Math Is Fun Forum

Please help me...

Hi Franklin,

Can you give me the detailed answer?

Please...

Hi Ant,

How did you get 17160 feet?

Thanks for all.

Finally, I have found the solution in anotyher method.

Here is the solution.

Problem:

Amy has fewer than 100 computer disks. When she stacks them by elevens, ten are left over. When she stacks them by tens, seven are left over, and three are left over when she stacks them by sixes. How many disk does she have?

Solution: Using Chinese Remainder Theorem:

When she stacks them by elevens, ten are left over.

It can be written as, x = 10 (mod 11) => x = 11t +10

When she stacks them by tens, seven are left over.

x = 7 (mod 10) => x = 10 t + 7

when she stacks them by sixes, three are left over.

x = 3 (mod 6)=> x = 6 t + 3.

x = 11t + 10.---------(A)

x = 10t + 7.

x = 6t + 3.

Substitute x = 11t+10 in the second statement.

We get,

11t+10 = 7 (mod10)

Casting out 10, we get,

t + 0 = 7 (mod 10)

It can be written as,

t = 10s+7.

Substitute this in (A), we get,

x = 11(10s+7)+10.

x = 110s + 77 + 10

x = 110s +87

From the third statement,

x = 3 (mod 6)

Substitute x = 110s+87 in the above,

110s + 87 = 3 (mod 6)

Casting out 3 we get,

2s + 3 = 3 (mod6)

2s = 0 (mod 6)

It can be written as,

2s = 6t.

Therefore, s = 3t

We found x = 110s +87

x = 330s + 87.

Therefore,the solutions 87, 417, 747,. . .

Thanks for all.

Can you give me a method and steps?

Hi sammy182,

The slope of a line measures the steepness of the line.

Most of you are probably familiar with associating slope with "rise over run".

Rise means how many units you move up or down from point to point.  On the graph that would be a change in the y values.

Run means how far left or right you move from point to point.  On the graph, that would mean a change of x values.

In another way,

The slope m = tan x.

Here, x is nothing but angle made by the horizontal line (x axis) with the slant line.

tanx is nothing but opposite side/adjescent side.

Opposite side is nothing but y axis.

That is, change in y coordinate.

Adjescent side is nothing but x axis.

That is, change in x coordinate.

Hope you will understand the concept.

When two points (x1 , y1) and (x2 , y2) are given, then the formula for midpoint is

                                   {(x1+x2)/2 , (y1+y2)/2}

Oops.. Thanks Ricky...

Hi luca-deltodesco,

Yes, you are right.

Thanks a lot!!!!!!!!

This is the formula for finding the equation of line when the two points ( x1, y1) and (x2, y2) are given,

              (y - y1)(x2 - x1) = (x - x1) (y2 - y1).

Using this formula, we can find an equation of a line for the given points.