Step 1: The Industrial Revolution began in England during the late 18th century, driven by the rise of the capitalist class that demanded large-scale labor for the growing number of factories and industries.
Step 2: England’s strong financial infrastructure, abundant raw materials, and an expanding workforce played key roles in fostering the Industrial Revolution.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]