linear equations in one variable

There are mainly four steps in the mathematical formulation of linear programming problem as a mathematical model. We will discuss formulation of those problems which involve only two variables. 1. Identify the decision variables and assign symbol..

Objective Function: The Objective Function is a linear function of variables which is to be optimised i.e., maximised or minimised. e.g., profit function, cost function etc. The objective function may be expressed as a linear expression. Constraints: A ..

Example: A rubber ball dropped from a certain height (h 1 ) on reaching the ground bounces up to a height less than the initial one (h 2 ). It continues to bounce but the height to which it rises keeps decreasing (h 3 , h 4 ). The distance covered by the ball in unit time decre..

Normally metals donate electrons from their valence shell so as to form positively charged ions such that the charge on the ion is equal to its electropositive valency. However, in transition elements, an atom loses electrons from the shell next to the valence shell (penultimate shell). In such a s..

Suppose a particle P is moving in a circle as shown below. Let O be the centre and OX be the X-axis. The position of the particle may be described by the angle q..

So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x 1 , x 2 , x 3 , ..... x n , which can optimise (maximize or minimize) the objective function Z, then we say that these va..

Let us consider a situation where the force is acting along the X-axis and the magnitude of the force is varying with position 'x'. Thus, as the ball moves, the magnitude of the work done by the force, on the ball, changes. The adjacent graph shows the plot of a one dimensional vari..

Random Variables and Probability Distributions - It is often very important to allocate a numerical value to an outcome of a random experiment. For example, consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome HH HT TH TT No. of heads (x) 2 ..

It is often very important to allocate a numerical value to an outcome of a random experiment. For example, consider an experiment of tossing a coin twice and note the number of heads (x) obtained. Outcome HH HT TH TT No. of heads (x) 2 1 1 0 x is called a random variable..

Let S be a sample space associated with a given random experiment. A real valued function X which assigns to each w i S, a unique real number, X( w i ) = x i is called a random variable . Two types of random variables are 1. Continuous random ..