The European Renaissance reached its peak during the 15th and 16th centuries, driven by significant advancements in various fields, such as art, science, literature, and philosophy. Several key factors contributed to this flourishing period:
In conclusion, the Renaissance flourished in the 15th and 16th centuries due to the synergy of artistic excellence, intellectual development, scientific breakthroughs, and favorable political and economic conditions.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]