HOW TO TAKE DECISIONS?

Tom has to decide whether to go to a college or take up a job.

SCENARIO I
If Tom belongs to a middle-class family, going to a good college and earning a degree will help his family and his career. Going to a job straight away will put him in a low-level job. And he may stick with it for his entire life. Here education yields more than a job.

SCENARIO II
Say, Tom belongs to a rich family. His father is running an industry employing hundreds of persons. His father is also ailing at present. So, for Tom education is not essential. It is only an ornament. If he takes up a job in the family business, he will earn valuable experience and move up the ladder in the company management quickly. He can study through distance education. Or he can go to part-time classes. He is not going to lose anything for want of higher education. Here work-experience yields more than education.

"The cost of what you do is what you miss or lose".

This sentence can be better understood by taking another example.
Say, you are running a shoe factory. You want to buy modern machines which will increase the production rate. But it cost about 500000 rupees. Is it wise to invest in the machines? A lakh rupee fetches the interest of 30000 rupees annually, when it is deposited a bank. (At the rate of 6% per annum). If you strongly believe the machines will give you more gain than 30000 rupees yearly than you can go ahead with machines.
Here 'what you do' is 'buying machines' and what you miss is "interest 30000 rupees". The missing element is called 'opportunity cost' in economics.
In every situation, calculate the opportunity cost and take decisions based on that. But the cost need not be material like money, it may also be abstract like 'happiness'.
The idea 'opportunity cost' can be employed to use your time efficiently. The decisions like 'go to college or cricket match today' can be easily made using this idea. If it is a practical class, you should attend it [oppurtunity cost - missing an important experiment]. If it is a dull lecture, you may go to the stadium.

To take voluntary retirement or not.
To study abroad or not.
To go for a second child or not.
To buy a house or lease a house
You can always use this technique in situations like the ones given above.

"The cost of something is what you give up to get it".
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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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