Introduction to my math answers sheet

Math is a family where we can declare any kind of the numbers like symbols, letters and the different numbers, complex numbers, real numbers, rational numbers etc...Math is a group of sciences (arithmetic, geometry, algebra, trigonometry, calculus etc..) that explains measures,magnitudes,area of the region, statistics. we are going to learn how to solve some of the math problems. In addition, math helps a lot in our daily life. Here we include some of the math problems to help you better.The answer sheet to the problems follows.

Math Answer Sheet to Given Problems

Ex 1: Let A = {1, 2}, B = {a, b}. Find some relations from A → B and B → A.

Sol:
Since relation from A to B is a subset of the Cartesian product A × B = {(1 , a) , (1, b) , (2 , a) , (2 , b)} any subset of A × B is a relation from A → B. Therefore{(1 , a), (1 , b), (2 , a), (2 , b)}, {(1, a), (1, b)}, {(1, b, (2, b)}, {(1 , a)} are some relations from A to B. Similarly any subset of B × A = {(a , 1), (a , 2), (b , 1), (b , 2)} is a relation from B to A. {(a , 1), (a , 2), (b , 1), (b , 2)}, {(a, 1), (b, 1)}, {(a, 2), (b, 1)} are some relations from B to A.

Ex 2: Evaluate the equation     2(-3x - 4) - (-x - 4) = -2(x + 1) + 2

Sol:
Given the equation  2(-3x - 4) - (-x - 4) = -2(x + 1) + 2
Multiply factors.
-6x - 8 + x + 4 = -2x - 2 +2
Grouping the terms.
-5x - 4 = -2x
-3x = 4
X = `(-4)/(3)`  is the answer to the math problem

Answer Sheet to Probelms on Math :

Ex 3: If x <4 -="-" 4="4" 5="5" nbsp="nbsp" p="p" simplify="simplify" x="x">
Sol:
Given the expression  |x - 4| - 5|-4|
If x <; 4 then x - 4 < 4 and if
x - 4 < 4 the |x - 4| = -(x - 4).
Substitute |x - 4| by -(x - 4) and |-4| by 4 .
lx - 4| - 5|-4|
= -(x - 4) -5(4)
= -x -16 is the answer to the math problem

Ex:4 Find the next two numbers in the number pattern.
 2, 6,18 , ___, ___,.
Sol:
Step 1: The given pattern is obtained by multiplying 3 to each number to get the next number in the pattern.
Step 2: The next two numbers in the pattern are 54,162.

Ans: 54,162 is the answer to the math problem

superposing a triangle on a triangle

Welcome to free online math help,
It is not entirely clear what is meant by "superposing a triangle on a triangle" means. It has been variously interpreted as actually moving one triangle to cover the other or as simply associating parts of one triangle with parts of the other. For the two triangles illustrated in the figure, you can actually slide one over the other in a continuous motion within the plane. Note, however, that if one triangle is the mirror image of the other, then any continuous motion would require moving one triangle outside of the plane. examples on math helper; But the triangles don't have to be same plane to begin with, and they often are not in the same plane when this proposition is invoked in the books on solid geometry.

Whatever the intended meaning of superposition may be, there are no postulates to allow any conclusions based on superposition. One possibility is to add postulates based on a group of transformations of space, or if restricted to plane geometry, on a group of transformations of the plane. Charles Dodgson (a.k.a. Lewis Carroll) would have said that using group theory is not appropriate to an elementary exposition of Euclidean geometry. Heath has described a more elementary conservative basis in his commentary on this proposition. learn more on free math tutoring.

abstract algebra

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In modern mathematics, axioms such as these would form the basis of an abstract algebra. Typically a presentation is given symbolically and in terms of set theory, although the set theory isn't necessary. examples given in free math; Here is an outline for a presentation for magnitudes. This outline doesn't have many of the details that would normally be included.

First, assume there is a binary relation on a set of magnitudes of the same kind called equality, denoted as usual with an equal sign as in x = y. (This equality is not identity as we want different magnitudes, such as two different triangles, to be equal. Alternatively, we could identify equal magnitudes so that equality is identity.) read more on online math forum.

Bisecting circles

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The diameters "also bisects the circle" should not be part of the definition, but either assumed as a postulate or proved as a proposition. It depends on the fact that circles are drawn on planes, and planes have constant curvature. examples on math forum; The analogous figure on a surface of nonconstant curvature does not have this property. For such figures the two "semicircles" on either side of a "diameter" need not be equal.

Although circles are used throughout Book I, the proper theory of circles doesn't begin until Book III. That book begins with more definitions relating to circles including the equality of circles, when circles touch (are tangent to) lines and other circles, and so forth. more examples on online math forum.

Angle element

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The concept of angle is a very important concept for all of Greek geometry. Many of the propositions require angles even for their statements.

The two lines are meant to emanate from the same point; two intersecting lines will actually make four angles.

The concept is also a difficult one, and, surprisingly, broader than our modern concept of angle.

