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ЮРА 777
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Математика

Postby ЮРА 777 » 06 Jul 2015, 21:08

It takes a river steamer 2 days to go with the stream from A to B and 3 days to return from B to A....
How many days will it take a raft to float from A to B
IF ITS SPEED is equal to the rate of flow of the river?
Last edited by ЮРА 777 on 06 Jul 2015, 23:07, edited 1 time in total.

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Re: Learn English!

Postby ЮРА 777 » 06 Jul 2015, 22:11

Solution.
Let S be the distance between A and B, X the true speed of the steamer and Y the speed of the raft.
( true speed--истинная скорость парохода..скорость в стоячей воде или в озере----neglecting the rate of flow of the river))..
OWN SPEED OF THE STEAMSHIP---собственная скоросnь парохода(????)
(Что более употребительно: steamer или STEAMSHIP ?)


It is required to determine S/Y,i.e the time which the raft will float from A to B.
By hypothesis, S=2( x+y)
S=3(X-Y)

Therefore, 3(x-y)=2(x+y) or x=5y
Hence,S= 12Y. Consequently,the required time is S/Y= 12 days.

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 13:24

By hypothesis--по предположению..
Hence--отсюда следует-
Consequently----следовательно.,поэтому..

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 14:13


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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:08

inear Systems with Two Variables
A linear system of two equations with two variables is any system that can be written in the form.


Image

where any of the constants can be zero with the exception that each equation must have at least one variable in it.
Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.
Here is an example of a system with numbers.


Image

Before we discuss how to solve systems we should first talk about just what a solution to a system of equations is. A solution to a system of equations is a value of x and a value of y that, when substituted into the equations, satisfies both equations at the same time.
For the example above and is a solution to the system. This is easy enough to check.

Image

So, sure enough that pair of numbers is a solution to the system. Do not worry about how we got these values. This will be the very first system that we solve when we get into examples.
Note that it is important that the pair of numbers satisfy both equations. For instance and will satisfy the first equation, but not the second and so isn't a solution to the system. Likewise, and will satisfy the second equation but not the first and so can't be a solution to the system.
Now, just what does a solution to a system of two equations represent? Well if you think about it both of the equations in the system are lines. So, let's graph them and see what we get.

Image

TwoEq_G1
As you can see the solution to the system is the coordinates of the point where the two lines intersect. So, when solving linear systems with two variables we are really asking where the two lines will intersect.
We will be looking at two methods for solving systems in this section.
The first method is called the method of substitution . In this method we will solve one of the equations for one of the variables and substitute this into the other equation. This will yield one equation with one variable that we can solve. Once this is solved we substitute this value back into one of the equations to find the value of the remaining variable.
In words this method is not always very clear. Let's work a couple of examples to see how this method works.



So, let's graph them and see what we get.----Давайте прооведем их и посмотрим,что мы получили
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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:14

Image

Image
Solution
Image

So, this was the first system that we looked at above. We already know the solution, but this will give us a chance to verify the values that we wrote down for the solution.
Now, the method says that we need to solve one of the equations for one of the variables. Which equation we choose and which variable that we choose is up to you, but it's usually best to pick an equation and variable that will be easy to deal with. This means we should try to avoid fractions if at all possible.
In this case it looks like it will be really easy to solve the first equation for y so let's do that.


This means we should try to avoid fractions if at all possible.
In this case it looks like it will be really easy to solve the first equation for y so let's do that.


Это значит,что мы должны попытаться избежать дробей ,если это вообще возможно..
В этом случае,похоже, действительно будет легче решить первое уравнение относительно у,так что сделаем это
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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:21

Image
Now, substitute this into the second equation.

Image

This is an equation in x that we can solve so let's do that

Image
So, there is the x portion of the solution.
Finally, do NOT forget to go back and find the y portion of the solution. This is one of the more common mistakes students make in solving systems. To so this we can either plug the x value into one of the original equations and solve for y or we can just plug it into our substitution that we found in the first step. That will be easier so let's do that.

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:26

Image

So, the solution is and as we noted above.

Image

With this system we aren't going to be able to completely avoid fractions. However, it looks like if we solve the second equation for x we can minimize them. Here is that work.

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:37

Image

Image
Now, substitute this into the first equation and solve the resulting equation for y .
Image

Image
Image

Image

Image

Finally, substitute this into the original substitution to find x .

Image

So, the solution to this system is
Image

Image
Last edited by ЮРА 777 on 07 Jul 2015, 20:45, edited 2 times in total.

