Different Types of Math

Introduction mathematics:

The mathematic is deals with the logical calculation and quantitative calculation. The shape of the object is the arrangement, order, it has involved from the counting, measuring. The most significant branches of mathematics are algebra and analysis. A theoretical representative method used in the study of numbers, shapes, structure and change and the relationships. The different types of the math are the algebra, geometry, trigonometry, calculus, linear algebra, differential equations.

Different Type of the Math:

Algebra:

An algebra type is the branch of mathematics which treats of the associations and properties of measure by way of letters and other symbols. It is suitable to those associations that are correct of every class of magnitude.

Geometry:

Geometry types are the division of mathematics which investigate the relationships, property, and quantity of solids, surfaces, lines, and angles; the science which treat of the property and associations of magnitudes; the art of the relatives of space.

Trigonometry

A trigonometry types is the subdivision of the mathematics which is identified by the relative of the edges, and angle of the triangles. These kinds methods is give the assured position of the required position and also give the general relationship among the trigonometrically functions of arcs or angles.

Calculus:

The rate of probability is the calculus. The calculus can be divided into two type’s calculus; these are the differential calculus, and integral calculus. Differential calculus determines the rate of modify of a measure. Integral calculus is calculating the measuring rate of the change.

Additional Type of the Math:

Linear algebra:

The system of the solving is called as the linear equation. The linear conversion and vector spaces is the more frequent to the linear algebra. The equations are modifying as the function is the linear conversion. The system of the equation is the system of the transformation.

Differential equations:

A differential equation is a mathematical equation for an unidentified function of single or multiple variables that relate the ideals of the function itself and its derivatives of a variety of commands. The rate of the modification is used for the differential equation. They are most common a type of the differential equation is the ordinary differential equation and the partial differential equation.

Guided Reading Answers

Introduction to guided reading answers

The guided reading answers are nothing but getting help from others to reading the subjects.In online only we can get the help of tutor for reading any subjects.Initially the math problems can be solved by using some arithmetic operations  like addition,subtraction,division and multiplications and these can be denoted by (+ ,`xx` ,`-` ,÷ ).The following aticle shows some guided reading answers.

Solved Math Problems with some Guided Reading Answers

Problem 1:

Solve the 56x + 47y = 2632 given equation on the x and y intercepts.

Given:

56x + 47y = 2632

Solution:

56x + 47y = 2632

To find the x intercept of y = 0 and solve for x.

56x + 47(0) = 2632

Solve the value of x.

x = `2632/56`

x = 47

To find the y intercept of x=0 and solve for y.

56(0) + 47y = 2632

Solve the value of y

47y = 2632

y = `2632/47`

y = 56.

The equations of x intercept on (47,0) and y intercept on (0,56).

Problem 2:

Solve the problem 185 + 35 ( 40 + 27 ) ÷ 67 – 60 in method of order of operation
Solution:

Given:

`=>`  185 + 35 ( 40 + 27 ) ÷ 67 – 60

Step 1: we need to simplify the parentheses

`=>` 185 + 35 `xx` 67 ÷ 67 – 60

Step 2: We need to simplify the multiplication

`=>` 185 + 2345 ÷ 67 – 60

Step 3: We need to simplify the division

`=>` 185 + 35 – 60

Step 4: We need to simplify the addition

`=>`220 –  60

Step 5: We need to simplify the subtraction

`=>` 160

Answer: 185 + 35 ( 40 + 27 ) ÷ 67 – 60 = 160

Solved more Math Problems with some Guided Reading Answers

Problem 3:

Solve the given problem 11(s – 9) – 6s ` - ` 26 = 13(s + 33)
The Solutions follows below:

Step 1: Given expression is,

11(s – 9) – 6s ` - ` 26 = 13(s + 33)

Step 2:Multiplying the integer terms

11s – 99 – 6s – 26 = 13s + 429.

Step 3:Grouping the above terms

5s –125 = 13s + 429

Step 4: Add 125 on both sides

5s –125 + 125 = 13s + 429 + 125

Step 5:Grouping the above terms

5s = 13s + 554

Step 6:Subtract 13s by on both sides

5s `-` 13s = 13s `-` 13s + 554

Step 7:Grouping the above terms

–8s = 554

S = `- 554/8`

The required answers is

S = `- 554/8`

Problem 4:

Solve the given problem (156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20)
Solution:

The problem can be solved in simplifying method .

