Find the current density when oxygen diffuses through a red cell of thickness 2.5 10-8 cm , the two ends of which are maintain at a fixed concentration C0 .
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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.
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 body of constant mass m is projected vertically upward with an initial velocity v0 in a medium offering a resistance k | v | , where k is a constant. Neglect changes in the gravitational force.
i) Find the maximum height xm attained by the body and the time tm at which this maximum height is reached.
ii) Show that if kv0 /mg < 1, then tm and xm can be expressed as
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.
Find the current density when oxygen diffuses through a red cell of thickness 2.5 10-8 cm , the two ends of which are maintain at a fixed concentration C0 .
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.
A tumour is grown in a laboratory with a plentiful supply of nutrients. The number of cells in the tumour is proportional to its volume V at time t . Its growth rate is then . The growth rate decreases exponentially with t . Its value at time t being found empirically to
, where a and l are positive constants.
i) express this empirical law as a differential equation
ii) find the solution of the differential equation obtain subject to the initial condition V = V0 at t = 0.