Consider the pay-off table for two players given below
Player B
By graphical procedure determine the value of the game and the optimal mixed strategy foreach player.
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In a perfectly competitive market, the supply function S(p) and demand function D(p) are given as follows:
, where p is the price:
i) Find the equilibrium prices
ii) Using Walrasian stability condition, determine whether the equilibrium prices are stable.
The rate of increase of susceptible SARS victims is proportional to the number of susceptible persons and number of infected persons. If there are S0 susceptible persons and 1-infected person at a time t0 then
i) set up the equation for the spread of the disease
ii) solve the resulting equation
iii) give a physical interpretation of the same by putting the epidemic curve
iv) write the limitations of this model.
A particle describe a central orbit ra = aa cos n under a force directed towards the pole. Find the law of Force.
(Rewrite the equation in terms of , take logarithms and differentiate with respect to
. Calculate
and use 3a) to find F.)
A particle is projected from the base of an inclined plane making an angle a with the horizontal. The initial velocity of projection is making an angle with the horizontal.
i) Derive the equation to the trajectory.
ii) Find the point at which the particle strikes the plane.
For the problem of finding the period of oscillation of a simple pendulum, obtain a formulation in the case when air resistance is proportional to the square of the velocity. Find a solution for this formulation.
Suppose we find the sum of solutions obtained in (i) and (ii) of (b) above. Does this give a solution of the equation describing the motion? If yes, what physical situation, this solution will be correspond to? When is the velocity of the pendulum maximum? What type of energy does the pendulum have at position of maximum velocity?
A particle moves from an initial velocity u at a constant acceleration f. Find an expression for the distance covered in time t using dimensional analysis.