Basic Math Blog

Level of Measurement

2011-07-28T21:54:00.000-07:00

Let's learn about the level of measurement in statistics in today's post.

There are four levels of measurement used in applied statistics. These four levels of measurement are as follows:

Ordinals
Intervals
Nominal
Ratio scales

Next time i will help you with the concept of statistical formula. Till then enjoy this learning and for more help you can connect with an online tutor and get your help. Not just statistics help but one can avail to algebra, geometry tutoring as well.

Do post your comments.

Comparing Fractions

2011-07-25T23:44:00.000-07:00

Comparing Fractions is one of the important concepts of fractions. In today's session, we will confine our learning to comparing fractions.

Comparing fractions is nothing but comparing two fractions in terms which one is greater, smaller and equal. In case of bigger fractions, the fractions are simplified in the first step. After simplify fractions is done, both the fractions are compared. As for example 2/3 and 7/8 are two given fractions. After comparing the fractions, we come to know that 7/8 is greater than 2/4.

For more help with this topic, understand the concept from an online tutor. Not just fractions, one can avail to calculus tutoring and so on.

Next time, we will move on to some other topic, till then keep practicing these problems. Also do post your feed backs.

PRIME NUMBERS

2011-01-16T20:44:00.000-08:00

Prime Numbers are studied under Arithmetic under Math. The Number system is classified into different types based on their properties as:

Whole Numbers
Natural Numbers
Rational and Irrational numbers
Integers
Prime Numbers

Prime Numbers are a type of numbers discussed here. Prime Numbers are those numbers which are divisible only by themselves and 1. For example :13 is only divisible by itself and 1.
In other words, prime Numbers are those which do not have any other factors apart from themselves and 1.

Prime numbers have the following characteristics:

2 is the only Prime number
0 and 1 cannot be considered as Prime numbers
A number ending with 5 or 0 is never prime as it is divisible by 5.

Students have to learn to differentiate between the kinds of numbers. The prime numbers are often used in finding Prime factors of a number(Prime factorization). Students should also learn about divisibility and the rules of divisibility.

Solve for x

2010-09-24T00:40:00.000-07:00

How to solve for x

Example 1: solve 3x 10 = 2x 5

Solution:

Step 1: First write the equation, in this equation we have to find the variable of x

3x + 10 = 2x + 5

Step 2: subtract 10 on both side, we take only left hand side

3x + 10 – 10 = 2x + 5 - 10

3x = 2x - 5

Step 4: subtract 2x on both side

3x – 2x = 2x – 5 - 2x

x = -5

To know more on:

Slope

Limit of a function

Triangle Square

2010-09-23T03:20:00.000-07:00

Triangle square:

Find the area and perimeter of triangle whose side 12 cm.

Sol:

All sides of equilateral triangle area equal.

Side of triangle, a = 12 cm

Area of the triangle (A) = a²x

= 12² x (1.732/4)

= 144 x 0.433

= 62.352 cm²

Perimeter of equilateral triangle (P) = 3a

= 3 x 12

= 36cm

To know more:

Volume calculations

sphere area

Quadrants

2010-09-17T00:32:00.000-07:00

Quadrants of a graph:

Division is the chat helps us describes the parts. If you draw beeline and erect lines, bisect the page into four parts, anniversary alleged a division graph.

Blueprint contains four quadrants.

Large bulk acclimated one is the 1st quadrants blueprint which is on the top right.

The larboard of it is declaring the additional quadrants.

The third is the one beneath the additional quadrants.

One on the blueprint that is beneath the aboriginal division is defined the fourth quadrants graphs.

To know more:

Mean

Substitution method

Help with math

2010-09-15T00:28:00.000-07:00

Help with Math word problems

A rectangle allowance the abject of the allowance is 28m and acme of the allowance 22m. The amount of bark the allowance is $18 per aboveboard meter; acquisition the absolute amount for white abrasion the absolute room.

Solution:

Let abject of the allowance b = 28 and

Height of the allowance h = 22.

The blueprint for breadth of the rectangle = abject Г— acme Therefore 28 Г— 22

= 616 sq. meters.

The amount of bark 1sq. beat is [$] 18,

The amount for bark the absolute allowance = 18 Г—616 = [$] 11088.

To know more:

Square foot calculator

9th grade algebra

Bar Graph

2010-09-13T23:55:00.000-07:00

A bar blueprint is a graphical analogy of abundance distributions of ungrouped information. It is a aesthetic affirmation of the arithmetical abstracts by a amount of confined of compatible amplitude erected angular with like agreement amid them.

Construction of Bar Graphs

The accomplish to draw a bar graphs are

Step 1:Draw accumbent and vertical axes on the blueprint paper.

Step 2:Take one set of the abstracts forth x-axis and added set of abstracts in y-axis.

Step 3:Now artifice the confined application accustomed data.

To know more:

Polygon cycles

How to divide fractions

A line plot

2010-09-08T00:26:00.000-07:00

A line pot

In order to plot a line plot a horizontal line is drawn with an appropriate scale with units matching the given information. For an occurrence of a number in the information an x is marked above the corresponding number on the plotted line. If the number is repeated another x is marked above the earlier x. This step is completed for the whole information. The resulting figure is called as a line plot.

More on:
prime factorization calculator

Prime Numbers

Linear Programming

2010-09-07T02:20:00.000-07:00

Linear Programming Examples:

Step1. Identify the unknowns in the given LPP. Denote then by x & y.
Step2. Formulate the aim function in terms of x & y. be sure whether it is to be maximized or
minimized.

Step3. Translate all the constraints in the kind of linear inequations.
Step4. Solve these in equations simultaneously. Mark the common area by shaded region. This is the

feasible region .
Step5. Find the coordinates of all the vertices of the feasible region
Step6. Find the worth of the aim function at each vertex of the feasible region.
Step7. Find the values of x & y for which the aim function

z = ax + by has maximum or maximum value

To know more:

Bar Graphs

Ogive graph

Acute angle

2010-09-05T23:52:00.000-07:00

What is acute angle:

Example 1: Is there is a chance for a triangle to have more than 1 obtuse angle?

