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Home » \(\cos \theta = \sqrt{\frac1625} = \frac45\) (positif dans le premier quadrant) - ToelettAPP

\(\cos \theta = \sqrt{\frac1625} = \frac45\) (positif dans le premier quadrant) - ToelettAPP

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Total percentage allocated: 30 + 25 + 20 = 75%. Remaining: 100 - 75 = 25%.

📌 Amount: 25% of $2,500,000 = 0.25 × 2,500,000 = 625,000.

📌 #### 625000

📌 A game developer designs a VR puzzle where a player must rotate a cube to align glowing faces. The cube’s identifier is determined by the least common multiple (LCM) of the numbers 12 and 18, which unlocks the final level. What is the LCM used?

📌 Prime factorization: 12 = \(2^2 \cdot 3\), 18 = \(2 \cdot 3^2\). LCM = \(2^2 \cdot 3^2 = 4 \cdot 9 = 36\).

📌 In a virtual ecosystem, the population of digital fireflies doubles every 3 hours. If there are initially 150 fireflies, how many fireflies will exist after 12 hours?

📌 Number of doubling periods: 12 / 3 = 4. Final population = \(150 \cdot 2^4 = 150 \cdot 16 = 2400\).

📌 A biotech startup models bacterial growth in a lab culture with the function \( P(t) = 500 \cdot e^{0.4t} \), where \( t \) is in hours. After how many hours will the population exceed 5000?

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t = \frac{4 \pm 2}{6}
t = \frac{6}{6} = 1 \quad \text{and} \quad t = \frac{2}{6} = \frac{1}{...
Both values satisfy the equation. Thus, the values of \(t\) are:
\boxed{1 \quad \text{and} \quad \frac{1}{3}}
Question:** A sequence of neural response intensities in a human-machi...
We simplify the expression:
a_n = \frac{n^2 + 1}{n + 1}
We attempt polynomial division or rewrite the numerator:
Note that \(n^2 + 1\) does not factor nicely over integers, so perform...
a_4 = \frac{4^2 + 1}{4 + 1} = \frac{16 + 1}{5} = \frac{17}{5}

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\boxed{83}
Question:** A plant biologist discovers a growth pattern in a drought-...
Solution:** The sequence 2, 5, 8, 11, ... is arithmetic with first ter...
The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence...
S_n = \frac{n}{2} (2a + (n - 1)d)
For \( n = 30 \):
S_{30} = \frac{30}{2} \left(2 \cdot 2 + (30 - 1) \cdot 3 \right) = 15...
Thus, the total number of root branches produced in the first 30 weeks...
\boxed{1365}
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