<p>If K is the area enclosed by two functions f and g then find the sum of digits in K, where<br>\(f = \max(|x|, |y|) = 8\)<br>\(g = \min(|x|, |y|) = 3\)</p>
Step-by-Step Solution
Key Concept: The curve f = max(|x|, |y|) = 8 forms a square with vertices at (±8, ±8), while g = min(|x|, |y|) = 3 forms a square with vertices at (±3, ±3). The enclosed area is the difference between these two squares.
<p><strong>Step 1:</strong> Interpret max(|x|, |y|) = 8. This means the larger of |x| and |y| equals 8. This forms a square with sides along x = ±8 and y = ±8, with vertices at (±8, ±8).</p><p><strong>Step 2:</strong> Interpret min(|x|, |y|) = 3. This means the smaller of |x| and |y| equals 3. This forms a square with sides along x = ±3 and y = ±3, with vertices at (±3, ±3).</p><p><strong>Step 3:</strong> Area of outer square max(|x|, |y|) = 8: Side length = 16 (from -8 to 8), Area = 16² = 256</p><p><strong>Step 4:</strong> Area of inner square min(|x|, |y|) = 3: Side length = 6 (from -3 to 3), Area = 6² = 36</p><p><strong>Step 5:</strong> Enclosed area K = Area of outer square - Area of inner square = 256 - 36 = 220</p><p><strong>Step 6:</strong> Sum of digits in K = 220: 2 + 2 + 0 = 4</p><p>∴ Answer: <strong>4</strong></p>
Correct Answer: 4