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Home » \( d = 400 \) - go-checkin.com

\( d = 400 \) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A = P(1 + r)^23 → 2700 = 500(1 + r)^23

📌 1 + r = 5.4^(1/23) ≈ 5.4^0.04348 ≈ 1.0687

📌 r ≈ 0.0687 = <<0.0687*100=6.87>>6.87%

📌 A homeschooled student models planetary motion and finds that Earth orbits the Sun in ~365.25 days at an average speed of 107,000 km/h. How many kilometers does Earth travel in one orbit?

📌 Time in hours = 365.25 × 24 = <<365.25*24=8766>>8766

📌 Distance = speed × time = 107,000 × 8766 = <<107000*8766=936822000>>936,822,000 km

📌 #### 936822000

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However, consider symmetry: for example, \((m,n)\) and \((n,m)\) give:
So symmetric about x-axis. But both are distinct unless \(y = 0\).
But since 506 ≠ 0, no solution has \(y = 0\) (would require \(m = n\),...
But each \((m,n)\) is distinct, so 16 solutions.
But let’s test a small one: \(m = 1\), \(n = 506\):
\(a = 2\), \(b = 1012\), then \(x = (2+1012)/2 = 507\), \(y = (1012 -...
Check: \(507^2 - 505^2 = (507-505)(507+505) = 2 \cdot 1012 = 2024\), c...
Another: \(m = -1\), \(n = -506\): \(x = -507/2\), not integer — wait!...
But when we list all divisor pairs \((m,n)\) with \(mn = 506\), we inc...
No: for each factorization, we get a point. But since \(m\) and \(n\)...

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