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Home » Let $ x = \fracab $. Then $ \fracba = \frac1x $, so: - Dachbleche24

Let $ x = \fracab $. Then $ \fracba = \frac1x $, so: - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Travel time one way = 30 / 4 = 7.5 seconds

📌 Travel time for full trip without stop = 2 × 7.5 = 15 seconds

📌 Charging stop = 2 minutes = 120 seconds

📌 Total time = 15 + 120 = <<15+120=135>>135 seconds

📌 A paleobotanist discovers a fossilized tree that grew in a region with seasonal rainfall patterns. If the tree grew 0.5 cm per month during wet months (7 months per year) and 0.1 cm per month during dry months, how much did it grow over 20 years?

📌 Wet month growth per year = 0.5 × 7 = 3.5 cm

📌 Dry month growth per year = 0.1 × 5 = 0.5 cm

📌 Annual growth = 3.5 + 0.5 = 4 cm/year

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N \equiv 4 \pmod{7}
Start with the first two:
Step 1: Solve \( N \equiv 3 \pmod{4} \) and \( N \equiv 2 \pmod{5} \)
Let \( N = 4a + 3 \). Substitute into second:
4a + 3 \equiv 2 \pmod{5} \Rightarrow 4a \equiv -1 \equiv 4 \pmod{5} \R...
So \( a = 5b + 1 \), then \( N = 4(5b + 1) + 3 = 20b + 7 \)
Thus, \( N \equiv 7 \pmod{20} \)
Step 2: Incorporate \( N \equiv 4 \pmod{7} \)
Let \( N = 20b + 7 \). Then:
20b + 7 \equiv 4 \pmod{7} \Rightarrow 20b \equiv -3 \equiv 4 \pmod{7}

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