## Tuesday, July 22, 2008

### Have questions about math problems

Have questions about math problems, get help on this website. You will learn the toughest questions with the easiest way to solve it!!

## Monday, July 21, 2008

Math Problems Solving: A peasant wants to sell his stuff and get some salt and other supply back home. However, he has to cross a river with a small boat. How can you help him carry a sheep, wolf as well as cabbage across the river? You can only carry one item across at one time.

Math problem solving: Hint, Remember, sheep eat cabbage, wolf eat sheep.

That us solve and analysis it together.

1) Carry the sheep first across and leave wolf and cabbage behind, because we know wolf does not eat cabbage.

2) Go back and get the wolf and leave only cabbage behind. Then come back with the sheep in the boat, so it is not eaten by the wolf. I know it takes a lot of effort.

3) Put sheep back and get the cabbage. Leave the cabbage with the wolf, and it won’t touch it!

4) Get the sheep across!!

We are successful!!

## Sunday, July 20, 2008

### Algebra: quick ways to solve

Solving math problems quickly: algebra

Do you know what is 5*5? 15*15? Or 25*25?

It gets harder and harder as you increase the numbers before 5. However, I have an easy way to help you get the answer without using a pen or calculator!!

Here is the way:

Please pay a close attention to the pattern:

5*5=25

15*15=225

25*25=625

35*35=1225

45*45=2025

:

What is the pattern? Correct! The results we get all have 25 as the last two digits. So how about the other digits?

Then you should find 1*2=2; 2*3=6; 3*4=12; and so on...

Then the other number should be the number before 5 multiple the same number plus 1.

Using this method, what is 65*65=?

Ans: 4225

What is 11*11=? 121

111*111=? 12321

1111*1111=? 1234321

What is 111111^2=?

Similar method!

Do you know what is 5*5? 15*15? Or 25*25?

It gets harder and harder as you increase the numbers before 5. However, I have an easy way to help you get the answer without using a pen or calculator!!

Here is the way:

Please pay a close attention to the pattern:

5*5=25

15*15=225

25*25=625

35*35=1225

45*45=2025

:

What is the pattern? Correct! The results we get all have 25 as the last two digits. So how about the other digits?

Then you should find 1*2=2; 2*3=6; 3*4=12; and so on...

Then the other number should be the number before 5 multiple the same number plus 1.

Using this method, what is 65*65=?

Ans: 4225

What is 11*11=? 121

111*111=? 12321

1111*1111=? 1234321

What is 111111^2=?

Similar method!

## Friday, July 18, 2008

### Math problems: 2 to the power of x, exponential equations

Hey, do you hate the high rate of interest at banks? Do you want to borrow money from me? I have a whole different system of rate! Start from 2 cents a day!

Here is my system:

If you borrow $100.00 from me, the first day the interest is 2^1 cents, that is 2 cents. The second day is 2^2 cents, that is 4 cents. The third day is2^3, 8 cents....do you know how many interest you have to pay after 5 days? 10 days?

Let’s calculate together!

Ans: 2^1+2^2+...+2^5=2+4+8+16+32=62 cents

For ten days:

62+2^6+2^7+...+2^10=62+64+128+256+512+1028=2050 cents that are $20.50

What a treat!!

Check out how much you have to pay me in a month that is going to be a nightmare for you!! So, remember nothing will come for free and remember the beauty of mathematics!!

Here is my system:

If you borrow $100.00 from me, the first day the interest is 2^1 cents, that is 2 cents. The second day is 2^2 cents, that is 4 cents. The third day is2^3, 8 cents....do you know how many interest you have to pay after 5 days? 10 days?

Let’s calculate together!

Ans: 2^1+2^2+...+2^5=2+4+8+16+32=62 cents

For ten days:

62+2^6+2^7+...+2^10=62+64+128+256+512+1028=2050 cents that are $20.50

What a treat!!

Check out how much you have to pay me in a month that is going to be a nightmare for you!! So, remember nothing will come for free and remember the beauty of mathematics!!

## Thursday, July 17, 2008

### dimensional questions

Math problems

: dimensional questions 2

There is an ant at the corner of a cube, and their destination is the opposite corner where there is a dead fly. The cube’s edges are 5 centimetres. What is the shortest way and how many centimetres?

Do you know the answer?

Ans:

2*5=10

10^2+5^2=ab^2=125

(125)^-2=ab

Do you know why? It is the shortest distance between two points method!! Just go straight without any turns will be the fastest way!! Try it yourself!

: dimensional questions 2

There is an ant at the corner of a cube, and their destination is the opposite corner where there is a dead fly. The cube’s edges are 5 centimetres. What is the shortest way and how many centimetres?

Do you know the answer?

Ans:

2*5=10

10^2+5^2=ab^2=125

(125)^-2=ab

Do you know why? It is the shortest distance between two points method!! Just go straight without any turns will be the fastest way!! Try it yourself!

## Wednesday, July 16, 2008

### Math Problems:

Math Problems:Solving quadratic equation

For some questions, you have some conditions that you don’t know. So you can use a symbol such as “n” to set up several equations according to the questions. Then solve the equations that you set up in order to get the value for “n”.

Here is an example:

If you spend five dollars on shoes, two dollars on gloves and after that you still have four dollars left. How many dollars do you have originally?

Ans: Make the amount of money you have originally “n”, so:

n-5-2=4

n=4+5+2=11

Thus, you have 11 dollars originally!!

Solving math problem-quadratics equation, and quadratics formula derivation:

Example 2:

ax^2+bx+c=0

1x^2+4x+4=0=

(x+2)^2

0=x+2

x=-2

quadratics formula derivation:

ax^2+bx+c=0 divide both side by a

x^2+b/ax+c/a=0, then put c/a to the other side

x^2+b/ax=-c/a,

x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a

(x+b/2a)^2=b^2/4a^2-c/a

x+b/2a=(+/- (b^2-4ac)/4a^2)^(-2)

x= (b+_(b^2-4ac))^(-2)/2a

For some questions, you have some conditions that you don’t know. So you can use a symbol such as “n” to set up several equations according to the questions. Then solve the equations that you set up in order to get the value for “n”.

Here is an example:

If you spend five dollars on shoes, two dollars on gloves and after that you still have four dollars left. How many dollars do you have originally?

Ans: Make the amount of money you have originally “n”, so:

n-5-2=4

n=4+5+2=11

Thus, you have 11 dollars originally!!

Solving math problem-quadratics equation, and quadratics formula derivation:

Example 2:

ax^2+bx+c=0

1x^2+4x+4=0=

(x+2)^2

0=x+2

x=-2

quadratics formula derivation:

ax^2+bx+c=0 divide both side by a

x^2+b/ax+c/a=0, then put c/a to the other side

x^2+b/ax=-c/a,

x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a

(x+b/2a)^2=b^2/4a^2-c/a

x+b/2a=(+/- (b^2-4ac)/4a^2)^(-2)

x= (b+_(b^2-4ac))^(-2)/2a

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