EARN WHILE YOU SLEEP

A man should earn because everything has a price even drinking water. A man starts earning after education. His income will not be proportional to his work. The earnings will be less than the quantum of his work initially. Because he is learning the trick and tools of the trade. During the middle age of a man (Man includes woman), his income will match his work output. When he further moves into the old age, his income will increase but work and duty may decline. Because, he mostly will do supervisory and management roles.
Incomes are two kinds. One is active and the other is passive. You earn active income by physically doing work, that is by doing day-job. Passive income comes from rent, interest etc . As you age, active income should decrease and passive income should rise.

HOW TO RAISE THE PASSIVE INCOME?
1. By renting your property like house, shop, car etc. Buying a new property and renting is not advisable or profitable. Your inherited or old property is good for renting.

2. Leasing your company, your land, car or house. By leasing your company, you will get a regular income without much effort in the old age.

3. By investing in deposits, shares (carries risk), corporate bonds, pension schemes, etc. The bonds are said to yield 10 to 12% of interest.

4. Being creative: Your books, paintings , songs, software, writings may sell like hot-cakes and may bring you royalties, if you are very very lucky and talented.

5. Digital income: You tube video, blog, online short courses, websites, online store 'apps' may bring you money, if you are persevere.

6. Reverse Mortgaging: If you have a good house, you can pledge it to a bank (SBI). You will get a regular income on it. And you can live in the house till end. After your life, your son may redeem it from the bank or the bank will auction it.

Money earns more money. Stand on your own leg. Do not expect from anybody, even from your children. Do not fall for unbelievable 'money making' advt.
Plan early, be honest. God will take care of you.
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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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