What a dorіvnyu value viraz. Znakhodzhennya value virazu: rules, lay down, solution. Calculating the value of viraz by rational methods
In the given statistics, it is clear that they know the meanings of mathematical variations. For some reason, from simple numerical variations and distant ones, we will be able to see the variations in the world of growth and folding. In the end, it is guided by a viraz, to avenge the letters of the meaning, bows, roots, special mathematical signs, steps, functions, etc. The whole theory, for tradition, be sure to clearly and report the butts.
Yak to know the value of the numerical viraz?
Numeric virazi, except for the one, additionally help to describe the mind problems by mathematical language. Mathematical variations can be as simple as betting numbers and arithmetic signs, or even folding, which can be used to reveal functions, steps, roots, bows, etc. Within the framework of enlightenment, it is often necessary to know the meaning of that viraz. About those, like the price, and let's go below.
simplest vip
Tse vypadki, if viraz does not take revenge on anything, except for numbers and arithmetic actions. For a successful knowledge, the meaning of such virazs is to know the order of the display of arithmetic diy without arches, as well as the submission of viconuity to diy with different numbers.
If the viraz is out of numbers and arithmetic signs "+", "·", "-", "÷", then they go to the right in the offensive order: a lot of times and days, sometimes more and more information. Put it on.
Butt 1. The value of the numerical virazu
Do not need to know the value of viraz 14 - 2 · 15 ÷ 6 - 3.
Viconmo collection of many and many days. otrimuєmo:
14 - 2 15 ÷ 6 - 3 = 14 - 30 ÷ 6 - 3 = 14 - 5 - 3.
Now the residual result is being recognized and acceptable:
14 - 5 - 3 = 9 - 3 = 6 .
Appendix 2. The value of the numerical virazu
Numerical: 0, 5 - 2 - 7 + 2 3 ÷ 2 3 4 11 12.
A selection of viconuєmo re-incarnations of fractions, dates and multiples:
0, 5 - 2 - 7 + 2 3 ÷ 2 3 4 11 12 = 1 2 - (- 14) + 2 3 ÷ 11 4 11 12
1 2 - (- 14) +2 3 ÷ 11 4 11 12 = 1 2 - (- 14) +2 3 4 11 11 12 = 1 2 - (- 14) +2 9.
Now we are busy with folding and changing. Grouped fractions and guided to the spilny banner:
1 2 - (- 14) + 2 9 = 1 2 + 14 + 2 9 = 14 + 13 18 = 14 13 18 .
Shukane meaning is known.
Virazi with temples
As soon as you take revenge on the arches, then the stench will start the order. A little bit of vikonuyuyutsya diya in the bows, and then all the rhymes. It will be shown on the butt.
Appendix 3. The value of the numerical virazu
We know the value of viraz is 0, 5 · (0, 76 - 0, 06).
In the case of the presence of the arches, there is a combination of the visually operating operation in the arches, and even then there is a lot.
0.5 (0.76 - 0.06) = 0.50.7 = 0.35.
The meaning of virazіv, scho to revenge the bows in the bows, is based on the same principle.
Appendix 4. The value of the numerical virazu
The numerical value is 1 + 2 · 1 + 2 · 1 + 2 · 1 - 1 4.
Viconuvati diy will be repaired from the inner bows themselves, passing to the last.
1 + 2 1 + 2 1 + 2 1 - 1 4 = 1 + 2 1 + 2 1 + 2 • 3 4
1 + 2 1 + 2 1 + 2 • 3 4 = 1 + 2 1 + 2 2, 5 = 1 + 2 6 = 13.
At the known value of the viraziv with the arms of the smut - after the end of the day.
Virazi with roots
Mathematical virazi, the meaning of which we need to know, can avenge the signs of the root. Moreover, the viraz itself can be a sign of the root. Yak bootie like that? For some it is necessary to know the meaning of the viraz from the root, and then the vityagti to the root from the number rejected in the result. According to the possibility of the roots in the numerical virases, it is necessary to be more beautifully amused, to substitute for the numerical values.
Appendix 5. The value of the numerical virazu
The numerical value of viraz from roots is 2 3 - 1 + 60 ÷ 4 3 + 3 2, 2 + 0, 1 · 0, 5.
Sphatku numbered rooted bend.