Solution:

Step 1: Let the angles of the triangle be L, M and N. Let L be the obtuse angle.

Step 2: The sum of all angles in any triangle is 180º. L + M + N = 180º.

If L > 90º then M + N must be less than 90º. Therefore, M and N must be acute angles.

Answer: No, triangle can have maximum one obtuse angle only.

More help on:

Linear formula

Acute triangle problems

Meters to centimeters

2010-09-03T02:52:00.000-07:00

Meters to centimeters:

Example 1:

The Scale A 25 millimeter in one hour. The second scale B 8 millimeters in one ground. What is the difference between the Scale A and B?
Solution:

Here scale A and scale B having the speed in unusual units. Here they must convert the speed in the equal unit and find the difference between Scale A and Scale B.

Scale A = one millimeter = 0.1 centimeter

So 25 millimeter = 25 * 0.1 = 2.5 centimeter

Scale B = 8 millimeter

Difference = 2.5 - 0.8 = 1.7 centimeter

To know more click on:

How to divide fractions

Fraction calculator

Square roots

2010-09-01T23:09:00.000-07:00

Square numbers:

Square number means multiply the given number as two times. For example square value of 2 is 4. Here we multiply the number 2 as two (2* 2 =4) times.

Cube numbers:

Cube number means multiply the given number as three times. For example cube value of the number 2 is 8. Here we multiply the number 2 as three (2 * 2 * 2 =8) times.

To know more:

Mid point

How to Find square roots

9th Maths

2010-09-01T03:07:00.000-07:00

Introduction of online 9th grade math practice tutoring:-
In grade (9) means ninth grade is a year of schooling in all over the world. The ninth grade is the post-kindergarten of nine year school. Students are usually 15 - 16 years elderly. Online tutoring is the new way for the scholars. Tutor show the geometry idea and give you practice issues. Students work the issues in own place. It is more help for practice check preparation and increases our own practice skills.
Topics in Online 9th Grade Math Practice Tutoring:-
In following basic topics involves the net 9th grade math practice tutoring Do You Know how to do trigonometry

1. Arithmetic
2. Commercial arithmetic
3. Algebra
4. Geometry
5. Statistics
6. Trigonometry
7. Find the Significance of Math

Know more on:

Online maths

Slope intercept calculator

Slope formula

2010-09-01T00:08:00.000-07:00

Slope work sheet formula:

Area of Circle Worksheet-formulas
Let C denotes circumference, A denotes the area, r denotes the radius, d denotes the diameter.
r = d/2
C = πd units
C = 2πr units
A = πr2 square units.

Get more help on:
Tangent

Math word problem work sheet

4th grade maths

2010-08-31T00:17:00.000-07:00

Example Problems for 4th Grade:

Example 1:

Find the number which corresponds to the expanded form.

9* 10000 + 5 * 1000 + 7 * 10 + 5

Solution:

9 * 10000 + 5 * 1000 + 7 * 10 + 5 = 90000 + 5000 + 70 + 5

95075

To know more:

4th grade maths

Pi and sine rule

Divide numbers

2010-08-30T03:13:00.000-07:00

How to divide numbers

Example: How to divide 3 by 6?

Given: 3 divided by 6
Mode of operations: Division
3/6=1/2

How to solve division?

How to solve division of following terms:

a) 2/4 b) 6/9 c) 25/5

Given: Mode of operation: Division

a) 2/4 = 2/(2x2) = 1/2
b) 6/9 = 3x2/(3x3) = 2/3
c) 25/5 = 5x5/5 = 5

More help on:

Algebra third grade

How to divide decimals

Rational method

2010-08-28T01:57:00.000-07:00

Solve the coefficient of the equation by rational method.

1 + 27 / (x² - 9) = 2

Sol:

Step1: This equation has a rational expression. Multiply the equation by the denominator term (x² – 9)
(x² - 9 )(1 + 27/ (x² – 9)) = (x² – 9) 2

Simplify.
(x² – 9)+ 27 = 2 (x² – 9)

Step2: Multiply factors and group like terms.
x² + 18 = 2 x² - 18

Step3: Add – (x² + 18) to both sides and simplify

x² = 36

Step4: x = -6 or +6

get to know more on:

Online maths
Parabola formula

square root problems

2010-08-27T01:56:00.000-07:00

square root of 196

Problem 1:

What is the square root of 1962?

Answer:

The concluding answer for what is the square root of 196 is 3√218.

Problem 2:

What is the square root of 1965?

Answer:

The concluding answer for what is the square root of 1965 is 44.328321.

Get to know more on:

F(x)maths

College algebra calculator

Introduction to solve math equation

2010-08-25T00:31:00.000-07:00

Introduction to Solve math equations for me:

Solving equations in math is simple and easy as we keep going with the formulae concepts.The equations may be having three types of roots(Solutions). They are

1) Equal roots.

2) Unequal roots.

3) Imaginary or Complex roots.

Here we use a quadratic formula for solving the equations of the form ax²+bx+c=0.

And the formula is

                           The value of √(b² - 4ac) Decides weather the roots are Equal or Unequal or Complex.
This value is commonly called as "Discriminant" .
also get help on:
Help on pre calculus
Types of lines

Trigonometric Identities

2010-08-24T04:32:00.000-07:00

Table of Trigonometric Identities:

Trig identity solver

Reciprocal Identities: sin

cosec u inverse function will be sin u

sec u inverse function will be cos u

Cot u inverse function will be Tan u

u inverse function will be co sec u

Cos u inverse function will be sec u

Cot u is the inverse function of Tan u

more details on

Factor rules

Trinomial calculator

Mean devaition

2010-08-23T03:20:00.000-07:00

What is Mean Deviation?

