How to solve Irrational numbers with out a calculator

In number theory tutorial, an irrational number is any real number that is not a rational number—that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n non-zero,we have fractions calculator to find fractions if any. Informally, this means numbers that cannot be represented as simple fractions. Equivalently, irrational numbers are real numbers that cannot be represented as terminating or repeating decimals, and this presentation is often used in textbooks in elementary mathematics. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational. Perhaps the best-known irrational numbers are π, e and √2.we will also get rational expression calculator

Question:-

Simplify

 3√24 - 2√18
-------------
    -√2

Answer:-

 3√24 - 2√18
-------------
    -√2

3√12x2 - 2√9x2
--------------
    -√2

3√2 x √12 - 2 x 3√2
-------------------
     -√2

3√12 - 6
---------
   -1

= 6 - 3√12

= 6 - 3√4x3

= 6 - 3 x 2√3

= 6 - 6√3

= 6(1-√3)

How to find the raius of a circle

a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

Question:-

A sector of a circle has an area of 90 cm²and a central angle of 0.2radians .Find it's radius.


Answer:-

Area of sector = 90 cm²

Central angle = 0.2 radians

We need to convert this central angle to degrees

degrees=radians x 180/π

degrees=0.2 x 180/3.142

=11.5 degrees

                 11.5
Area of sector= -------- x area of the circle
                 360

    
             11.5
        90= ------ x πr2 
              360
The above step is having area of a circle formula
Let's find the radius (r) from the above equation

             90 x 360
            ---------- = r2
              11.5 π

          
             90 x 360
            ---------- = r2
             11.5x3.142


              896.8= r2


               r = √896.8 = 29.9

      So radius is approximately equal to 30 is the answer
We can use this in circumference of a circle formula to get the
circumference of the circle,similar ,if know the area of sector
for earth we can even find the radius of earth


                        

How to solve a linear equation

Topic : linear equation

When you enter an problem or equation into the calculator, the calculator will get the answer by simplifying the problem whether it is numerical or algebraic expression. Then it will attempt to solve the equation by using one or more of the the following : addition, subtraction, division, or by taking the square root of each side,factoring , and completing the square
This can be done with help of algebra calculator online two variables

Here are some example:

Question: Find X for the following 1.)-4 = 5 - 3x
Answer:

- 4 = 5 - 3x
5 - 3x = - 4
  - 3x = - 4 -5
  - 3x = - 9
     x = 3

2.) -2x -3 = 7

Answer:

- 2x - 3 = 7
- 2x = 7 + 3
- 2x = 10
   x = - 5

How to find the slope of a line

Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. It is also always the same thing as how many rises in one run.

Question:-

In the xy-coordinate system,find the slope of a line which passes through origin and which is equidistant from two fixed points A(1,11)and B(7,7)

Answer:-

Let the slope of thr required line passing through origin be 'm' hence the equation of line is y=mx

So, mx-y=0

Since above line is equidistant from the points (1,11)and (7,7)

  m(1)-11     m(7)-7
--------- =  ----------
 √m2+1          √m2++1

m-11 = 7m-7

 m-11 = ±(7m-7)

m-11=+(7m-7) or -(7m-7)

If we solve futher

we get m= -2/3 or 2.25

Hence ,there is only one line satisfy in above condition with slope "1".

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How to solve a simple linear equation

Topic:- Linear Equation


A mathematical expression that has an equal sign and linear expressions is called a Linear equation.

A number that you don't know,often represented by "x" or "y" is called a variable.

We solving linear equations by clicking and dragging a number to the "other" side of the equal sign. Remember that you are "isolating" the unknown "X" to solve the problem.
(Example is provided below.)

Question :-

Solve 2x-11=31

Answer:-

This math help is a part of linear equations.
   2x-11=31

 Add 11 on both sides


   2x-11+11=31+11

     2x=42

Divide by 2 on both sides

 2x     42
---- = ------
 2       2


 x=21

So 21 is the answer.

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speed and distance question

Topic:Speed and Distance

Speed is the rate of motion, or equivalently the rate of change of distance.

If the speed of an object is given ,We can find the Distance and similarly ,if the speed has given we can find the speed as well .

Here is an example problem ...
Question : A train travels 360km at a uniform speed. If the speed had been 5km/h more it would have taken 1 hour less for the same journey. find the speed of the train?

 
Let the speed of the train be x km/hr.
Distance travelled by the train =360 km
                Distance     360
So time taken =  --------- = ----
                 speed       x
Now the new speed =(x+5)km/hr.

                        360
So the time taken will be------ hr
                        x+5

Now the new time is 1 hour lesser.

So the equation will be

    360          360
  -------  -  ------- = 1 
     x            x+5
Making the denominator equal

  360(x+5)    360x
 --------- - ------- = 1
      x       x+5
  360x+1800-360x
  ---------------  = 1
      x(x+5)
1800 = x(x+5)

 1800 = x2+5x

Quadratic formula:
        -b+√b2-4ac
 x= ----------------------
           2a

Here a=1,b=5,c=1800

      -5+√52-4*1*1800
So x= --------------------------
               2*1
       -5+√25+7200
     = -------------
            2
        -5+√7225
     = ------------
           2
         -5+85
     =   --------
            2
So   x= 40 km/hr is the Answer

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Problem on Distribution in Algebra

Topic :- Distribution property


distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example:


Question:- How to Solve 2(3x+5)=5x-11


Ans:-


Step 1:- Use the distribution rule to solve 2(3x+5)

2*3x + 2*5

=6x+10

So,6x+10=5x-11


Step 2:- Subtract 5x from both sides


6x+10=5x-11
-5x -5x
----------------------------
x+10= -11

Step 3:- Subtract 10 from both sides


x+10= -11
-10 -10
----------------------
x = -1

So x= -1 is the Answer.


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