2 3 - 1 + 60 ÷ 4 3 = - 6 - 1 + 15 3 = 8 3 = 2
2, 2 + 0, 1 0, 5 = 2, 2 + 0, 05 = 2, 25 = 1, 5.
Now it is possible to calculate the value of all viraz.
2 3 - 1 + 60 ÷ 4 3 + 3 2, 2 + 0, 1 0, 5 = 2 + 3 1, 5 = 6.5
Often to know the meaning of viraz from roots, it is often necessary to carry out a re-creation of a viral turn. Explainable for one more butt.
Appendix 6. The value of the numerical virazu
Skіlki bude 3 + 1 3 - 1 - 1
Yak Bachimo, we have a lot of opportunities to replace the roots with exact values, which will speed up the process of rakhunku. However, in this vipadku you can use the formula for fast multiplying.
3 + 1 3 - 1 = 3 - 1 .
In this rank:
3 + 1 3 - 1 - 1 = 3 - 1 - 1 = 1 .
Virazi with steps
As soon as you have a viraz in the world, it is necessary to count the first one, not to start before all the other things. Buvah so, he himself is an indicator of some steps є viraz. In such a way, the list of values is counted as cich viraziv, and then also the value of the step.
Appendix 7. The value of the numerical virazu
We know the value of virazu 2 3 4 - 10 + 16 1 - 1 2 3, 5 - 2 • 1 4.
Fix it in order.
2 3 4 - 10 = 2 12 - 10 = 2 + 2 = 4
16 1 - 1 2 3, 5 - 2 1 4 = 16 * 0, 5 3 = 16 1 8 = 2.
It was late only to carry out the operation of additional data and knowledge of the value of the viraz:
2 3 4 - 10 + 16 1 - 1 2 3, 5 - 2 • 1 4 = 4 + 2 = 6.
It is also often dozіlno buvaє to carry out a forgiven viraz against the vicarious powers of the step.
Appendix 8. The value of the numerical virazu
The number of offensive virazu values is calculated: 2 - 2 5 4 5 - 1 + 3 1 3 6.
Indicators of the steps are known to the extent that the exact numerical value cannot be rejected. Probably vyhіdne viraz, sob to know its meaning.
2 - 2 5 4 5 - 1 + 3 1 3 6 = 2 - 2 5 2 2 5 - 1 +3 1 3 6
2 - 2 5 2 2 5 - 1 +3 1 3 6 = 2 - 2 5 2 2 5 - 2 + 3 2 = 2 2 5 - 2 - 2 5 +3 2
2 2 5 - 2 - 2 5 + 3 2 = 2 - 2 + 3 = 1 4 + 3 = 3 1 4
Virazi with fraction
If you want to take revenge on fractions, then when calculating such a virase, all the fractions in a new one need to be represented in the view of extraordinary fractions and counting their values.
As in the number and the denominator of the fraction of the presence of the viraz, then the number of cich virazi is counted, and the final value of the fraction itself is recorded. Arithmetic works are listed in the standard order. I will make the butt clearer.
Appendix 9. The value of the numerical virazu
We know the value of a viraz to avenge fractions: 3, 2 2 - 3 · 7 - 2 · 3 6 ÷ 1 + 2 + 3 9 - 6 ÷ 2.
Yak bachimo, in the wicked viraz there are three fractions. The number of їх values is numbered.
3, 2 2 = 3, 2 ÷ 2 = 1, 6
7 - 2 • 3 6 = 7 - 6 6 = 1 6
1 + 2 + 3 9 - 6 ÷ 2 = 1 + 2 + 3 9 - 3 = 6 6 = 1.
We can rewrite our viraz and its numerical value:
1, 6 - 3 1 6 ÷ 1 = 1, 6 - 0.5 ÷ 1 = 1, 1
Often, when the value of viraz is known, it is possible to carry out a quick shot by hand. There is a tacit rule: be it a viraz in front of the knowledge of its meaning, to simplify as much as possible, to build everything up to the most simple ones.
Butt 10. The value of the numerical virazu
Numerous viraz 2 5 - 1 - 2 5 - 7 4 - 3.
We cannot do without the rest of the vitality of the roots of the five, we can only save the way out of the way.