As can be seen from the next definition of rectilinear angle, online math forum ; angles do not have to have straight sides; they can have curves as sides. The size of the angle does not depend on the length of the sides, but is determined only by how the two sides meet. In the Elements nearly all the angles are rectilinear, but angles with curved sides appear in proposition. continue reading on math forum.

Geometry Elements

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The Elements is the prime example of an axiomatic system from the ancient world. Its form has shaped centuries of mathematics. An axiomatic system should begin with a list of the terms that it will use. This definition says that one term that will be used is that of point. The next few definitions give some more terms that will be used. Although there is some description to go along with the terms, examples on math helper ; that description is actually never used in the exposition of the axiomatic system. It can, at most, be used to orient the reader.

The description of a point, "that which has no part," indicates that Euclid will be treating a point as having no width, length, or breadth, but as an indivisible location.

Later definitions will define terms by means of terms defined before them, but the first few terms in the Elements are not defined by means of other terms; they're "primitive" terms. Their meaning comes from properties about them that are assumed later in axioms. In the Elements, the axioms come in two kinds: postulates and common notions. The first postulate, I.Post.1, for instance, gives some meaning to the term "point." It states that a straight line may be drawn between any two points. Other postulates add more meaning to the term "point." more on math help.

Unproven math

Welcome to math help com,

Yes, there are certainly things in
mathematics that are unproven, and these generally fall into three
categories:

(1) Simple statements that we accept without proof;

(2) Statements that we simply haven't been smart enough to prove or
disprove yet;

(3) Statements that cannot be proven true or false.

Statements of type (1) are called "axioms," and they're the
fundamental building blocks of mathematics. examples on help in math;
They're obvious statements
like "1 is not equal to 0," or "given two points, exactly one line
goes through them." If we accept these basic statements as our
foundation, we can prove all other provable results from them.

So in a
sense, unproven statements are right at the heart of mathematical
thought. In fact, mathematics _never_ says anything is true - it only
says that certain things are true IF you accept the basic axioms. This
isn't really a problem, since the axioms are usually so obvious that
most people accept them without qualms. learn more on online math forum.

TEN COMMANDMENTS of Math

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Thou shalt read thy problem...carefully.

2. Whatsoever thou doest to one side of thy equation, do ye also to
the other.

3. Thou must use thy "common sense", else thou wilt have flagpoles
9,000 feet high. Yea, even fathers younger than sons.

4. Thou shalt ignore the teachings of false prophets to do all thy
work in thy head.

5. When thou knowest not, thou shalt look it up; and if thy search
still elude thee, thou shalt ask thy All-Knowing Teacher.

6. Thou shalt master each step before putting thy heavy foot down on
the next.

7. Thy correct answer does not prove that thou hast worked thy problem
correctly. This argument convincest none, more examples on math forum; least of all thy
Teacher.

8. Thou shalt first see that thou hast copied thy problem correctly,
before bearing false witness that the answer book lieth.

9. Thou shalt look back even unto thy youth and remember thy
arithmetic.

10. Thou shalt learn, read, write ,speak, and listen correctly in the
language of mathematics, and verily A's and B's shall follow thee
even unto graduation. continue learning on online math forum.

Making math easier

Welcome to math tutoring,
'Easier said than done', you're thinking? Well, it's not as difficult
as you may think. One way to get interested in anything is to read
books (or listen to lectures) by people who really love the subject,
because that kind of love can be contagious.

If you want to learn
physics, you can't do better than to listen to Richard Feynman lecture
about it. free math; If you want to learn how the mind works, the best places to
start (in my opinion) are with Doug Hofstadter's book _Godel, Escher,
Bach_ (but just read the dialogs between the chapters to start) and
Marvin Minsky's book _The Society of Mind_.
more examples on online math forum.

Math as game

Welcome to online math help,

One of the things it took me a long time to realize was that math is
largely a game, and the game works this way: We make up a set of rules,
and then we try to see what consequences follow from the rules.

For example, one game is called 'arithmetic'. We define what it means
to be a number, i.e., the first number is zero, similar examples on online math forum;
and if we have any
number, we can define another number by adding 1 to it:

0 + 1 = 1
1 + 1 = 2
2 + 1 = 3

Of course, to do this, we also have to define what we mean by
'addition'. Now, having made up these rules, we start playing with
them to see what happens. One thing that happens is that we notice
certain patterns, and we use these patterns to add new rules.
Now let us understand math with free math tutor.

Math is Interesting

Hi
Welcome to help with math

mathematicians are interested not only in what happens
when you adopt a particular set of rules, but also in what happens
when you change the rules.

For example, mathematicians in Germany and
Russia started with Euclid's geometry, but asked: "What if parallel
lines _could_ intersect each other? How would that change things?"
And they ended up inventing an entirely new branch of geometry, which
turned out to be just what Einstein needed for his theory of general
relativity.

I hope this help with math was useful. Write back if you'd like to discuss this some
more, or if you have any other questions about math help.

Math over centuries

Welcome to math helper,

Math over centuries :

you can start out with a few rules like:

A point has only location.
A line has direction and length.
Two lines interesect at a point.

and so on, and then you see where that takes you. That's what Euclid
did, and ended up more or less inventing geometry. And that's what
other mathematicians have done over the centuries, inventing
arithmetic, and number theory, and calculus, and group theory, and so
on.

