Question: Solve the equation \(2 \sin^2(x) - 3 \sin(x) + 1 = 0\) for \(0 \leq x \leq 2\pi\).
Answer: \(x = \frac{\pi}{3}\) or \(x = \frac{5\pi}{3}\).
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Question: Find the sum of the first 10 terms of the arithmetic sequence: 3, 6, 9, 12, ...
Answer: Sum = \(\frac{n}{2}(a_1 + a_n) = \frac{10}{2}(3 + 30) = 165\).
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Question: Calculate the area of a sector of a circle with radius \(8\) units and central angle
\(60^\circ\).
Answer: Area = \(\frac{60}{360} \times \pi \times 8^2 = \frac{64\pi}{3}\) square units.
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Question: If \(f(x) = \frac{x^2 - 4}{x + 2}\), find \(f(-2)\).
Answer: \(f(-2)\) is undefined because it results in division by zero.
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Question: Determine the solution set for the inequality \(4x + 5 \leq 3x - 2\).
Answer: \(x \leq -7\).
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Question: Find the equation of the line passing through the points \((-1, 4)\) and \((3, -2)\).
Answer: The equation is \(y = -\frac{3}{2}x + \frac{5}{2}\).
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Question: Solve the equation \(3^{2x - 1} = 27\).
Answer: \(x = 2\).