2 5 - 1 = 2 5 + 1 5 - 1 5 + 1 = 2 5 + 1 5 - 1 = 2 5 + 2 4
Pochatkove viraz nabuva viglyadu:
2 5 - 1 - 2 5 - 7 4 - 3 = 2 5 + 2 4 - 2 5 - 7 4 - 3 .
The numerical value of the viraz is:
2 5 + 2 4 - 2 5 - 7 4 - 3 = 2 5 + 2 - 2 5 + 7 4 - 3 = 9 4 - 3 = - 3 4 .
Virazi with logarithms
If there are logarithms in the presence of logarithms, it is worthwhile to count on the ear itself. For example, in the rotated log 2 4 + 2 · 4 it is possible to immediately change the log 2 4 to write the value of the logarithm, and then to select all the actions. Otrimaєmo: log 2 4 + 2 4 = 2 + 2 4 = 2 + 8 = 10.
By the very sign of the logarithm, and in the first place there can also be a number of virazi. In such a vypadku, in the first place there are їkh meaning. Vіzmemo viraz log 5 - 6 ÷ 3 5 2 + 2 + 7.maymo:
log 5 - 6 ÷ 3 5 2 + 2 + 7 = log 3 27 + 7 = 3 + 7 = 10.
It’s hard to calculate the exact value of the logarithm, forcing it to help you know the value of the logarithm.
Appendix 11. The value of the numerical virazu
The known virase value is log 2 log 2 256 + log 6 2 + log 6 3+ log 5 729 log 0, 2 27.
log 2 log 2 256 = log 2 8 = 3.
By the power of logarithms:
log 6 2 + log 6 3 = log 6 (2-3) = log 6 6 = 1.
I know the stagnant power of logarithms, for the rest of the fraction in a twisted turn we can think of it:
log 5 729 log 0, 2 27 = log 5 729 log 1 5 27 = log 5 729 - log 5 27 = - log 27 729 = - log 27 27 2 = - 2.
Now you can go to the calculation of the value of the outward turn.
log 2 log 2 256 + log 6 2 + log 6 3 + log 5 729 log 0, 2 27 = 3 + 1 + - 2 = 2.
Virasi with trigonometric functions
Buvah, in the rotated trigonometric functions of the sine, cosine, tangent and cotangent, as well as the functions, reverberating im. The third value is counted before the vikonannyam of all arithmetic works. In іnshomu vipadku, viraz say goodbye.
Butt 12. The value of the numerical virazu
Know the value of the viraz: t g 2 4 π 3 - sin - 5 π 2 + cosπ.
The list is numbered trigonometric functions, Scho to enter at the viraz.
sin - 5 π 2 = - 1
The given value for viraz and the numerical value is:
t g 2 4 π 3 - sin - 5 π 2 + cosπ = 3 2 - (- 1) + (- 1) = 3 + 1 - 1 = 3.
The value of virazu is known.
Often, in order to know the meaning of the virase with trigonometric functions, it is necessary to re-create it in front of it. Explained on the butt.
Butt 13. The value of the numerical virazu
It is necessary to know the value of the viraz cos 2 π 8 - sin 2 π 8 cos 5 π 36 cos π 9 - sin 5 π 36 sin π 9 - 1.
For the re-implementation, we will vikoristovuvati trigonometric formulas of the cosine of the subcutaneous kut and the cosine of sumi.
cos 2 π 8 - sin 2 π 8 cos 5 π 36 cos π 9 - sin 5 π 36 sin π 9 - 1 = cos 2 π 8 cos 5 π 36 + π 9 - 1 = cos π 4 cos π 4 - 1 = 1 - 1 = 0.
Zagalny vipadok of numerical virazu
In the zagalnyy vypadku trigonometric viraz can be a revenge of all the descriptive elements: arches, steps, root, logarithms, functions. I will formulate bogey rule the meaning of such viraziv.
Yak know the meaning of virazu
- Root, steps, logarithms, etc. replace them with values.
- Vykonuyutsya diy in the arches.
- Reshta dії vikonuyutsya in order of evil to the right. With a few - a lot and a date, sometimes - additional and additional dates.
Take out the butt.
Butt 14. The value of the numerical virazu
It is computable that the value of the viraz is 2 · sin π 6 + 2 · 2 π 5 + 3 π 5 + 3 ln e 2 + 1 + 3 9.
