What is the area of the region bounded by |x| \leq 2k and |y| \leq k, where k is a positive <strong>REAL</strong> number?
- A. 2k^{2}
- B. 4k^{2}
- C. 5k^{2}
- D. 8k^{2} ✓
Correct Answer: D. 8k^{2}
Explanation
The inequality |x| \leq 2k implies -2k \leq x \leq 2k, which gives a horizontal width of 4k. The inequality |y| \leq k implies -k \leq y \leq k, which gives a vertical height of 2k. The region is a rectangle, and its area is base \times height = 4k \times 2k = 8k^2.
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