The latest trends in geography include:
1. Geospatial technology: The use of Geographic Information Systems (GIS) and Remote Sensing (RS) for mapping, environmental monitoring, and urban planning.
2. Sustainability and climate change: The growing importance of studying climate change, sustainability, and environmental impact in geographical studies.
3. Urbanization: An increasing focus on the study of urban geography, including issues of urbanization, migration, and the impact of cities on the environment.
4. Human geography: The study of the relationship between people and their environments, focusing on cultural, economic, and political geography.
5. Globalization: Analyzing the effects of globalization on local cultures, economies, and environments. These trends reflect the dynamic nature of geography as a discipline, incorporating technological advances and global concerns.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]