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Home » a_7 = a_6 + a_5 = 21 + 13 = 34 \\ - AMAZONAWS

a_7 = a_6 + a_5 = 21 + 13 = 34 \\ - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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Time for the first part of the journey is \( \frac{120}{80} = 1.5 \) h...
Time for the second part of the journey is \( \frac{180}{90} = 2 \) ho...
Total distance is 120 km + 180 km = 300 km.
Total time is 1.5 hours + 2 hours = 3.5 hours.
Average speed is \( \frac{300}{3.5} = 85.71 \) km/h.
#### 85.71
A cylindrical tank with a radius of 3 meters and a height of 5 meters...
Volume of the cylindrical tank is \( \pi \times 3^2 \times 5 = 45\pi \...
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Height of water in the rectangular tank is \( \frac{45\pi}{12} = \frac...

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Solution:** The sequence 3, 9, 15, 21, ... is arithmetic with first te...
The \( n \)-th term is:
a_n = 3 + (n - 1) \cdot 6 = 6n - 3
We want the largest \( n \) such that \( a_n \leq 500 \):
6n - 3 \leq 500
\Rightarrow 6n \leq 503
\Rightarrow n \leq \frac{503}{6} \approx 83.83
So the largest integer \( n \) is 83.
Thus, there are 83 stable molecular points in the first 500 cubic unit...
\boxed{83}

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