The following table gives the sales of an item produced by a company since 1999.
| Year | Sales (in crores of rupees) |
| 1999 2000 2001 2002 2003 2004 | 10 12 9 13 12 14 |
Obtain the least square trend-line equation by using 1999 as zero year.
The first year 1999 is assumed to be 0, 2000 would become 1, 2001 would be 2 and so on. The various steps are outlined in the following table.
The above table yields the following values for various terms mentioned below :
| Year | Sales (Y) | _____ ________ _________ ______ ________ __________.
| Year | Sales (in crores of rupees) |
| 1999 2000 2001 2002 2003 2004 | 10 12 9 13 12 14 |
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.
The motion of a simple pendulum is described by
Find a solution of the above problem in the following two situations.
i) pendulum being released from a point with angular distance and initial velocity zero.
ii) the bob of the pendulum is at the equilibrium position and the initial velocity is
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.
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.
Consider the following first-order ODE formulation = a{L- n(t)}, n(t0) = n0
.
Associate the variables {t, n(t)} and the parameters {a, L} to a physical system so that the above formulation becomes a mathematical model for population changes.