Subjects physics

Median Density 186F7E

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Median Density 186F7E


1. **State the problem:** We need to determine if a median density (дундж нягт) triangle can be formed and find the maximum and minimum values of the median density. 2. **Understanding median density:** Median density is typically the average density of a mixture or composite. To form a triangle with given densities, the sum of any two densities must be greater than the third (triangle inequality). 3. **Triangle inequality for densities:** Let the densities be $d_1$, $d_2$, and $d_3$. The conditions are: $$ \begin{cases} d_1 + d_2 > d_3 \\ d_2 + d_3 > d_1 \\ d_3 + d_1 > d_2 \end{cases} $$ 4. **Maximum and minimum median density:** The median density lies between the minimum and maximum of the three densities. The maximum median density is the largest density, and the minimum median density is the smallest density. 5. **Conclusion:** If the three densities satisfy the triangle inequality, a median density triangle can be formed. The minimum median density is $\min(d_1,d_2,d_3)$ and the maximum median density is $\max(d_1,d_2,d_3)$. This completes the solution for the median density triangle problem.