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:39

As with single equations we could always go back and check this solution by plugging it into both equations and making sure that it does satisfy both equations. Note as well that we really would need to plug into both equations. It is quite possible that a mistake could result in a pair of numbers that would satisfy one of the equations but not the other one.
Let's now move into the next method for solving systems of equations. As we saw in the last part of the previous example the method of substitution will often force us to deal with fractions, which adds to the likelihood of mistakes. This second method will not have this problem. Well, that's not completely true. If fractions are going to show up they will only show up in the final step and they will only show up if the solution contains fractions.
This second method is called the method of elimination . In this method we multiply one or both of the equations by appropriate numbers ( ie multiply every term in the equation by the number) so that one of the variables will have the same coefficient with opposite signs. Then next step is to add the two equations together. Because one of the variables had the same coefficient with opposite signs it will be eliminated when we add the two equations. The result will be a single equation that we can solve for one of the variables. Once this is done substitute this answer back into one of the original equations.
As with the first method it's much easier to see what's going on here with a couple of examples.

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Re: Learn English!

Postby ЮРА 777 » 07 Jul 2015, 20:53

Example 2 Solve each of the following systems of equations.
a
Image
b
Image

a
Image

This is the system in the previous set of examples that made us work with fractions. Working it here will show the differences between the two methods and it will also show that either method can be used to get the solution to a system.
So, we need to multiply one or both equations by constants so that one of the variables has the same coefficient with opposite signs. So, since the y terms already have opposite signs let's work with these terms. It looks like if we multiply the first equation by 3 and the second equation by 2 the y terms will have coefficients of 12 and -12 which is what we need for this method.
Here is the work for this step.

Image


So, as the description of the method promised we have an equation that can be solved for x . Doing this gives, which is exactly what we found in the previous example. Notice however, that the only fraction that we had to deal with to this point is the answer itself which is different from the method of substitution.
Now, again don't forget to find y . In this case it will be a little more work than the method of substitution. To find y we need to substitute the value of x into either of the original equations and solve for y . Since x is a fraction let's notice that, in this case, if we plug this value into the second equation we will lose the fractions at least temporarily. Note that often this won't happen and we'll be forced to deal with fractions whether we want to or not.


Image

Again, this is the same value we found in the previous example.


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Re: Математика

Postby ЮРА 777 » 08 Jul 2015, 22:38

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Re: Learn English!

Postby ЮРА 777 » 08 Jul 2015, 22:45

the system is incompatible---- система несовместна( нет решений)

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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 08:20

y is arbitary------
произвольный, случайный

arbitrary choice — случайный выбор; выбор наудачу
Their whole scheme of interpretation is purely arbitrary. — Вся их схема объяснения совершенно произвольна

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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 11:32

Интересные фразы о математике на английском языке:
to take accelerated maths — изучать математику по ускоренной программе
His work in maths needs to be brought up to the standard of the others
— ему нужно подтянуться по математике.
maths master — учитель математики
to be a shark at maths — отличаться по математике; "в математике собаку съел"
new maths, new mathematics — новый метод преподавания математики в начальной школе, основанный на теории множеств
mathematics syllabuses — программы, учебные планы по математике
My mathematics are not poor — я неплохо знаю математику
ability in mathematics — математические способности
abstract mathematics — чистая математика
accredited authority in mathematics — признанный авторитет в математике
to apply oneself to mathematics — усердно заниматься математикой
The father assisted his son with his mathematics — отец помогал сыну в математике.
His course of study comprises English, French, and mathematics
— в программу его занятий входят английский язык, французский язык и математика.
At school he developed a great gift for mathematics
— в школе у него обнаружились недюжинные математические способности.
dissertation on /upon/ mathematics — диссертация по математике

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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 11:36

Интересные фразы о математике на английском языке:
to take accelerated maths — изучать математику по ускоренной программе
His work in maths needs to be brought up to the standard of the others
— ему нужно подтянуться по математике.
maths master — учитель математики
to be a shark at maths — отличаться по математике; "в математике собаку съел"
new maths, new mathematics — новый метод преподавания математики в начальной школе, основанный на теории множеств
mathematics syllabuses — программы, учебные планы по математике

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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 11:37


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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 11:44


ЮРА 777
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Re: Learn English!

Postby ЮРА 777 » 09 Jul 2015, 14:24

http://trinity-edu.com.ua/math_in_english_1/

Математика на английском
Чтобы поступить в учебные заведения США, совершенно не обязательно ехать в страну и сдавать экзамены, стать американским студентом можно и находясь дома.
Для этого Вам придется сдать стандартизированные тесты и отправить результаты по почте.
Экзамены, требующиеся для поступления в американские вузы – это
SAT;
GRE;
GMAT
.
Считается, что не один из этих экзаменов не проверяет у будущего студента знание английского, а больше нацелен на проверку аналитических и математических способностей. Хотя надо признать, что при среднем уровне знаний английского сдать SAT, GRE, GMAT будет нелегко.
необходим для поступления на первый курс в колледжи и университеты;
важен для поступления на Master’s Degree и PhD;

а поступить в бизнес-школы невозможно без GMAT.

Система два преподавателя
Подготовка к SAT, GRE, GMAT в TRINITY осуществляется по системе «два преподавателя».
Один преподаватель готовит к вербальной и аналитической части;
От другого преподавателя студенты получают знания по математике.


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