6.(5.4) how many nonnegative integer solutions are there to x1 + t2+x3 +x4 + x5 = 27 with: (1) no restriction? (2) х1 — 0 or 1? (3) 21 > 2, х2 > 3, х3 > 1, х4 > 5, х; > 4?

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8