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Home » Don’t Miss These Thursday Morning Blessings – They’ll Spark Real Positivity! - inBeat

Don’t Miss These Thursday Morning Blessings – They’ll Spark Real Positivity! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \( S_5 = 4 \cdot \frac{(\frac{3}{2})^5 - 1}{\frac{3}{2} - 1} = 4 \cdot \frac{\frac{243}{32} - 1}{\frac{1}{2}} = 4 \cdot \frac{\frac{211}{32}}{\frac{1}{2}} = 4 \cdot \frac{211}{32} \cdot 2 = 8 \cdot \frac{211}{32} = \frac{1688}{32} = 52.75 \).

📌 As fraction: \( \frac{1688}{32} = \frac{211}{4} \).

📌 #### \( \frac{211}{4} \)

📌 Combine logs: \( \log_2(x(x - 2)) = 3 \) → \( x(x - 2) = 2^3 = 8 \).

📌 So, \( x^2 - 2x - 8 = 0 \) → factor: \( (x - 4)(x + 2) = 0 \).

📌 So \( x = 4 \) or \( x = -2 \). But \( x > 2 \) for log to be defined, so \( x = 4 \).

📌 A ladder 10 meters long leans against a wall, forming a 75° angle with the ground. How high up the wall does the ladder reach? (Round to nearest tenth)

📌 Height = \( 10 \cdot \sin(75^\circ) \).

🔥 Popular Posts

A function \(f(x) = ax^2 + bx + c\) passes through the points (1, 2),...
Set up equations:
\(a(1)^2 + b(1) + c = 2 \rightarrow a + b + c = 2\)
\(a(2)^2 + b(2) + c = 3 \rightarrow 4a + 2b + c = 3\)
\(a(3)^2 + b(3) + c = 6 \rightarrow 9a + 3b + c = 6\)
Solving these, subtract the first from the second:
\(3a + b = 1\)
\(5a + b = 3\)
Subtract these: \(2a = 2 \rightarrow a = 1\).
Substitute \(a = 1\) into \(3a + b = 1\):

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