Step 1:(156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20)

Step 2: 156x2 – 141x – 91 + 213x2 – 181x – 144 + 916x2 `-`    41x `-` 20

Step 3:  1285x2 – 363x – 255

The required answer is

(156x2 – 141x – 91) + (213x2 – 181x – 144) `-` (–916x2 +   41x + 20) = 1285x2 – 363x – 255

Trigonometry Test Answers

Introduction to trigonometry test answers:

Trigonometry is an important branch of Mathematics. The word Trigonometry has been consequent from three Greek words Tri (Three), Goni (Angles), Metron (Measurement). Literally it means “measurement of triangles”. The fundamental trigonometric functions are Sine, Cosine and Tangent functions of a triangle takes an angle and give the sides of the triangle. The ordinary trigonometric terms are Sine, Cosine and Tangent.

Solving Trigonometric Functions on Trigonometry Test Answers:

Trigonometry test answers 1:

Solve the trigonometric equation.

(Find all solutions) 2 Cos x + 2 = 3

Solution:

First we have to solve for Cos x

2Cos x + 2 = 3

2Cos x =3 – 2

2Cos x = 1

Cos x = 1 / 2

X = Cos-1x (1/2)

X = 60

Trigonometry test answers 2:

Find the solutions for the trigonometric function:

-5 Cos 2x + 9 Sin x = -3

Solution:

-5 Cos2x + 9 Sin x = -3

-5(1- Sin2x) + 9Sinx = -3

-5 -5n2x + 9Sinx = -3

-5 -5Sin2x + 9Sinx +3 = 0

-5Sin2x + 9Sinx -2 = 0

Let us take y = Sin x

-5y2+ 9y – 2 = 0

Y = -2                                                     Y =-.2

Now plug y =sin x

Sin x = -2                                              Sin x = .2

X = Sin-1(-2)                                             X = Sin2(- .2)

X = - Sin-1(2)                                            X =-Sin-1(.2)

Trigonometry Test Answers 3 on Trigonometry Test Answers:

Prove (tanx+secx)/(cosx-tanx-secx)=-cscx

(tanx+secx) / (cosx-tanx-secx)
[(sinx+1)/cosx] / [(cos²(x)/cosx - sinx/cosx - 1/cosx]
[(sinx+1)/cosx] / [-(1-cos²x)/cosx - sinx/cosx]
[(sinx+1)/cosx] / [-sin²(x)/cosx - sinx/cosx]
[(sinx+1)/cosx] / [(-sin²(x)-sinx)/cosx]
[(sinx+1)/cosx]*[cosx/(-sin²(x)-sinx)]
(sinx+1)/-sin²(x)-sinx
sinx+1 / -sinx(sinx+1)
1/-sinx = -cscx

Trigonometry test answers 4:

Problem for trigonometric cosine function:

In a triangle adjacent side is 5 and hypotenuse is 25 then finds the angle A of the triangle?

Cos A= (adjacent) / (hypotenuse)

Cos A = 5/25

A = cos-1(5/25)

A = 78.46.

Trigonometry test answers 5:

Problem for trigonometric cosine function:

In a triangle adjacent side is 7 and hypotenuse is 2 then finds the angle A of the triangle?

Cos A= (adjacent) / (hypotenuse)

Cos A = 7/2

A = cos-1(7/2)

A = 0.998

How to Learn Fractions Exercises

In this article we shall discuss about how to learn fractions exercises. Here, fractions are also denoted as division of a whole. A fraction is can be creation over to a decimal all through dividing the upper digit, or numerator, during the lower digit, or denominator. Fractions are as an alternative of as ratios, and significance for fraction which is one of the main math processes. Thus the fractions `5/7` are also used to point out the ratio 5:7 and the fractions 5 ÷ 7 as well.



Example Problems Based on How to Learn Fractions Exercises:

The example problems based on how to learn fractions exercises are given below that,

Example 1:

How to learn fractions exercises of 129 divide by 5?

Solution:

Step 1:

Here, 129 divide by 5 is meant by `129/5` .

Step 2:

Now, 129 divide by 5 is given below that,

Here, using long division method. So, long division method is shown given below that,

25.8

5)129             [129 > 5, now divide `129/5` ]

125             [(hint: 25 × 5 = 125)]

40           [4 < 5, so add one zero]

40           [(hint: 8 × 5 = 40)]

0

Step 3:

The final answer is 25.8

Example 2:

How to learn fractions exercises of 467 divide by 13?

Solution:

Step 1:

Here, 467 divide by 13 is meant by `467/13.`

Step 2:

Now, 467 divide by 13 is given below that,

Here, using long division method. So, long division method is shown given below that,

35.92

13)467            [467 > 13, now divide `467/13`]

455            [(hint: 35 × 13 = 455)]

120          [12 < 13, so add one zero]

117          [(hint: 9 × 13 = 117)]

30        [3 < 13, so add one zero]

24        [(hint: 2 × 13 = 26)]

6

Step 3:

The final answer is 35.92





Practice Problems Based on How to Learn Fractions Exercises:

The practice problems based on how to learn fractions exercises are given below that,

Problem 1:

How to learn fractions exercises of 383 divide by 5?

