Step 1: Japan’s surrender in the Second World War was mainly due to the devastating effects of the atomic bombings of Hiroshima and Nagasaki by the United States in August 1945.
Step 2: The bombings caused widespread destruction and loss of life, leading to Japan’s decision to surrender shortly after.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]