Viraz to reach the foldable і thunderbolt. We didn’t look like this butt, trying to fit in all the descriptions of this butt. Yak know the meaning of such a viraz?
Seemingly, when calculating the value of a folding conventional form, the number of times the number and the denominator is shown as a fraction. We will lastly reconfigure and ask for hanging.
In front of the numerical value of the radical bend 2 · sin π 6 + 2 · 2 π 5 + 3 π 5 + 3. As a rule, it is necessary to know the value of the sinus, і virazi, like є argument of the trigonometric function.
π 6 + 2 2 π 5 + 3 π 5 = π 6 + 2 2 π + 3 π 5 = π 6 + 2 5 π 5 = π 6 + 2 π
Now you can know the meaning of the sinus:
sin π 6 + 2 2 π 5 + 3 π 5 = sin π 6 + 2 π = sin π 6 = 1 2.
The numerical value of the radical turn is:
2 sin π 6 + 2 2 π 5 + 3 π 5 + 3 = 2 1 2 + 3 = 4
2 sin π 6 + 2 2 π 5 + 3 π 5 + 3 = 4 = 2.
With the denominator, the fraction is simpler:
Now we can write down the meaning of all fractions:
2 sin π 6 + 2 2 π 5 + 3 π 5 + 3 ln e 2 = 2 2 = 1.
I'll look around at the tse, we will write down all the viraz:
1 + 1 + 3 9 = - 1 + 1 + 3 3 = - 1 + 1 + 27 = 27 .
Residual result:
2 sin π 6 + 2 2 π 5 + 3 π 5 + 3 ln e 2 + 1 + 3 9 = 27.
In this case, we could calculate the exact values of roots, logarithms, sinuses, etc. Since such an opportunity is dumb, you can try to get used to them by the way of mathematical re-creation.
Calculating the value of viraz by rational methods
Numeric values are required last and accurately. The Danish process can be rationalized and quickened, viciously developed by the numbers. For example, seemingly, there are zero additional items, if there are zero items, you want one of the multipliers. With the urahuvannya of the power of power, one can immediately say that the viraz is 2 · 386 + 5 + 589 4 1 - sin 3 π 4 · 0 to zero. At the same time, it is not obligatory to visit them in the order described in the statistics.
It is just as easy to win the power of the given numbers. Chi does not vikonuyuchi any actions, you can replace, but the value of viraz is 56 + 8 - 3, 789 ln e 2 - 56 + 8 - 3, 789 ln e 2 is also expensive to zero.
Another trick that allows you to speed up the process is the registration of the same re-making of such a group as a result of the formation of a multiplier and a winery zagalny multiplier by the temples. Rational pidhid before calculating virases with fraction - the speed of the same viraz in the number and denominator.
For example, vіzmemo viraz 2 3 - 1 5 +3 · 289 · 3 4 3 • 2 3 - 1 5 +3 · 289 · 3 4. Do not look in the bows, but fast, you can say that the value of viraz is expensive 1 3.
Knowing the value of viraz in the wake of the winter
The meaning of the letters virazіv і virazі zі znіnnye is for specific assignments the meaning of the letters і wіmіnnіy.
Knowing the value of viraz in the wake of the winter
In order to know the meaning of letters and changes, it is necessary to set the meaning of letters and changes in the outgoing viraz, in order to calculate the value of a rejected numerical virase.
Butt 15. The value of viraz with changes
Calculate the value of viraz 0, 5 x - y for given x = 2, 4 and y = 5.
The value of the winter at the viraz is calculated and it is calculated:
0, 5 x - y = 0, 5 2, 4 - 5 = 1, 2 - 5 = - 3, 8.
In some way, it is possible to re-create viraz, so that you can reject this meaning just as the meaning of the name of the letters and changes. For all kinds of letters and changes in viraz, it is necessary, according to the possibilities, to get overwhelmed, to reimagine the power of arithmetic actions and all possible methods.
For example, viraz x + 3 - x, obviously, has a value of 3, and for the calculation of the value of a call, it is not necessary for the nobility of the meaning of a change ix. The value of the viraz is important for all the values of the change in the region of the permissible values.
Another butt. The value of viraz x x is the most appropriate one for all positive xx.
