Online equation solver program. Equations
The use of equations is widespread in our life. They are used in many calculations, building construction, and even sports. Man used equations in ancient times and since then their application has only increased. Power or exponential equations are equations in which the variables are in powers and the base is a number. For example:
Solving the exponential equation comes down to 2 fairly simple steps:
1. It is necessary to check whether the bases of the equation on the right and on the left are the same. If the grounds are not the same, we are looking for options to solve this example.
2. After the bases become the same, we equate the degrees and solve the resulting new equation.
Let's say given exponential equation as follows:
Start solution this equation stands with a baseline analysis. The bases are different - 2 and 4, and for the solution we need to be the same, so we transform 4 according to the following formula - \ [(a ^ n) ^ m = a ^ (nm): \]
Add to the original equation:
Take out the brackets \
We express \
Since the degrees are the same, we discard them:
Answer: \
Where can an exponential equation be solved with an online solver?
You can solve the equation on our website https: // site. A free online solver will allow you to solve an equation online of any complexity in a matter of seconds. All you have to do is just enter your data into the solver. You can also watch a video instruction and learn how to solve the equation on our website. And if you still have questions, you can ask them in our Vkontakte group http://vk.com/pocketteacher. Join our group, we are always happy to help you.
Let us consider two types of solutions to systems of equations:
1. Solution of the system by substitution method.
2. Solution of the system by term-by-term addition (subtraction) of the equations of the system.
In order to solve the system of equations substitution method you need to follow a simple algorithm:
1. We express. We express one variable from any equation.
2. Substitute. We substitute the obtained value into another equation instead of the expressed variable.
3. Solve the resulting equation in one variable. We find a solution to the system.
To solve system by term addition (subtraction) necessary:
1.Choose a variable for which we will make the same coefficients.
2. We add or subtract equations, in the end we get an equation with one variable.
3. Solve the resulting linear equation. We find a solution to the system.
The solution to the system is the intersection points of the function graphs.
Let us consider in detail the solution of systems using examples.
Example # 1:
Let's solve by substitution method
Solving a System of Equations by the Substitution Method2x + 5y = 1 (1 equation)
x-10y = 3 (2 equation)
1. We express
It can be seen that in the second equation there is a variable x with a coefficient of 1, from which it turns out that it is easiest to express the variable x from the second equation.
x = 3 + 10y
2. After we have expressed, we substitute 3 + 10y in the first equation instead of the variable x.
2 (3 + 10y) + 5y = 1
3. Solve the resulting equation in one variable.
2 (3 + 10y) + 5y = 1 (expand brackets)
6 + 20y + 5y = 1
25y = 1-6
25y = -5 |: (25)
y = -5: 25
y = -0.2
The solution to the equation system is the intersection points of the graphs, therefore we need to find x and y, because the intersection point consists of x and y. Find x, in the first paragraph where we expressed there we substitute y.
x = 3 + 10y
x = 3 + 10 * (- 0.2) = 1
It is customary to write dots in the first place we write the variable x, and in the second the variable y.
Answer: (1; -0.2)
Example # 2:
Let's solve by the method of term-by-term addition (subtraction).
Solving a system of equations by the addition method3x-2y = 1 (1 equation)
2x-3y = -10 (2 equation)
1.Choose a variable, say, choose x. In the first equation, the variable x has a coefficient of 3, in the second 2. It is necessary to make the coefficients the same, for this we have the right to multiply the equations or divide by any number. We multiply the first equation by 2, and the second by 3 and get overall ratio 6.
3x-2y = 1 | * 2
6x-4y = 2
2x-3y = -10 | * 3
6x-9y = -30
(2) Subtract the second from the first equation to get rid of the variable x. Solve the linear equation.
__6x-4y = 2
5y = 32 | :5
y = 6.4
3. Find x. Substitute the found y into any of the equations, let's say in the first equation.
3x-2y = 1
3x-2 * 6.4 = 1
3x-12.8 = 1
3x = 1 + 12.8
3x = 13.8 |: 3
x = 4.6
The intersection point will be x = 4.6; y = 6.4
Answer: (4.6; 6.4)
Do you want to study for exams for free? Online Tutor is free... No kidding.
The free calculator presented to your attention has a rich arsenal of possibilities for mathematical calculations. It allows you to use the online calculator in various fields of activity: educational, professional and commercial... Of course, the online calculator is especially popular with students and schoolchildren, it makes it much easier for them to perform a variety of calculations.
However, the calculator can become useful tool in some areas of business and for people different professions... Of course, the need to use a calculator in business or labor activity is determined primarily by the type of activity itself. If the business and profession are associated with constant calculations and calculations, then it is worth trying an electronic calculator and assessing the degree of its usefulness for a particular case.
This online calculator can
- Correctly execute standard math functions written in one line like - 12*3-(7/2) and can handle more numbers than we can count huge numbers in an online calculator We don't even know how to call such a number correctly ( there are 34 signs and this is not the limit at all).
