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Math Homework Help

Learning linked to sleep

published on July 30th, 2006 . by Vanaja

Students who study hard all week and party on the weekends may lose a lot what they learned. Sleep deprivation on critical nights after learning may cause a 30% loss. Carlyle Smith, a professor of psychology at Trent University in Peter borough, Ontario researched the effect of sleep deprivation on learning by controlling the sleep of students the night they were taught a complex logic game and a list of paired words.

Smith found that when students were tested on paired words, a week later there was no learning deficit among the students deprived of sleep, but when tested on complex logic game, the students deprived of sleep showed a 30%
learning deficit when compared to the group of students not deprived of sleep.
Sleep deprivation on the 3rd night after learning had the same results showing a deficit of about 30% for the complex logic game. Sleep deprivation the 2nd night after learning seemed to have no effect.

This means that if you party all night on Friday after a rough week in the school you will lose 30% of the learning you acquired on Wednesday and Friday. If you lose sleep on Saturday night then Thursday’s learning is also affected.
Ref: Mathematics today

Sides of a Triangle

published on July 28th, 2006 . by Vanaja

Today let’s discuss one problem from geometry.

I‘ll ask you one question. What is the area of a right triangle with sides 4cm 5cm and 9cm? Before trying to answer, please read the question once more.




Answer
It is not possible to make a triangle with the given measurements.
In a triangle, the sum of the two sides will be greater than the third side. Here in this case sum of two sides 4cm+5cm=9cm, which is not greater than the third side of measurement 9cm.

Locus -Definition

published on July 23rd, 2006 . by Vanaja

Locus: When a point moves subject to certain specified conditions, the path traced out by it is called locus.

Equation of a locus: Equation to a locus is the algebraic relation that exists between x and y coordinates of a general point on the locus.

Example:
Find the equation of the locus of points such that the sum of its distances from (0,3) and (0,-3) is 8.

Solution:

(To solve this problem you must know Distance Formula)

Let P(x,y) be any point of the locus and A and B be the points (0,3) and
(0,-3) respectively.

Have a Short Break

published on July 22nd, 2006 . by Vanaja

Watch this Illusion picture.

Liked?

Operations with Fractions

published on July 22nd, 2006 . by Vanaja

Addition and Subtraction

When adding or subtracting fractions, if the denominators are same, simply add or subtract the numerators and write the denominator given.

If the denominators are different, convert each fraction so that its denominator is equal to the Lowest Common Multiple of the denominators of the given fractions. This means multiplying both the numerator and denominator by the same term. For example, say the LCM is 24 and one fraction in the problem is 5/6, then to convert that fraction to denominator of 24 you must multiply numerator and denominator by4, so the fraction becomes 20/24. You follow this same procedure for each term, add or subtract as indicated by the sign of each term and divide the total by the LCM

For example:


Multiplication of Fractions
is straightforward. You just multiply the numerators and multiply the denominators and then reduce the fraction to its lowest term, if possible

When we divide Fractions, we actually multiply the numerator by the reciprocal of the denominator. A reciprocal is a fraction turned upside down. For example, 3/4 divided by 5/6 = 3/4*6/5 = 18/20 = 9/10



Help with fractions

published on July 19th, 2006 . by Vanaja

It appears that many students, even some students of grade 9 and grade 10 are struggling with fractions. So I have prepared this lesson.Not in a thorough but simplified manner.

A term which is of the form a/b is called a fraction. The top Numbers a’ is called the numerator and the bottom number ‘b’ is called the denominator.

Proper fraction: If the numerator is less than the denominator, it is called a proper fraction
Example:1/2,4/7

Improper Fraction: If the numerator is greater than the denominator, it is called an improper fraction.

Example:5/2,9/7

Mixed Fraction: - A term consisting of an integer (5) followed by a proper fraction (2/3), written as 5 2/3 is called a mixed fraction.

see you tomorrow

Some basic math lessons

published on July 19th, 2006 . by Vanaja

I n the coming days I’ll post some basic math lessons . Since this blog is not compatible with math symbols I can not put all topics. But some basic principles and topics in algebra, geometry, trigonometry and calculus will be given. In between I’ll also post as earlier, some math puzzles, brain teasers and Illusion pictures.

So keep visiting and enjoy this math fun site.

You and an elephant have the same weight!!!?

published on July 15th, 2006 . by Vanaja

Don’t be get angry. I am going to show this.

What is wrong? My calculations or your eating habbits!?

EINSTEIN’S BRAIN

published on July 12th, 2006 . by Vanaja


The secret of Einstein’s immense intellect may finally have been uncovered. One area of his brain was significantly different from most people’s.

Albert Einstein died in 1955, at the age of 76. His brain was then removed and preserved for scientific research. Scientists at McMaster University, Canada compared the size and shape of Einstein’s brain with those of 35 men and 56 women with average intelligence.

In general, Einstein’s brain was the same as all the others except one particular area-the region responsible for mathematical thought and the ability to think in terms of space and movement.

Extensive development of this region meant that his brain was 15% wider than the other brains studied.

Uniquely Einstein’s brain also lacked a groove that normally runs through this area. The researchers suggest that its absence may have allowed the neurons to communicate much more easily.

This unusual brain anatomy may explain why Einstein thought the way he did. Einstein allowed his brain to be studied after his death.

Ref: Mathematics today

From Lilavati

published on July 11th, 2006 . by Vanaja

Here is an ancient problem from Bhaskaracharya’s (Indian Mathematician ) Lilavati:

A beautiful maiden, with beaming eyes, asks me which is the number that, multiplied by 3, then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied by itself, diminished by 52, the square found, addition of 8,division by 10 gives the number 2?

Well, it sounds complicated, doesn’t it? No, not if you know how to go about ?



Answer:
28

The method of working out this problem is to reverse the whole process.


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