As soon as you have noted a pardon in the text, be weasel, see and natisnit Ctrl + Enter
In the course of algebra, 7 classes were engaged in the reincarnation of a number of virazs, i.e., E. Viraz, summed up from numbers and changes for an additional date, as well as on a number, as seen from zero. So, tsіlimi є turn
On vidminu from them virazi
Krim dddavannya, vidnimannya and a lot, to replace the rosodil on viraz with the change. Such virazi are called shot viraz.
Cycle and shot virazi are called rational virases.
Cyle viraz maє sense at any values of those entering the new winter, so as for the meaning of the whole viraz it is necessary for the viconati of the child, as they are able to.
Shot twisting at deyakim meanings of the wintry may not be mother sensu. For example, viraz is not a mass sensu at a = 0. For all the values of a visliv mass sens. Viraz massens with quiet values x і у, if х ≠ у.
The values of the changes, for such viraz massens, are called the permissible values of the changes.
Viraz is kind of called, yak vidomo, fraction.
Дріб, the numeral and the denominator of a polynomial, is called a rational fraction.
Butts of rational fractions serve as fractions
In rational fractions, acceptable are the meanings of the minions, for which the denominator of the fraction does not turn to zero.
Butt 1. It is known that the value of the negative in the fraction is permissible
Decision To know, for any values and the denominator, the fraction turns to zero, it is necessary to virishity rivnyannya a (a - 9) = 0. Tse rivnyannya has two roots: 0 і 9. Otzhe, the admissible values of the serpentine a є all numbers, crim 0.
Butt 2. For each value, the value of the fraction 
to zero?
DecisionДріб дівняє zero todі and only todі, if а - 0 і b ≠ 0.
Also, if the number viraz is summed up from the numbers і signs +, -, · і:, then in order of evil to the right, you need a collection of viconaties and times, and then - additional information and information, so that you can allow the shukane to know the meaning of the virus.
Guidedly fixing the attachments for clarification.
Butt.
Calculate the value of viraz 14-2 · 15: 6-3.
Decision.
In order to know the meaning of viraz, it is necessary to determine all the meanings in the new day, according to the accepted order. The list in order of evil to the right of the visonumo many times and days, we will 14-2 15: 6-3 = 14-30: 6-3 = 14-5-3... Now, in the order of evil to the right, the viconuєmo rashtu krokіv: 14-5-3 = 9-3 = 6. So we knew the meaning of the vicious turn, which is the most important 6.
as follows:
14-2 15: 6-3 = 6.
Butt.
Know the meaning of viraz.
Decision.
In the given application, we need a selection of multiple 2 (-7) and multiples in turns. Having guessed, how to be victorious, it is known 2 
, for what 
, I vikonuєmo: 
.
Pіdstavlyaєmo otrimanі meanings from vihіdne viraz :.
And yak buti, if the root sign is a numerical viraz? To correct the meaning of such a root, it is necessary to know the meaning of the root rotation from time to time, after receiving the accepted order of the viconan diy. For example ,.
In numerical virases, the root is followed by a number, and the root is completely substituted for these meanings, because of whom the meaning of the rejected virase without roots is known, and the meaning of the child is taken into account.
Butt.
Know the meaning of the virus from the roots.
Decision.
We know a lot of the meaning of the root 
... For tsiy, in Perche, the value of the radical turn is numbered, maєmo -2 3 - 1 + 60: 4 = -6 - 1 + 15 = 8... And in a different way, we know the meaning of the root.
Now the value of the other root is numbered.
Nareshty, we can know the meaning of the outward turn, replacing the root with the meanings:
as follows:
To finish often, it became possible to know the meaning of the virus from the roots, beforehand it was brought about to carry out this transformation. Let's show the solution to the butt.
Butt.
Yake meaning virazu 
.
Decision.
We cannot substitute the roots for three exact values, but we do not allow us to calculate the value of the virase by the described method. However, we can calculate the meaning of a turn, having seen awkward re-creation. zastosuєmo the formula for the difference of squares:. I will look at, I will 
... Such a rank, the meaning of a vicious turn of the road 1.
as follows:
.
in steps
If the base and the indicator of the step are є in numbers, then the їх value is calculated for the value of the step, for example, 3 2 = 3 · 3 = 9 or 8 -1 = 1/8. There are also recordings, if there is an indicator of the step є with deceptive virases. In cich vipadkah, it is necessary to know the meaning of virase in pіdstavі, the meaning of viraza in the indicator, in order to calculate the value of the self-level.