First dispersion used in the each computation is mean deviation. It is the mean of the difference between the each mean and each value. The mean deviation is also called as mean absolute deviation. mean deviation is a discrete distribution. It has two steps.

1. Find the mean value

2. Subtract the mean from each value; take the absolute value of each difference, sum the absolute values, then divide by the number of values.

Mean Deviation=∑ |x-x¯| / n

The average of difference (without sign) between each value in the given set is called as mean deviation.

get to know more on:

Area of a rectangle

12th grade maths

Introduction to Algorithm

2010-06-29T00:02:00.000-07:00

Introduction to Algorithm:

Algorithm are defined in mathematics as one of the efficient method for solving many of the maths problems.Algorithm are having many number of sequence steps for solving the maths problem.Algorithm are mainly used for the purpose of calculation in mathematics and the data processing unit in the other fields.For learning an algorithm many of the instructions have been followed.

Example for Learning Algorithm:

Sample example for writing algorithm:

Input: Non-empty N.

Output: smallest number is N

Smallest ← N₀

For each item(Length(L)≥1), do

if item >smallest, then

Smallest← the item

Return smallest

here are many characteristics for learning an algorithm.They are mentioned below in the following,

1. By using algorithm we can get an accurate result.

2. By using algorithm, the efficiency of the product is good.

3. By using the algorithm, the calculation is very faster.

4. By using the algorithm, the time can be decreased.

Trigonometry Problems

2010-06-28T23:42:00.000-07:00

Trigonometry Problems:

Question:

Answer:

problem 2:

Question:

Answer:

Identify Hexagon

2010-06-28T07:27:00.000-07:00

Which of the figures is a Hexagon?

A ) Figure 1
B ) Figure 2
C ) Figure 3
D ) Figure 4

Steps to derive:

1 A six-sided polygon is called a hexagon.
[Hexa means six.]

2 Figure 1 has 5 sides. So, it is a pentagon.

3 Figure 2 is a closed figure formed by six sides. So, it is a hexagon.

4 Figure 3 is not at all a polygon, as it contains intersecting line segments.
[Polygons do not have intersecting line segments.]

5 Figure 4 has 4 sides. So, it is a quadrilateral.

6 So, Figure 2 is the only hexagon among the figures. This answer is given by choice B.

2010-06-28T07:22:00.000-07:00

Hexagon and Pentagon:

Pentagon:

A Pentagon is one of the polygon, The name of the five shaped image is known as pentagon. The pentagon has five sides. The pentagon can be divided as regular and irregular pentagon. A pentagon will have five sides and five interior angles.
Always a pentagon will have five vertices.

Hexagon:

A hexagon is one of the polygon, the hexagon has six sides,six interior angles.
Always a pentagon will have six vertices.

Introduction to basic algebra

2010-06-23T05:34:00.000-07:00

Basic algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.
Together with geometry, analysis, topology, combination, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary or basic algebra is often part of the curriculum in secondary education and introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition.In this article we shall discuss about basics of algebra

Sample Problem for Basic Algebra:

Example 1:

Solve the algebra equation.
|2x – 1| = 7
Solution:

Step 1: The absolute value of the given equation is already inaccessible.

Either 2 x-1 = +7 or 2 x - 1= -7

Step 2: Solve the equation 2 x – 1 =+7

2 x – 1 = 7

2 x = 8

X = 4

Step 3: Solve the equation 2x-1=-7

2 x – 1 = -7

2 x = -6

X = -3

The answers are 4 and -3. The answers may not be solutions to the equation.

Check the answer x=4 by replacement 4 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.

Left side: |2 (4) – 1 | = 7

Right Side: 7

Check the answer x = -3 by replacement -3 in the given equation for x. If the left side of the equation sum value is equals the right side of the equation sum value after the replacement of x value, you have got the exact answer.

Left Side: | 2 ( -3) – 1 | = - 7
Right Side: -7

The answer of the equation are x=4 and -3.

Writing Math

2010-06-23T05:27:00.000-07:00

Normally, the writing math is classified into three types.

They are

Word form
Standard form
Expanded form

Writing math in Word form:

Writing the given number in alphabetical form is called as word form.

Example for Word form:

Write 8795 in word form:

Solution:

The place value should be taken in account.

8000 = Eight thousand

700 = Seven hundred

90 = ninety

5 = five

8795 = Eight thousand seven hundred and ninety five.

Writing math in Standard Form:

Writing the given number in reduced form is said to be standard form.

Example for standard form:

Express 567000 in standard form:

Solution:

567000 = 5.67 × 10⁵

Here we have shifted the decimal to 5 places.

Writing math in expanded form:

Writing the given number in abbreviated form is said to be expanded form.

Example for Expanded form:

Expand the number: 9542

Solution:

9542 = 9000 + 500 + 40 + 2.

Classifying math diagrams - Square

2010-06-16T04:42:00.000-07:00

Classifying math diagrams - Square:

Square has four equal sides.
The side length of the square is denoted as S.
Total angle of the square is 360°
All the four sides have the same angle 90°
Square has two diagonals and both the diagonals are equal in length
Area of the square is s²

Theorem of MatrIces

2010-06-15T03:31:00.000-07:00

Theorem of Matrice:
From the definition of inverse of a matrix, we have (AB)(AB)^-¹ = I

or A^-¹ (AB)(AB)^-¹ = A^-¹ I (Pre-multiplying both sides by A^-¹)

or (A^-¹A) B (AB)^-¹ = A^-¹ (Since A^-¹ I = A^-¹)

or I B (AB)^-¹ = A^-¹

or B (AB)^-¹ = A^-¹

or (B^-¹B)(AB)^-¹ =B^-¹A^-¹

or I(AB)^-¹= B^-¹A^-¹

or (AB)^-¹ = B^-¹A^-¹

Properties of Arithmetic

2010-06-14T05:48:00.000-07:00

Properties of Arithmetic:

The properties of arithmetic define when the order of operations can be changed in an initial calculation, so that we can get a second calculation which is equal to the first obtained result. The arithmetic operations that involving real numbers and/or real extents that uses the properties of arithmetic.

