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Home » Divide both sides by 500,000: - Midis

Divide both sides by 500,000: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Combine logs: \( \log_2((x+1)(x-1)) = 3 \).

📌 So, \( (x+1)(x-1) = 2^3 = 8 \).

📌 Then \( x^2 - 1 = 8 \).

📌 \( x^2 = 9 \), so \( x = \pm 3 \).

📌 Since \( x-1 > 0 \), \( x > 1 \), thus \( x = 3 \).

📌 The function \( f(x) = rac{2x^2 - 3x + 1}{x - 1} \) has a removable discontinuity. Find the value of \( f(1) \) after removing the discontinuity.

📌 Factor numerator: \( 2x^2 - 3x + 1 = (2x - 1)(x - 1) \).

📌 So \( f(x) = rac{(2x - 1)(x - 1)}{x - 1} = 2x - 1 \) for \( x

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Now compute \( (x + 2y)^2 \):
x + 2y = 3 + 2(2) = 3 + 4 = 7
\boxed{49}
\]Question: An entrepreneur is analyzing signal patterns for an AI-dri...
Solution: We are to maximize the expression
for $0 < x < \frac{\pi}{2}$.
First, expand both squares:
Now sum them:
\sec^2 x + \csc^2 x + 2\sec x \csc x + 1 + 2\sin x \cos x
Recall that $\sec^2 x = 1 + \tan^2 x$, $\csc^2 x = 1 + \cot^2 x$, but...

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