Butt.
Know the meaning through the steps of the mind 2 3 4-10 + 16 (1-1 / 2) 3.5-2 1/4.
Decision.
Viral viraz has two steps 2 3 4-10 and (1-1 / 2) 3.5-2 1/4. Їх values need to be counted up to vikonannya інші дій.
Mostly from degrees 2 3 4-10. In the indicator there is a numerical turn, the calculated value: 3 · 4-10 = 12-10 = 2. Now it is possible to know the value of the self-level 2 3 · 4-10 = 2 + 2 = 4.
The step indicator (1-1 / 2) 3.5-2 maєmo (1-1 / 2) 3.5-2 1/4 = (1/2) 3 = 1/8.
Now we have turned to the cob viraz, replaced in a new step by their meanings, and we know the value of the viraz we need: 2 3 4-10 + 16 (1-1 / 2) 3.5-2 1/4 = 4 + 16 1/8 = 4 + 2 = 6.
as follows:
2 3 4-10 + 16 (1-1 / 2) 3.5-2 1/4 = 6.
Respect Varto, for more widening of the drop, if you do forgiven viraz with steps on the basis.
Butt.
Know the meaning of viraz 
.
Decision.
Judging from the indicators of the steps, how to be found in a given viraz, the exact meaning of the steps cannot be rejected. I will try to forgive the viraz, maybe I can help you to know its meaning. maєmo 
as follows:
.
The steps in virases are most often to go hand in hand with logarithms, but we will talk about the meaning of virases with logarithms in one z.
We know the value of viraz with a fraction
Numbers virazi in their own record can take revenge fractions... There, de it is necessary to know the meaning of such a turn, the fraction, the view of the earliest fractions, then replace them with the meanings of the first ones.
The number and the denominator of fractions (as seen from the earliest fractions) can be used to change both numbers as well as virazi. To count the value of such a fraction, it is necessary to count the value of the viraz in the number, to count the value of the viraz in the denominator, if you count the value of the fraction itself. This order will be explained by the way, drib a / b, de a і b - deyaki virazi, by day it is a part of the form (a) :( b), so yak.
I will make the butt clearer.
Butt.
Know the value of viraz with a fraction 
.
Decision.
There are three fractions in the outgoing numerical rotation 
i. In order to know the meaning of a wicked turn, we need a collection of fractions, replace them with values. Zrobimo tse.
The numeral and the denominator of the fraction have numbers. To know the meaning of such a fraction, to replace the risk of a shot with a sign of delight, and a viconuєmo qiu diyu: 
.
In the number of the fraction, the viraz is 7-2 · 3, it is easy to know the value: 7-2 · 3 = 7-6 = 1. In this rank,. You can go to the meaning of the third fraction.
The third person in the numeral and the denominator is to take revenge on the numeral virazi, to the one that needs to be counted from the list, and not to allow to know the meaning of the fraction itself. maєmo 
.
It was too late to give the knowledge of the value at the viraz, and the viconati rushtu krokiv :.
as follows:
.
Often, when the value of viraz is known with a fraction, it is brought to the visonuvati quickened shotgun turns, It is based on the performance of fractions and on fast fractions.
Butt.
Know the meaning of viraz 
.
Decision.
The root of the remainder is not to be found, so for the knowledge of the meaning of the external turn for the ear, it is quite possible. For tsyogo letting go of the spiritual in the banner first fraction: 
... Pislya tsyogo vikhidne viraz nabude viglyadu 
... If the fractions are violated, the root will disappear, so we will be allowed to know the meaning from the set of the given viraz :.
as follows:
.
3 logarithms
If you can take revenge on the number of viraz, and if you have the opportunity to shake yourself off to them, then it is important to take pride in the visibility of those actions. For example, if the value of virase is log 2 4 + 2 6 = 8.
