Complementary function and Particular Integral

Complementary function (or complementary solution) is the general solution to a differential equation dy/dx + 3y = 0.

Particular integral (I prefer "particular solution") is any solution you can find to the whole equation.

The general solution of a differential equation, involving an arbitrary constant, represents more than one, even infinitely many, solutions.

The solutions obtained by assigning definite value to the constant is called a particular solution. typically, the value is determined by making the solution satisfy a given condition, traditionally referred to as initial condition.

What is Probability and It's types

Probability theory mathematically formulates incomplete knowledge pertaining to the likelihood of an occurrence. For example, a meteorologist might say there is a 60% chance that it will rain tomorrow. This means that in 6 of every 10 times when the world is in the current state, it will rain.


Probability can of 3 types counting,geometry and algebra


Probability of counting

Let P(event) be
the probability of some event occurring. We can often determine P(event) by counting the number
of successful outcomes and then dividing by the total number of equally likely outcome


Probability as a geometry

Sometimes it is impossible to count the total number of events because there are infinitely many
possibilities. Some problems involve evaluating points on a line segment or in space, or particular
values of a continuous variable such as time.

Probability as Algebra

Here we view probabilities as variables. We then apply algebraic methods to find the values of those variables.

Source: http://www.artofproblemsolving.com/Resources/Files/probarticle.pdf

We will discuss some questions on these 3 on next posts

Sales by Product



Sales by Location of Company(multiply each value by 10 so sales at paulo is 550 millions and so on)





Now I have a question
Q If 20% of Domestic footwear were from Paulo.What was the value of the sales of other products in paulo?

Population in rural areas below poverty

From the above Image calculate the the population in rural areas below poverty line for the year 1973-74.If it is given that population below poverty line in total was 20 crore during that period?

Whos Family can you guess?

Of Abdul, Binoy, and Chandini:

a)Each member belongs to the Tee family whose members always tell the truth or to the El family whose members always lie.

b)Abdul says ''Either I belong or Binoy belongs to a different family from the other two."

Whose family do you name of?

Find Value of E?

   
   A+B+C
       +
       D
       +
       E+F+G
           +
           H
           +
           I

Each alphabet represents digits from 1-9 in the above figure.No two alphabets can have same digit

Also
A+b+C=13
C+D+E=13
E+F+G=13
G+H+I=13

Find the value of E?

Find My Secret Word

One of my secret words is from AIM,DUE,MOD,OAT,TIE.If I tell you that word you will be able to easily guess out the vowels in it from its pronunciation.Which is my secret word?