Question: Solve the equation \(2 \log_2(x) - 3 = 1\).
Answer: \(x = 8\).
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Question: Find the area of a rhombus with diagonals \(6\) units and \(8\) units.
Answer: Area = \(\frac{1}{2} \times 6 \times 8 = 24\) square units.
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Question: If \(f(x) = \frac{2x + 1}{x - 3}\), find \(f(3)\).
Answer: \(f(3)\) is undefined because it results in division by zero.
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Question: Calculate the volume of a cone with radius \(5\) units and height \(12\) units.
Answer: Volume = \(\frac{1}{3} \times \pi \times 5^2 \times 12 = \frac{300\pi}{3} = 100\pi\) cubic
units.
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Question: Determine the solution set for the inequality \(-2x + 3 > x + 8\).
Answer: \(x < -5\).
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Question: Find the value of \( \tan(30^\circ) \) using the unit circle.
Answer: \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \).
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Question: Solve the equation \(5e^{2x} = 125\).
Answer: \(x = \frac{2}{3} \ln(5)\).
