In my view, Spain’s prosperity greatly surged following the establishment of its colonies in the Americas. The Spanish Empire reaped immense economic rewards from these colonies, which were instrumental in Spain’s rise as a dominant European power during the Age of Exploration and thereafter.
In conclusion, Spain’s establishment of colonies in the Americas was pivotal to its prosperity, making it one of the wealthiest and most powerful empires of its time.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]