Answer: The final answer is 76.6

Problem 2:

How to learn fractions exercises of 461 divide by 8?

Answer: The final answer is 57.625

Problem 3:

How to learn fractions exercises of 567 divide by 9?

Answer: The final answer is 63

Math and Multplication

Introduction to math multiplication:

Multiplication (symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division). (Source from Wikipedia)

For example:

2*4 = 2*2*2*2 = 8

Here we are going to study about different method s of multiplication in math and its example problems.

Example Problems for Math Multiplication:

Example: 1

Multiply the following integer

23*46

Solution:

Here we have to perform simple normal math multiplication

2 3

4 6 *

-----------------

1 3 8          (6 multiply with 23 we get 138)

9 2             (4 multiply with 23 we get 92)

-----------------

1 0 5 8         (Add both the numbers we get final answer)

-----------------

There fore the final answer is 1058.

Example: 2

Multiplication of binomial

(2x+3) (3x+3)

Solution:

Here we have two binomial terms

First we take the first term 2x multiply with other terms

6x2 + 6x

Next term 3

9x+ 9

Combine the like terms we get

= 6x2 + 6x+ 9x+ 9

= 6x2+15x+9

Therefore the final answer is 6x2+15x+9

Example: 3

Multiplication of exponential

Solve 2x3y4.3x4.2y3

Solution:

We know the multiplication property of exponents

am.an = a ( m+n)

Combine the like terms first

2x3 3x4 y4 2y3

2*3 x (3+4) .2y(4+3)

Simplify the above expression we get

6x7.2y7

Therefore the final answer is 6x7.2y7

Example: 4

Fraction multiplication

`(3/4)` * `(2/4)`

First we have to multiply the numerator

3*2 = 6

Next multiply the denominator we get

4*4 = 16

= `6/16`

The simplest fraction is `3/8`

Therefore the final answer is `3/8`

Example for Math Multiplication: 5

Find the area of rectangle with base 8 meter and height 6 meter.

Solution:

We know that area of rectangle is multiplication base and height

Area = base * height

Substitute base and height value in the above formula we get

Area = 8 * 6 =48 meter square

Therefore area of given rectangle is 48 meter square.

Whole Number Word Problems

Introduction to whole number word problems

Whole number word problems are about the word problems that we work out with under many chapters in mathematics. Some of the chapters to solve whole number word problems are arithmetic operations, number system and many more. Whole numbers are the numbers that do not contains any decimal numbers fractional part or rational numbers. Working on whole number word problems will be simple and easier one.

Example of Whole Number Word Problems

A school consists of 4320 boys and 3840 girls. There are 983 teachers working in the school. What is the total strength of the school including the teachers?

Solution

Number of boys in the school        = 4 3 2 0
Number of girls in the school         = 3 8 4 0
Number of teachers in the school =     9 8 3 +
-------------
Total strength of the school    =  9 1 4 3
-------------
2.  The sum of the ages of Daniel and his brother David is 46 years. If the age of the David is 24 years what will be the age of the Daniel?

Solution:

Let the age of Daniel be x years.

The age of his brother David = 24 years.

Sum of both of their ages =(x+ 24) years.

But this sum is given as 46years.

So x + 24 = 46.

x =46 - 24

x =22

Thus the age of the Daniel is 22 years.

3. Jack plays basketball and can sink the ball in the basket 80% of the time. If he takes 120 shots, how many did Jack will sink?

Solution

Jack can sink = 80%                                   

Number of shots attempted = 120

Total sink Jack made = 80% of 120

= `80 / 100` * 120

= 96 sinks

Practice Problems of Whole Number Word Problems

1. For a foot ball tournament 32 teams participated. Each team has 16 players and 2 coaches. Find the total number of players and coaches participated in the tournament.

2. The sum of the ages of Nancy and his sister Mary is 42 years. If the age of Mary is 19 what will be the age of the Nancy?

Answers for practice problem of whole number word problems.

Total members = 576
Nancy age = 23

Degree of Polynomial Calculator

INTRODUCTION ABOUT DEGREE OF POLYNOMIAL CALCULATOR:       

In arithmetic, a polynomial is an expression of finite length constructed from variables and constants, using only the addition, subtraction, multiplication operations, and non-negative, whole-number exponents. The maximum power of the variable in a polynomial is called the degree of the polynomial. A term with no variables is called a constant term and its degree is zero.I like to share this Polynomial Solver with you all through my article.