- except tangent, cosine, sinus and others standard functions- calculator supports calculation operations arctangent, arc cotangent and others.
- Available in the arsenal logarithms, factorials and other cool features
- This online calculator knows how to build graphs!!!
To build graphs, the service uses a special button (gray graph is drawn) or a letter representation of this function (Plot). To build a graph in an online calculator, just write a function: plot (tan (x)), x = -360..360.
We took the simplest graph for the tangent, and after the decimal point, we indicated the range of the X variable from -360 to 360.
You can build absolutely any function, with any number of variables, for example this: plot (cos (x) / 3z, x = -180..360, z = 4) or even more difficult, which you can think of. Pay attention to the behavior of the variable X - the interval from and to is indicated using two dots.
The only minus (although it is difficult to call it a minus) of this online calculator it is that he does not know how to build spheres and other three-dimensional figures - only a plane.
How to work with the Math Calculator
1. The display (calculator screen) displays the entered expression and the result of its calculation in ordinary symbols, as we write on paper. This field is just for viewing the current operation. The entry is shown on the display as you type a mathematical expression in the input line.
2. The expression input field is intended to record the expression to be calculated. It should be noted here that the mathematical symbols used in computer programs do not always coincide with those that we usually use on paper. In the overview of each function of the calculator, you will find the correct designation for a specific operation and examples of calculations in the calculator. On this page below you will find a list of all possible operations in the calculator, also indicating their correct spelling.
3. Toolbar - These are calculator buttons that replace manual input of mathematical symbols to indicate the corresponding operation. Some calculator buttons (additional functions, unit converter, solution of matrices and equations, graphs) supplement the taskbar with new fields where data for a specific calculation is entered. The "History" field contains examples of spelling mathematical expressions as well as your six most recent entries.
Please note when you press the call buttons additional functions, unit converter, solving matrices and equations, plotting graphs, the entire calculator panel moves up, covering part of the display. Fill in the required fields and press the "I" key (highlighted in red in the figure) to see the display in full size.
4. The numeric keypad contains numbers and symbols for arithmetic operations. The "C" button deletes the entire record in the expression input field. To delete characters one by one, you need to use the arrow to the right of the input line.
Try to always close parentheses at the end of an expression. For most operations, this is not critical, the online calculator will calculate everything correctly. However, in some cases, errors are possible. For example, when raising to a fractional power, unclosed parentheses will cause the denominator of the fraction in the exponent to go into the denominator of the base. On the display, the closing bracket is indicated in a pale gray color, it must be closed when the recording is finished.
| Key | Symbol | Operation |
|---|---|---|
| pi | pi | Constant pi |
| e | e | Euler's number |
| % | % | Percent |
| () | () | Open / Close brackets |
| , | , | Comma |
| sin | sin (?) | Sine angle |
| cos | cos (?) | Cosine |
| tan | tan (y) | Tangent |
| sinh | sinh () | Hyperbolic sine |
| cosh | cosh () | Hyperbolic cosine |
| tanh | tanh () | Hyperbolic tangent |
| sin -1 | asin () | Inverse sine |
| cos -1 | acos () | Inverse cosine |
| tan -1 | atan () | Reverse tangent |
| sinh -1 | asinh () | Inverse hyperbolic sine |
| cosh -1 | acosh () | Inverse hyperbolic cosine |
| tanh -1 | atanh () | Inverse hyperbolic tangent |
| x 2 | ^2 | Squaring |
| x 3 | ^3 | Cube |
| x y | ^ | Exponentiation |
| 10 x | 10^() | Exponentiation in base 10 |
| e x | exp () | Exponentiation of Euler's number |
| vx | sqrt (x) | Square root |
| 3 vx | sqrt3 (x) | Root 3rd degree |
| y vx | sqrt (x, y) | Extracting the root |
| log 2 x | log2 (x) | Binary logarithm |
| log | log (x) | Decimal logarithm |
| ln | ln (x) | Natural logarithm |
| log y x | log (x, y) | Logarithm |
| I / II | Collapse / Call additional functions | |
| Unit | Unit converter | |
| Matrix | Matrices | |
| Solve | Equations and systems of equations | |
| Plotting | ||
| Additional functions (call with the II key) | ||
| mod | mod | Division with remainder |
| ! | ! | Factorial |
| i / j | i / j | Imaginary unit |
| Re | Re () | Selecting the whole real part |
| Im | Im () | Exclusion of the valid part |
| | x | | abs () | The absolute value of a number |
| Arg | arg () | Function argument |
| nCr | ncr () | Binomial coefficient |
| gcd | gcd () | Gcd |
| lcm | lcm () | NOC |
| sum | sum () | The total value of all decisions |
| fac | factorize () | Prime factorization |
| diff | diff () | Differentiation |
| Deg | Degrees | |
| Rad | Radians | |
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Solving Equations matrix method is to find inverse matrix A.
