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Home » \( P(10) = -200 + 400 - 150 = 50 \) - Abu Waleed Tea

\( P(10) = -200 + 400 - 150 = 50 \) - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A geophysicist monitors seismic activity and records an earthquake every 18 days at location X and every 24 days at location Y. If both locations experienced an earthquake today, after how many days will both locations experience an earthquake on the same day again?

📌 Find the LCM of 18 and 24.

📌 Prime factors of 18: \(2^1 \times 3^2\)

📌 Prime factors of 24: \(2^3 \times 3^1\)

📌 LCM = \(2^3 \times 3^2 = 8 \times 9 = 72\)

📌 Both locations will experience an earthquake on the same day again in 72 days.

📌 An online course offers a math module over 200 hours, where a student improves their proficiency by 2% every day. If they start with 50% proficiency, after how many days will they reach at least 90% proficiency?

📌 Initial proficiency: 50%

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The perimeter is given by:
\[ 2(w + 2w) = 72 \]
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\[ w = 12 \]

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Next, consider the case where \(\cos(z) = 0\):
\cos(z) = 0 \quad \Rightarrow \quad z = 90^\circ, \quad z = 270^\circ
We verify these solutions in the original equation:
For \(z = 90^\circ\), \(\sin(180^\circ) = 0\) and \(\cos(90^\circ) = 0...
For \(z = 270^\circ\), \(\sin(540^\circ) = 0\) and \(\cos(270^\circ) =...
Thus, the angles \(z \in [0^\circ, 360^\circ]\) that satisfy the equat...
z = 30^\circ, \quad 150^\circ, \quad 90^\circ, \quad 270^\circ
oxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}
An electrical engineer is optimizing a power grid model and encounters...
We are given a linear transformation defined by:

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