If there is a sign of the logarithm і / or in the first place there are numerical virazi, then there is a range of values, for which the value of the logarithm is calculated. For the butt, the viraz is visible from the logarithm of the form 
... At the sign of the logarithm, there is a number of virazi, which is known to mean:. Now we know the logarithm, for which the calculation is completed:
If the logarithms are not exactly virahuvav, then you can know the meaning of the outward turn, you can help the foreground forgiveness to the victors. If you need a good amount of material statty re-incarnation of logarithmic virases.
Butt.
Know the value of virase with logarithms 
.
Decision.
Almost from the calculation of log 2 (log 2 256). So yak 256 = 2 8, then log 2 256 = 8, also, log 2 (log 2 256) = log 2 8 = log 2 2 3 = 3.
Logarithms of log 6 2 and log 6 3 can be grouped. Sum of logarithms log 6 2 + log 6 3 equal to the logarithm of log 6 (2 log 6 2 + log 6 3 = log 6 (2 3) = log 6 6 = 1.
Now we are going to get rid of the fractions. For the cob, the logarithm in the denominator is rewritten in the viglyad of the snake fraction yak 1/5, for which the speed is by the powers of the logarithms, to allow us to reject the value of the fraction: 
.
If it’s too late to present it, the results in the outgoing viraz and if the value were changed: 
as follows:
How can I know the value of trigonometric viraz?
If the number of viraz is to take revenge or the like, then this value will be counted before the vikonannya of the other dey. As the sign of trigonometric functions stands for the number of virazi, then the list of values is counted, for which the values of trigonometric functions are found.
Butt.
Know the meaning of viraz 
.
Decision.
Having turned up to the statti, I will 
і cosπ = -1. Pidstavlyaєmo ci meaning at vikhidne viraz, vono typing in 
... To know the meaning, you need to know what you need to know in the steps, if you want to finish the calculation.
as follows:
.
Varto means that the value of viraz is calculated with sines, cosines, etc. often vimagaє in front transformation of trigonometric viraz.
Butt.
What is the value of trigonometric viraz 
.
Decision.
In this case, we will need the formula of the cosine of the subcutaneous kut and the formula of the cosine of sumi: 
Viconani re-creation helped us to know the meaning of viraz.
as follows:
.
Zagalny Vipadok
In the zealous vipad, the number of turns can be revenge and root, and steps, and fraction, if functions, and bows. The knowledge of the significance of such attacks of the field at the viconance of the offensive is:
- a set of roots, steps, fractions, etc. to be replaced by their meanings,
- distant diy in arches,
- і in order of evil, to the right, the sasht of the crocs is displayed - a lot and a day, and after them - an additional date and a date.
Pererakhovanі dії vikonuyutsya until otrimannya final result.
Butt.
Know the meaning of viraz 
.
Decision.
Kind of tsyogo viraz to finish folding. In tsomu virazi mi bacimo drib, root, step, sine and logarithm. How can I know this meaning?
Prosuvayuchis on the record of evil on the right, mi natikamosya on another mind 
... We know that with robots with folding fractions, we need to calculate the value of the numeral, okremo - the denominator, and, nareshty, know the value of the fraction.
At the number of my mother, the roots of the mind 
... Calculate the value of the radical turn 
... Here є sine. It is possible to know its meaning without the need for calculating the value of viraz 
... Tse mi mogo zrobiti :. Todi, stars i 
.
With the banner, everything is simple:
In such a rank, 
.
To adjust the result in a vyhіdne viraz, vono viglyad. In the renounced virazi there are steps. To know the meaning of the indicator, how to get to know the meaning of the exponent, maєmo 
.
Otzhe ,.
as follows:
.
Since there is no way to calculate the exact values of roots, steps, etc., then you can try to get around them for help, if you turn around to calculate the value for the indicated scheme.
Rational ways of calculating the value of viraz
The calculation of the value of numerical variations in the form of lasting and accurateness. So, it is necessary to take the endorsement of the vikonannya diy recorded in in front points, It is not necessary for the price to be weak and mechanically. We would like to say that it is often possible to rationalize the processes of meaningful viraz. For example, it is significant to speed up and to simplify the transfer of meaning to the value of allowing the deeds of power with numbers.
For example, we know that there is a lot of power: if one of the multipliers for the creature is zero, then the value for the creature is zero. Vikoristovuyuchi tsiu power, we can say at once, which means viraz 0 (2-3 + 893-3234: 54 65-79 56 2.2)(45 36-2 4 + 456: 3 43) to zero. Yakby, we adopted the standard order of visibility, then some of them were able to count the meaning of bulky virazs in the bows, and it took a lot of an hour, and as a result, all one viyshov was zero.
