \), and \( 18 \equiv 0 \p...
\equiv 0 \pmod{9}
Alternatively, \( 78 \equiv 78 \mod 9 \): \( 7 + 8 = 15 \Rightarrow 1...
Thus, the remainder is \( \boxed{0} \).
Question:** What is the remainder when \( 1001 + 1003 + 1005 + 1007 +...
Solution:** Compute the sum:
+ 1003 + 1005 + 1007 + 1009 = 5 \cdot 1005 = 5025
Now compute \( 5025 \mod 11 \). Use alternating sum for modulo 11:
\( 5 - 0 + 2 - 5 = 2 \), or directly:

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Yes.
Now use that instead.
A science educator compares kinetic energies: a 1000-kg car moving at...
Car KE = 0.5 × 1000 × (20)² = 500 × 400 = 200,000 J
Ball KE = 0.5 × 2 × (100)² = 1 × 10,000 = 10,000 J
A cartographer overlays two map layers with resolutions 1 meter/pixel...
Area = 2 km² = 2,000,000 m²
Each 0.5 m pixel has area 0.25 m²
Number of pixels = 2,000,000 ÷ 0.25 = <<2000000/0.25=8000000>>8,000,00...
#### 8000000

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