There are three types of arithmetic properties. They are,

Associative property
Commutative property
Distributive property

The addition or multiplication of a group of values is similar to the how the numbers are grouped. There are three or more values involved in associative property. The parenthesis refers the terms that are considered one unit. The combination (Associative Property) are within the parenthesis. Therefore, the values are 'associated' together. For multiplication, the product is always same as the grouping. In Associative Property grouping the brackets are done first.

Associative property of addition:

a+(b+c)=(a+b)+c

Associative property for multiplication:

a×(b×c)=(a×b)×c

Example:

Find the associative property of 2+(3+9) and 2(85)

Solution:

2+(3+9)=(2+3)+9

2×(8×5)=(2×8)×5)

Commutative property is the property that altering the order of the values and does not alter the final result. It is a basic property of many binary operations. Many mathematical proofs based on it.

Distributive property of addition:

a+b=b+a

Distributive property for multiplication:

ab=ba

Example:

Find the Commutative property for 4+6 and 6×9

Solution:

4+6=6+4

6×9=9×6

Distributive properties used to distributing something or we can split something or broken up into parts.

This is defined as,

a(b+c)=ab+ac

Example:

Multiply 3 x 17 by using the distributive law.

Solution:

Given 3 x 17
=3(10 +7)
=3(10) + 3(7)
=30 + 21
Therefore 3 x 17=51.

Introduction to arithmetic terms

2010-06-14T05:31:00.000-07:00

Introduction to arithmetic terms:
In mathematics the arithmetic terms are the basic one. It is used for calculating the additional, difference operations and etc. The arithmetic functions also used to computer science for writing coding. The basic math functions are including in this arithmetic terms. Here we will see about the basic four functions.

Functions:

The following 4 functions is the arithmetic terms.

Addition
Subtraction
Multiplication
Division

Trigonometry application

2010-06-11T05:38:00.000-07:00

Trigonometry application:

Triangulation technique is used in astronomy to measure the distance of nearby stars.

It is also used to measure the distance between the landmarks.
It is used to calculate the oscillation (the waves that moves in a space. There are so many waves like sound waves, earthquake waves, matter waves and the light waves)
The most important wave is the sin wave. It turns up all over the place, these wave forms can always be broken down into a series of superimposed sin waves of various frequencies. So this process is called as Fourier transform.

Table of Trigonometric identities

2010-06-11T05:18:00.000-07:00

Table of Trigonometric identities:

reciprocal Identities: sin u = \frac{1}{csc u} cos u = \frac{1}{sec u} tan u = $\frac{1}{cot u}

csc u = \frac{1}{sin u} sec u = \frac{1}{cos u} cot u = \frac{1}{tan u}

sin u is the inverse function of cosec u

cos u is the inverse function of sec u

Tan u is the inverse function of Cot u

Cosec u is the inverse function of Sin u

Sec u is the inverse function of Cos u

Cot u is the inverse function of Tan u

Examples for Solve Length of side fire Triangle

2010-06-10T05:16:00.000-07:00

Examples for Solve Length of side fire Triangle:

1) Solve the length of two side’s fire triangle is 29 cm and 30cm. If perimeter of the fire triangle is 81 cm, what is the length of third side of the fire triangle?

Solution:

Let third side length of the triangle is x cm then,

20 + 30 + x = 81

50+ x = 81

x = 81 -50

x = 31cm

Therefore length of third side of the fire triangle is 31cm.

How to find slope of a line?

2010-06-10T05:05:00.000-07:00

Find the slope of the line where the points are ( 9,5) and (7,3) by using straight line tools.

Solution:

The formula for slope m = (y₁-y₂) / (x₁-x₂).

M = (5-3) / (9 -7).

M = 2 / 2.

= 1.

Thus the slope of line is 1.

General rules for multiplication

2010-06-09T05:50:00.000-07:00

General rules for multiplication:

Positive x positive = positive

Negative x negative = positive

Positive x negative =negative

Negative x positive = negative

Positive x positive = positive:

Example:

x 4 =12

This two number are positive integers. So, answer is positive.

Negative x negative = positive

For example,

-4 x -3 = 12

This two number are negative integers .so, answer is positive.

Positive x negative =negative

For example,

4 x 3 =-12

One positive integer and one negative integer .so, answer is negative.

Negative x positive = negative

For example,

-4 x -3 =-12

One negative integer and one positive integer.so, answer is negative.

Solve the algebraic expression

2010-06-09T05:34:00.000-07:00

Solve the algebraic expression:

4(x -1) + 2y - 5(x -y -4) + 5

Multiplying the integer terms

= 4x - 4 + 2y -5x + 5y + 20 + 5

Grouping the above terms

= -x + 7y + 21

Geometry Problem and Solution

2010-06-08T07:13:00.000-07:00

Problem: Can two vertically opposite angles be supplement to each other? Draw a diagram to illustrate your answer

Let AB and CD bisect each other at right angles as shown in figure.

( Vertically opposite angles can be
supplements to each other)

Arithmetic Progressions

2010-06-03T04:49:00.000-07:00

Arithmetic Progressions:
Consider the following lists of numbers :
(i) 1, 2, 3, 4, . . .
(ii) 100, 70, 40, 10, . . .
(iii) – 3, –2, –1, 0, . . .
(iv) 3, 3, 3, 3, . . .
(v) –1.0, –1.5, –2.0, –2.5, . . .
Each of the numbers in the list is called a term. In (i), each term is 1 more than the term preceding it. In (ii), each term is 30 less than the term preceding it. In (iii), each term is obtained by adding 1 to the term preceding it. In (iv), all the terms in the list are 3 , i.e., each term is obtained by adding (or subtracting) 0 to the term preceding it. In (v), each term is obtained by adding – 0.5 to (i.e., subtracting 0.5 from) the term preceding it. In all the lists above, we see that successive terms are obtained by adding a fixed number to the preceding terms. Such list of numbers is said to form an Arithmetic Progression ( AP ). So, an arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

Slope of a Line

2010-06-02T06:31:00.000-07:00

Slope of a Line:
A line in a coordinate plane forms two angles with the x-axis, which are supplementary.
The angle (say) θ made by the line l with positive direction of x-axis and measured anti clockwise
is called the inclination of the line. Obviously 0° ≤ θ ≤ 180° (below Fig ). We observe that lines parallel to x-axis, or coinciding with x-axis, have inclination of 0°. The inclination of a vertical line (parallel to coinciding with y-axis) is 90°.