Find the Degree of Polynomial:

CONDITION FOR POLYNOMIAL:

In polynomial the variable should not involve in division operation.

Ex: `x^2 -4x+7, x^3 +5x^2-x+6, ` it is a polynomial.

Ex: `x^2 -4/x+3/2,` not a polynomial.

General form for degree of Polynomial Calculator:

A polynomial function is a function that can be defined as,

`f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0`

Where n is a non-negative integer and `a_0, a_1,a_2,` ...,` a_n ` is constant coefficients.

First Degree of polynomial calculator:  

The first degree polynomial is the polynomial that has only one variable. The variable may be x, y or z and it is easy to find the value for the variable. The combinations of two first degree polynomials are called as second degree polynomial.

Second degree polynomial calculator:

In this equation 6x2+5x+2  the power of x is 2. so it is a second-degree polynomial or a polynomial of degree 2.

POLYNOMIAL CALCULATOR:

To solve the polynomial in calculator, first we have to enter the two polynomials then click anyone of the button like add, subtract, multiply, division and factor and the equivalent operation will be performed and answer will be displayed. Thus the polynomial calculator is shown below.



Example and Practice Problem for first and Second Degree Polynomial Calculator:

First degree polynomial calculator:

Example 1:

Determine the value for the first degree polynomial 2x+10 = 12.

Solution:

The given first degree polynomial is 2x+10 = 12.

For the above polynomial, subtract 10 on both sides of the equation.

2x +10-10 =12-10

2x = 2

Divide by 2 on both sides of the above equation.

`(2x)/2 = 2/2`

x = 1

The value for the first degree polynomial 2x+10 = 12 is 1.

Second degree polynomial calculator:

Example 1

Find whether the given expression is a second degree polynomial or not.

(x - 1) (x - 2) = 0

Solution:

Multiply two expressions in the left hand side,

(x - 1) (x - 2) = 0

x(x-2) -1(x-2) =0

x2 -2x -x + 1(2) = 0

x2 -3x +2 = 0

So, the highest exponent of variable x is 2.

So, the given polynomial equation is second degree polynomial equation.

Practice Problem for first Degree Polynomial:

1.Find the value for the first degree polynomial of 2x+ 5 = 6.

Answer: x= 1/2.

2.Compute the value for the first degree polynomial 4x+12 = 24.

Answer: x=3.


Practice Problem for Second Degree Polynomial:

1.    Find whether the given expression is a second degree polynomial or not.

(x - 10) (x - 5) = 0

Answer: The polynomial equation is second degree polynomial equation.

Lower Quartile

Introduction to lower quartile:

In descriptive statistics, a quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents one fourth of the sampled population. Lower Quartile is one type of quantile.In that quartile, the 25 % of data which lie in the lower half of the data set is called as lower quartile. We can also define it as the middle value of the lower half.

For example,

21, 5, 22, 33, 17, 36, 14, 42, 15, 35, 27


Arrange the data in ascending order,

5, 14, 15, 17, 21, 22, 27, 33, 35, 36, 42

In the above Data set,

15 is lower quartile.

Calculation of Lower Quartile:

Lower Quartile for Odd data set:

Let us see how to calculate the lower quartile of the data set that contains odd numbers.

Step1:  First find the median of the data set. The median divide the data set into upper and lower part.

Step2:  Find the median for lower part of the data set .That median is called as lower quartile.                    

Ex: Data Set: 8, 49, 53, 19, 45, 44, 11, 41, 47, 51, 39

Ordered Data set: 8, 11, 19, 39, 41, 44, 45, 47,49,51,53

Median (Mid value) =44

Lower part = 8, 11, 19, 39, 41

Upper part = 45, 47,49,51,53

Lower quartile (Median of lower part) = 19

Lower Quartile for Even Data set:

Let us see how to calculate the lower quartile of the data set that contains even numbers.

Step 1: Find the Median of the data set by calculating the average of the data set.

Step 2: Next in the lower part, find the median by calculating the average. That value is known as lower quartile.

Ex: Data set: 13, 6, 24, 33, 9, 38, 16, 46, 19, 53, 26, 65

Ordered data set: 6,9,13,16,19,24,26,33,38,46,53,65

Median: (24+26)/2= 25

Lower quartile:  (24+33)/2= 28.5



Practice Problems on Lower Quartile

Find the lower Quartile for the following;

1.   17,11,47,27,69,20,6,34,12,93,33

2.   7,4,18,23,30,20,14,36,41,11,48,64

Answer Key:

1.12

2.12.5