Question: Solve the equation \(4 \cdot 2^{x - 1} = 32\).
Answer: \(x = 4\).
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Question: Find the length of the arc intercepted by a central angle of \(60^\circ\) in a circle with
radius \(5\) units.
Answer: Length of arc = \(\frac{60}{360} \times 2\pi \times 5 = \frac{\pi}{3} \approx 5.24\) units.
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Question: If \(f(x) = \frac{1}{x}\), find \(f(f(x))\).
Answer: \(f(f(x)) = \frac{1}{\frac{1}{x}} = x\).
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Question: Calculate the surface area of a sphere with radius \(3\) units.
Answer: Surface area = \(4\pi r^2 = 4\pi \times 3^2 = 36\pi\) square units.
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Question: Simplify the expression \(\frac{3x^2}{6x}\).
Answer: \(\frac{x}{2}\).
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Question: Determine the solution set for the inequality \(2x - 7 \geq 3x + 2\).
Answer: \(x \leq -9\).
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Question: Find the midpoint of the line segment with endpoints \((-3, 2)\) and \((5, -4)\).
Answer: Midpoint \(= \left(\frac{-3 + 5}{2}, \frac{2 + (-4)}{2}\right) = (1, -1)\).