Definition 1 If θ is the inclination of a line l, then tan θ is called the slope or gradient of the line l. The slope of a line whose inclination is 90° is not defined. The slope of a line is denoted by m. Thus, m = tan θ, θ ≠ 90° It may be observed that the slope of x-axis is zero and slope of y-axis is not defined.

Perimeter and Area of a Circle

2010-06-01T04:02:00.000-07:00

Perimeter and Area of a Circle:
circumference of a circle bears a constant ratio with its diameter. This constant ratio
is denoted by the Greek letter π (read as ‘pi’). In other words

Circumference/Diameter=π
circumference = π × diameter = π × 2r (where r is the radius of the circle) = 2πr

The great Indian mathematician Aryabhatta (A.D. 476 – 550) gave an approximate
value of π. He stated that π =62832/20000 which is nearly equal to 3.1416.
However, for practical purposes, we generally take the value of π as 22/7 or 3.14, approximately

area of the circle =1/2× 2πr × r = πr2

Introduction to Matrices

2010-05-31T03:19:00.000-07:00

Introduction to Matrices:

The knowledge of matrices is necessary in various branches of mathematics. Matrices are one of the most powerful tools in mathematics. This mathematical tool simplifies our work to a great extent when compared with other straight forward methods. The evolution of concept of
matrices is the result of an attempt to obtain compact and simple methods of solving system of linear equations. Matrices are not only used as a representation of the coefficients in system of linear equations, but utility of matrices far exceeds that use. Matrix notation and operations are used in electronic spreadsheet programs for personal computer, which in turn is used in different areas of business and science like budgeting, sales projection, cost estimation, analyzing the results of an experiment etc. Also, many physical operations such as magnification, rotation and reflection through a plane can be represented mathematically by matrices. Matrices are also used in cryptography. This mathematical tool is not only used in certain branches of sciences, but also in genetics, economics, sociology, modern psychology and industrial management.

Volume of cube calculation

2010-05-28T05:52:00.000-07:00

Volume of cube calculation:
Problem:

A child playing with building blocks, which are of the shape of cubes, has built a structure as shown in Fig. below the edge of each cube is 3 cm, find the volume of the structure built by the child.

Solution:

Volume of a Cube = edge × edge × edge = a3

Solution : Volume of each cube = edge × edge × edge= 3 × 3 × 3 cm3
= 27 cm3 Number of cubes in the structure = 15 Therefore,
volume of the structure = 27 × 15 cm3 = 405 cm3

(here cm3 is cm to the power three)

How to find Surface area of a block?

2010-05-26T06:04:00.000-07:00

How to find Surface area of a block?

The decorative block shown in below fig is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.
(Take (pie π =22/7 ).

Solution : The total surface area of the cube = 6 × (edge)2 = 6 × 5 × 5 cm2 = 150 cm2. Note that the part of the cube where the hemisphere is attached is not included in the surface area. So, the surface area of the block = TSA of cube – base area of hemisphere + CSA of hemisphere = 150 – πr2 + 2 πr2 = (150 + πr2) cm2

= 150 cm2+(22/7+4.2/2+4.2/2)cm2

= (150 + 13.86) cm2 = 163.86 cm2

Probabiliy problem

2010-05-25T03:50:00.000-07:00

Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.

In the experiment of tossing a coin once, the number of possible outcomes

is two — Head (H) and Tail (T). Let E be the event ‘getting a head’. The number of

Outcomes favorable to E, (i.e., of getting a head) is 1. Therefore,

P (E) = P (head) = Number of outcomes favorable to E = 1/2

Number of all possible outcomes

Similarly, if F is the event ‘getting a tail’, then P(F) = P(tail) =1/2

to understand more about Probabilities these website links may help you,
Probability explainations, and conditional probability

The origin of the term "Sine" in Mathematics

2010-05-25T02:23:00.000-07:00

The origin of the term "Sine" Mathematics:
The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyam
by Aryabhatta, in A.D. 500. Aryabhatta used the word ardha-jya for the half-chord, which was shortened to jya or jiva in due course. When the Aryabhatiyamm was translated into Arabic, the word jiva was retained as it is. The word jiva was translated into sinus, which means curve, when the Arabic version was translated into Latin. Soon the word sinus, also used as sine, became common in mathematical texts throughout Europe. An English Professor of astronomy Edmund Gunter (1581–1626), first used the abbreviated notation ‘sin’.

The origin of the terms ‘cosine’ and ‘tangent’ was much later. The cosine function arose from the need to compute the sine of the complementary angle. Aryabhatta called it kotijya. The name cosinus originated with Edmund Gunter. In 1674, the English Mathematician Sir Jonas Moore first used the abbreviated notation ‘cos’.

Theorem of Triangle

2010-05-24T04:28:00.000-07:00

Theorem of Triangle:

If in two triangles, corresponding angles are equal, then their
corresponding sides are in the same ratio (or proportion) and hence the two
triangles are similar.

Theorem of Triangle is explained below to understand it better:

This criterion is referred to as the AAA (Angle–Angle–Angle) criterion of similarity of two triangles. This theorem can be proved by taking two triangles ABC and DEF such that
∠ A = ∠ D, ∠ B = ∠ E and ∠ C = ∠ F (see Fig. 6.24)

Cut DP = AB and DQ = AC and join PQ.