It is also easy to read the power of reading the equal numbers: if the number is equal to the number, then the result will be zero. The power of power can be seen more broadly: the difference between two of the same numerical viraz is to zero. For example, if the value of the viraz is not calculated in the arches, you can know the value of the viraz (54 6-12 47362: 3) - (54 6-12 47362: 3) This is zero, because the viraz is a difference of the same viraz.
The rational calculation of the viraz value can be taken into account the same re-creation... For example, buvaє korisna ugrupnye dodankiv and multiplier, Not less often vikorist wine multiplier for the bows... So the value of the viraz is 53 5 + 53 7-53 11 + 5 it is even easier to find a multiplier of 53 for the arches: 53 (5 + 7-11) + 5 = 53 1 + 5 = 53 + 5 = 58... Bezposredn calculation took more than an hour.
At the end of the point, I have a lot of respect for the rational response to the calculation of the value of virazs with a fraction - however, the multipliers in the number and the denominator of the fraction speed up. For example, the speed of the same virazs in the number and the denominator of the fraction 
allowing you to immediately know the meaning of the word 1/2.
Significant meaning of letters virazi and virazi with wintry
The meaning of the letters viraziv and virazi with the winters to be found for specific assignments the meaning of letters and letters. Tobto, mova yde about the meaning of the letter viraz for the given meaning of the letters, or about the meaning of the letter of the change for the reverse meaning of the change.
the rule The meaning of the letters is different for the given meaning of the letters and the meanings of the letters are different for the given meaning of the letters.
Butt.
Calculate the value of virase 0.5 x-y at x = 2.4 and y = 5.
Decision.
To know it will be necessary to install the rotation, and it is necessary to provide the data of the winners at the current viraz, for which the viconati is: 0.5 · 2.4-5 = 1.2-5 = -3.8.
as follows:
−3,8 .
At the end, it is notable that it is just the re-creation of the letters and the changes with the change permitting to reject the meanings, the meaning of the letters and the changes is not indispensable. For example, viraz x + 3-x can be forgiven, if someone else is looking at it. 3. You can create a picture, which means viraz x + 3-x, 3 for any value of a snake x z ї Areas of Acceptable Values (ADV)... More butt: the value of virazu is 1 for all positive values of x, so the area of admissible values of the change x in the viraz is without positive numbers, and in the whole region there is little parity.
List of literature.
- Maths: Navch. for 5 cl. zagalnoosvit. installation / N. Ya. Vilenkin, V. I. Zhokhov, A.S. Chesnokov, S.I. Schwarzburd. - 21st ed., Ster. - M .: Mnemosyna, 2007 .-- 280 p.: Il. ISBN 5-346-00699-0.
- Maths. Class 6: navch. for zalnoosvit. install / [N. Ya. Vilenkin and others]. - 22nd ed., Rev. - M .: Mnemosyna, 2008 .-- 288 p.: Il. ISBN 978-5-346-00897-2.
- algebra: navch. for 7 cl. zagalnoosvit. install / [Yu. N. Makarich, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; ed ed. S. A. Telyakovsky. - 17th ed. - M .: Education, 2008 .-- 240 p. : Ill. - ISBN 978-5-09-019315-3.
- algebra: navch. for 8 cl. zagalnoosvit. install / [Yu. N. Makarich, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; ed ed. S. A. Telyakovsky. - 16th ed. - M .: Education, 2008 .-- 271 p. : Ill. - ISBN 978-5-09-019243-9.
- algebra: 9th class: navch. for zalnoosvit. install / [Yu. N. Makarich, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; ed ed. S. A. Telyakovsky. - 16th ed. - M .: Education, 2009 .-- 271 p. : Ill. - ISBN 978-5-09-021134-5.
- algebra and cobs analysis: Textbook. for 10-11 cl. zagalnoosvit. ustanovka / A. N. Kolmogorov, A. M. Abramov, Yu. P. Dudnіtsin i іn.; Pid ed. A. N. Kolmogorov. - 14th view. - M.: Education, 2004.384 p.: Il. - ISBN 5-09-013651-3.