The Commonwealth of Nations offers a variety of benefits to its member countries, fostering collaboration across multiple sectors such as trade, diplomacy, education, and social development. It serves as a platform for mutual support and collective goals.
In conclusion, the Commonwealth of Nations provides its members with valuable benefits, including economic growth, political support, educational opportunities, and social development.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]