So, Δ ABC ≅ Δ DPQ (Why ?)
This gives ∠ B = ∠ P = ∠ E and PQ || EF (How?)
Therefore,
( / notation used to represent divided by) *

DP/PE =DQ/QF

AB/DE =AC/DF
Similarly,
AB/DE=BC/EF and also AB/DE=BC/EF=AC/DF

Remark : If two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angles will also be equal.

Problem related to Arithmetic Progression

2010-05-24T04:08:00.001-07:00

Which term of the Arithmetic Progression : 21, 18, 15, . . . is – 81? Also, is any term 0? Give
reason for your answer.

Here is the step by step explanation to the A.P problem,

Solution : Here, a = 21, d = 18 – 21 = – 3 and an = – 81, and we have to find n.

As an = a + ( n – 1) d,

we have – 81 = 21 + (n – 1)(– 3)

– 81 = 24 – 3n

– 105 = – 3n

So, n = 35

Therefore, the 35th term of the given AP is – 81.

Next, we want to know if there is any n for which an = 0. If such an n is there, then

21 + (n – 1) (–3) = 0,

i.e., 3(n – 1) = 21

i.e., n = 8

So, the eighth term is 0.

For more math help,You can refer the below links which are very helpful,
www.tutorvista.com ,tutor.com, other links

Algebraic Method of Solving a Pair of Linear Equation

2010-05-21T02:44:00.000-07:00

Algebraic Method of Solving a Pair of Linear Equations:

Substitution Method : We shall explain the method of substitution by taking
some examples.

Example 1 :
Solve the following pair of equations by substitution method:
7x – 15y = 2 (1)
x + 2y = 3 (2)
Solution :
Step 1 : We pick either of the equations and write one variable in terms of the other.
Let us consider the Equation (2) :
x + 2y = 3
and write it as x = 3 – 2y (3)

Step 2 : Substitute the value of x in Equation (1). We get
7(3 – 2y) – 15y = 2
i.e., 21 – 14y – 15y = 2
i.e., – 29y = –19
Therefore, y =19/29
Step 3 : Substituting this value of y in Equation (3), we get
x = 3 – 2 (19/29) =49/29

Therefore, the solution is x =49/29 , Y =19/29

Verification : Substituting x =49/29 and Y=19/29

,you can verify that both the Equations
(1) and (2) are satisfied.

Step 1 : Find the value of one variable, say y in terms of the other variable, i.e., x from
either equation, whichever is convenient.
Step 2 : Substitute this value of y in the other equation, and reduce it to an equation in
one variable, i.e., in terms of x, which can be solved. Sometimes, as in Examples 9 and
10 below, you can get statements with no variable. If this statement is true, you can
conclude that the pair of linear equations has infinitely many solutions. If the statement
is false, then the pair of linear equations is inconsistent.
Step 3 : Substitute the value of x (or y) obtained in Step 2 in the equation used in
Step 1 to obtain the value of the other variable.

Quadratic Equations

2010-05-21T02:20:00.000-07:00

Quadratic equations:

Quadratic Equations come up when we deal with
many real-life situations. For instance, suppose a
charity trust decides to build a prayer hall having
a carpet area of 300 square meters with its length
one meter more than twice its breadth. What
should be the length and breadth of the hall?
Suppose the breadth of the hall is x meters. Then,
its length should be (2x + 1) meters. We can depict
this information pictorially as shown in Fig below

Now, area of the hall = (2x + 1). x m2 = (2x2 + x) m2
So, 2x2 + x = 300 (Given)
Therefore, 2x2 + x – 300 = 0
So, the breadth of the hall should satisfy the equation 2x2 + x – 300 = 0 which is a
quadratic equation.

Euclid’s five postulates

2010-05-20T04:20:00.000-07:00

Euclid’s five postulates

Postulate 1 : A straight line may be drawn from any one point to any other point.

Axiom 5.1 : Given two distinct points, there is a unique line that passes through

them.

How many lines passing through P also pass through Q (see Fig. 5.4)? Only one,

that is, the line PQ. How many lines passing through Q also pass through P? Only one,

that is, the line PQ. Thus, the statement above is self-evident, and so is taken as an

axiom.

Postulate 2 : A terminated line can be produced indefinitely.

Note that what we call a line segment now-a-days is what Euclid called a terminated

line. So, according to the present day terms, the second postulate says that a line

segment can be extended on either side to form a line (see Fig. 5.5).

Postulate 3 : A circle can be drawn with any centre and any radius.

Postulate 4 : All right angles are equal to one another.

Postulate 5 : If a straight line falling on two straight lines makes the interior

angles on the same side of it taken together less than two right angles, then the

two straight lines, if produced indefinitely, meet on that side on which the sum of

angles is less than two right angles.

find the slope for the graph of the equation

2009-08-18T04:17:00.000-07:00

Before we know how to find the slope for the graph of the equation ,lets see what is slope.

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.

Using calculus, one can calculate the slope of the tangent to a curve at a point.

The concept of slope, and much of this article, applies directly to grades or gradients in geography and civil engineering.

Question:-

Draw the graph of 2x-3y=12. Use the graph to find the slope of line and area between the axes.

Answer:-

This Online help with math shows us ,how to draw the graph for the above problem.

by simplifying the equation we get.

y=0, x=6
y=-2, x=3
y=-4, x=0

We also use the slope formula to get the slope on the line .

A problem on pythogoras theorm

2009-08-12T00:03:00.000-07:00

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The theorem can be written as an equation:

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

Question:-

Calculate the value of cos θ in the above triangle.

Solution:-


Use Pythagoras theorem to evaluate the length of PR.

PR=√12²+20²

       adjacent
Cosθ= ----------
       hypotenuse

   RQ
= ----
   PR

    12
 = -----
   √544


 = 0.514 is the Answer

For more help on this ,you can reply me.

