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Home » You Won’t Believe How Humans Fall Flat—The Full, Hilarious Truth! - 500apps

You Won’t Believe How Humans Fall Flat—The Full, Hilarious Truth! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \cdot 2^{n-1} > 500

📌 2^{n-1} > \frac{500}{3} \approx 166.67

📌 Now compute powers of 2:

📌 $ 2^7 = 128 $, $ 2^8 = 256 $

📌 So $ 2^{n-1} > 166.67 $ implies $ n-1 \geq 8 $, thus $ n \geq 9 $.

📌 On day 9, the count is $ 3 \cdot 2^8 = 3 \cdot 256 = 768 > 500 $.

📌 On day 8: $ 3 \cdot 2^7 = 384 < 500 $, so day 9 is the first.

📌 Question: A self-healing polymer film repairs itself over time, with the repair rate modeled by $ r(t) = \sqrt{(t - 8)^2} $ millimeters per hour. For how many integer values of $ t $ is the repair rate exactly 4 mm/hour?

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The sum of an arithmetic series with 10 terms is 150, and the first te...
Sum formula: \( S_n = \frac{n}{2}(2a + (n-1)d) \)
\( 150 = \frac{10}{2}(2 \times 5 + 9d) \)
\( 150 = 5(10 + 9d) \)
\( 150 = 50 + 45d \)
\( 100 = 45d \)
\( d = \frac{100}{45} = \frac{20}{9} \)
#### \(\frac{20}{9}\)
If \( \log_2(x) + \log_2(x-1) = 3 \), find the value of \( x \).
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