The maximum kinetic energy of a photoelectron is equal to the energy provided by the photon minus the work function of the material. The kinetic energy is given by:
\[ K.E. = eV = 1.5 \, {eV} \] where \( e \) is the charge of the electron and \( V \) is the stopping potential.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]