How to find the factors for an equation

2009-08-04T21:50:00.000-07:00

Topic:-Factors of an equation

what is factorization : the decomposition of an object a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into prime factors as 3 × 5, and the polynomial x² − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained. However, factors are not needed to divide evenly because they are still divisible by any number. For example, technically 3 and 8/3 are factors of 8. But, when factoring for tests teachers are looking for the even divisibility of the numbers.

Let's look an example on it.

Question:-

Solve x²+16x+69=6

Answer:-
x²+16x+69=6

x²+16x+69-6=0

x²+16x+63=0

For factoring it ,we find two factors of 63
which add up to 16,they are 9 and 7

x²+9x+7x+69=6

Pair these terms

x(x+9)+7(x+9)=0

(x+9)(x+7)=0

x+9=0 0r x+7=0

x= -9 or x= -7

So x= -9 or -7 is the answer.

For more help on this ,you can reply me.

A word problem on Distance

2009-07-20T22:48:00.000-07:00

Distance is a numerical description of how far apart objects are. In everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").

If we have a map which shows the distance between two cities and they have given distance as well.

Let's see how to find the actual distance ...

Question:-

On a road map ,if 10 miles is equal to 1 cm.Them find the value for 40 miles and find the actual distance as well.

Answer:-


10 miles=1 cm

40 miles=?

Let's take it as 'x'

We take the ratio and equate them.

10       40
----- = -------
 1        x

      40
 x = ------
      10


 x =4
So
40 miles = 4 cm on map

Now,using the same ratio


Distance on map = 45 cm

  we know 1 cm = 10 miles

Actual Distance = 45*10

               = 450 miles

For more help on this ,you can reply me.

Probability problems

2009-06-18T02:55:00.000-07:00

Topic:Probability

Probability, is a way of expressing knowledge or belief that an event will occur or has occurred.

Here is some probability problems ,which help you to understand the concept much better.

Questions & Answers

1- Julie was given two bags full of goodies. There were 10 chocolate bars and 5 mint
candies in bag A. There were 7 chocolate bars and 2 strawberry mini-pies in bag B.
She wanted to eat a chocolate bar. From which bag should she take the candy (so that
the probability of taking a chocolate bar was greater)?

Ans:-

She should take a candy from bag B, because P (A) = 0.67 < P (B) = 0.78.

2- Mike’s class made a project about pets. There were 21 students in his class. Nine had
dogs, five had only cats, three had cats and hamsters and the rest had no pets at all.
They randomly picked out a name.
a) What was the probability that that student had a dog?
b) It turned out the student didn’t have any pets. They randomly picked out a
second name (excluding the first chosen). What is the probability that that
student had at least a cat?

Ans:

a) The probability that the student had a dog is 9/21, so P = 0.43.

b) The probability that the student had at least a cat is 8/20, so P = 0.4.

I hope it helped you ,for more math help ,you can reply me.

Question to Find the Slope of given Straight line Equation

2009-05-15T04:31:00.000-07:00

Here is a Linear Programming problem on Slope and y intercept of a Straight line, Straight line equation is a linear equation in two variables.
Slope is a the ratio of the altitude change to the horizontal distance between any two points on the line.
y-intercept is the y-value of the point where the graph of the function or a relation intercepts the y-axis of the rectangular coordinate system (x = 0)

Topic : Slope and y-intercept of a Straight Line

This the simple and direct question to find slope and y intercept.

Problem : Given straight line is 4x -8y - 32 = 0, find the slope and y-intercept of the straight line.

Solution :
Slope is always denoted by 'm'
and Slope = - Co-efficient of x / Co-efficient of y
So from the given straight line 4x - 8y - 32 = 0
=> - 4/- 8 = 1/2
Slope = 1/2

Now to find y-intercept
put x = 0 in the given straight line linear equation,
So 4x - 8y - 32 = 0
-8y - 32 = 0
=> - y = 32/8
=> y = - 4
=> y-intercept is (0,-4)

You can find lot more problems related to the linear programming problems in geometry help and algebra help.

Word Problem on Equation of Circular Orbit of a Satellite

2009-05-04T02:01:00.000-07:00

Satellites revolving around the earth forms a circular orbit, hence below word problem describes how to derive equation of that circular orbit which is same as finding equation of circle.

Topic : Circular Orbit of a Satellite

Circular Orbit is considered from the center of the earth.

Question : Weather Satellites. Earth is represented on a map of a portion of the solar system so that its surface is the circle with equation. A weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth. Find the equation of the orbit of the satellite on this map.

Solution :

Equation is x² + y² + 2x + 4y - 4091 = 0

adding and subtracting 1 and 4 ;

x² + 2x + 1 + y² + 4y + 4 = 4091 + 1 + 4

(x+1)² + (y+2)² = 4096

(x+1)² + (y+2)² = 64²

So the earth is represented by (x+1)² + (y+2)² = 64²

given a weather satellite circle 0.6unit above earth with the center of its circular orbit at the center of earth.

So radius of this orbit would be 64.6

Thus the equation of orbit is

(x + 1)² + (y + 2)² = (64.6)² = 4173.16

x² + 2x + 1 + y² + 4y + 4 = 4173.16

x² + y² + 2x + 4y + 4 = 4173.16

x² + y² + 2x + 4y = 4173.16

x² + y² + 2x + 4y = 4168.6

So orbit is represented by the equation x² + y² + 2x + 4y -4168.6 = 0

Please leave back your comments or queries in the space provided.

Question to List Formulas for Volume of Geometrical Figures

2009-04-07T04:01:00.000-07:00

Topic : Volume Formulas

Question : List the Formula for all kind of Geometrical figures.

Solution :

Problem to Find Unknown Values of Angles of Triangles

2009-04-03T02:42:00.000-07:00

Topic : Angles of Triangle

Question to Indicate Order of Place Value with with an Example

2009-03-30T01:42:00.000-07:00

Topic : Place Value

Question : Indicate Order of Place Value in a Number.

Solution :

A Simple Integration Problem

2009-03-24T02:27:00.000-07:00

Topic : Integration

Problem : Integrate x^3 ln x

Solution :

Solved Differential Equation

2009-03-19T01:47:00.000-07:00

Topic : Differential Equation

Problem : If y = 4 Sin 3x prove y" + 9y = 0

Solution :
y = 4 Sin 3x
differentiate with respect to x
y' = 4 Cos 3x . 3
y' = 12 Cos 3x
Again differentiate with respect to x
y" = 12 (- Sin 3x . 3)
y" = - 36 Sin 3x

Now consider y" + 9y = 0
Substitute the value of y and y"
-36 Sin 3x + 9(4 Sin 3x)
-36 Sin 3x + 36 Sin 3x = 0
Hence proved

2009-03-16T02:24:00.000-07:00

Topic : Integration

Question : Solve by Integration using Trignometric Values
∫Cos³ 2x Sin² 2x dx

Solution :
∫Cos³ 2x Sin² 2x dx
∫Cos² 2x Sin² 2x(Cos 2x) dx

Now Sin 2x = 2 Sin x Cos x
Sin 4x = 2 Sin 2x Cos 2x
Sin² 4x = 4 Sin² 2x Cos² 2x
Multiplying and dividing by 4

¼ ∫4 Sin² 2x Cos² 2x(Cos 2x) dx
¼ ∫ Sin² 4x Cos 2x dx
Now Cos 2x = 1 – 2 Sin² x
2 Sin² x = Cos 2x – 1
Sin² x = (Cos 2x – 1) / 2
Sin² 4x = (Cos 8x -1) / 2

So,
¼ ∫ [(Cos 8x -1) / 2] Cos 2x dx
1/8 ∫ (Cos 8x Cos 2x - Cos 2x) dx
1/8 [ ∫ (Cos 8x Cos 2x ) dx - ∫ Cos 2x dx ]

Now 2 Cos A Cos B = Cos (A+B) + Cos (A-B)
1/8 [ ∫ Cos 10x + Cos 6x dx - ∫ Cos 2x dx ]
1/8 {[ (Sin 10x)/10 + (Sin 6x)/6] – (Sin 2x)/2}
1/8 [(3 Sin 10x + 5 Sin 6x – 15 Sin 2x) / 30]
3 Sin 10x + 5 Sin 6x – 15 Sin 2x) / 240

Problem on Multistep Equation

2009-03-10T23:33:00.000-07:00

Topic : Multistep Equation

Problem : Solve 7x + 2 = -54

Solution :
7x + 2 = -54
7x = -54-2
7x = -56
dividing both sides by 7
7x/7 = -56/7
x=-8
So the solution is x = -8

Question on Parabola

2009-03-05T23:57:00.000-08:00

Topic : Parabola

Question : Natural bridge is a stone arch formed over a river or stream. The longest natural bridge in the world is rainbow bridge in Utah. if the origin is placed at one end of the arch, the cure of the arch can be modeled by the equation h=-0.042d^2+3.57d where h meters represents the height and d meters represents the horizontal distance.
a. what is the max height of the arch, to the nearest meter?
b. at a horizontal distance of 10 m from the vertex, what is the height of the arch, to the nearest meter

Answer :

H(d) = -0.042d^2 + 3.57d
where h(d) represents the height of the arch and d represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
-------------------
Max and min problems use the 1st derivative of the function..
h(d) = -0.042d^2 + 3.57d
Set the 1st derivative to zero.
0 = -0.084d + 3.57
0.084d = 3d = 42.5 meters
------------
h(42.5) = -0.042*(42.5^2 )+ 3.57*(42.5)= -75 .8625+ 151.725h = 75.8625 meters = 76 appx..
At a horizontal distance of 10 m from the vertex, what is the height of the arch, to the nearest meter
h(d) = -0.042d^2 + 3.57d
h(10) = -0.042*10^2 + 3.57*10
=-4.2+35.7=31.5 meters

Question on Factorisation using identities:

2009-03-03T02:57:00.000-08:00

Topic : Factorisation using identities:

Question : Factorise 4y^2 – 12y + 9

Solution :
We know that (a + b)^ 2 = a^2 + 2ab + b^2 …………… (I)
(a – b)^2= a^2 – 2ab + b^2………….. (II)
(a + b) (a – b) = a^2 – b^2………… (III)
let us use these identities for factorisation

Observe 4 y^2 = (2y) 2, 9 = 3^2 and 12y = 2 × 3 × (2y)
Therefore, 4 y^2 – 12y + 9 = (2y)^ 2 – 2 × 3 × (2y) + (3)^2
= (2y – 3)2 (required factorisation)

Factorising a Quadratic Equations

2009-02-23T03:46:00.000-08:00

Topic : Quadratic Equations

Questions : Explain the procedure involved during Factorisation of Quadratic Equation.

Solution :

The general form of a quadratic equation is :
ax² + bx + c = 0
In order to factor this we need to find two numbers such that, the sum of those two numbers is b, which is the co-efficient of the middle term and the product of those two numbers is ac, where a is the co-efficient of leading term and c is called the constant term.

Suppose, the two numbers are p and q
then p + q = b
and pq = ac

ax² + bx + c = ax² + (p + q)x + pq/a
= (ax² + px) + (qx + pq/a)
= ax(x + p/a) + q (x + p/a)
= (ax + q) + (x + p/a)

Hope the method of how to solve a quadratic equation helps you to solve number of questions like this.

Question to Find the Area of Region

2009-02-09T22:59:00.000-08:00

Topic : Area of the Region

Question : Find the area of the region obtained by the intersection of a plane perpendicular to x-axis and passing through(2,0,0) with 2x^2+3y^2+4z^2=24.

Answer :

Putting x=2 in the equation
gives us 3y^2+4z^2=16
get this in to ellipse standard form
and use Pi*a*b
to get 8pi/sqrt(3).

Hope the hint will help you to solve the problem easily.