Thanks for visiting free math, Now let us learn about free online math tutoring

Tangent to a Curve

Let us study about Tangent to the Curve,

We know that Tangent to a curve at a given point is a line that touches the curve at that point and has the slope as the curve at that point. Normal to a curve is the line that is perpendicular to the Tangent at that point.

Why do we need all these tangent normal? This finds application in Physics. The spokes of the wheel are placed normal to the circular shape of the wheel at that point where it is connected with the centre.

If a car skids on the road, then the car continues in the direction tangent to the curve. well this helps in designing the car. Again, we find angular momentum, torque, gravity, velocity, acceleration where differentiation plays a major role. The analysis of study of these motions lead to better designing in car, rocket etc.

I hope the above explanation was useful, now let us study about Exponential Series

Explain Integrating factor

Let us study about integrating factor,

The equations integrating factor is the method to find the solution of Linear Differential Equations. Linear Differential Equation :

A differential equation is linear if the dependent variable (y or x) and its derivative appear only in first degree. The differential equation of the form :

dy / dx + Py = Q

where, P and Q are constants or functions of x only, is known as a first order linear differential equation.

I hope the above explanation was useful, now let us study independent variable definition.

Explain Even function

Let us study about Even function and odd function,

Even function

A function f : AB is said to be an even function if
f(x) = f(-x) for all xA.

how to find domain and range of f depends on the definition of the function.
Examples of even function are

y = cosx, y = x2, y = secx
A polynomial with only even powers of x is an even function.


I hope the above explanation was useful.

Grams & Kilograms

Let us study about Grams and kilograms,

Grams : Unit of mass equal to 0.001 kilogram , the basic unit of mass in the metric system . The gram is the unit of mass in the cgs system . It is approximately equal to 0.035 avoirdupois ounce, or 0.0022 pound; a 1-pound mass equals about 453.6 grams.


Kilograms : Fundamental unit of mass in the metric system , defined as the mass of the International Prototype Kilogram, a platinum-iridium cylinder kept at Sèvres, France, near Paris. Copies of this standard are deposited at bureaus of standards throughout the world, and other units of mass are defined in terms of it. When the metric system was originally devised, the kilogram was defined so that 1,000 cubic centimeters (1 cubic decimeter) of pure water has a mass of exactly 1 kilogram.

Now guess how to convert grams to kilograms,

just convert grams to kilograms by dividing by 1000.

I hope the above explanation was useful.

How to divide numbers

Let us study how to divide numbers,
Meaning of the term division is dividing the group into equal parts. Use of the term division is dividing. During the division we can get the quotient and the remainder. We can do division in single digit, double digit, treble digit, 4 digits and 5 digits etc. Let us see 4 digit divisions in this article.
Division:

Division means divide the group into dividend. Division is represented by the symbols ‘/’, ‘) (‘or ‘ [] ’. Normally division has one operator and two operands.

For example:

a [] b here the variable ‘a’ and b is called as operands and the symbol’ [] ’is called as operator. By the way of division we get quotient and remainder.

I hope the above explanation was useful, now let me give some examples of dividing numbers.

Subtracting integers

let us study about Integers,
n number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers. Two sums which only differ in the order of their summands are considered to be the same partition; if order matters then the sum becomes a composition. A summand in a partition is also called a part. The number of partitions of n is given by the partition function p(n).

I know how to subtract integers

To subtract integers, rewrite as adding opposites and use the rules for addition of integers.

Recall that rules for addition of integers is:

Rule 1:

The sum of two or more positive integers is a positive integer.
The sum of two or more negative integers is a negative integer.

Rule 2:

To find the sum of a positive and a negative integer:
Subtract the two numbers (ignore the signs) and then keep the sign of the larger integer.

Example:

9 -14 = 9 + (-14) = -5

-12 - 6 = -12 + (-6) = -18

-10 - (-7) = -10 + (- - 7) = -10 + 7 = -3

I hope the above explanation was helpful.

Cumulative Line Graph

Let me explain about Cumulative Line Graph ( Ogive ),
Data may be expressed using a single line. An ogive (a cumulative line graph) is best used when you want to display the total at any given time. The relative slopes from point to point will indicate greater or lesser increases; for example, a steeper slope means a greater increase than a more gradual slope. An ogive, however, is not the ideal graphic for showing comparisons between categories because it simply combines the values in each category and thus indicates an accumulation, a growing or lessening total. If you simply want to keep track of a total and your individual values are periodically combined, an ogive is an appropriate display.

For example, if you saved $300 in both January and April and $100 in each of February, March, May, and June, an ogive would look like Figure 1 .

Figure 1

Ogive of accumulated savings for one year.

An ogive displays a running total. Although each individual month's savings could be expressed in a bar chart you could not easily see the amount of total growth or loss, as you can in an ogive.
I guess the above explanation was helpful, now let me explain you graphing linear inequalities in two variables.

Introduction to Angleshttp://www.blogger.com/img/blank.gif

Let us study about Angles :

An angle is a measure of rotation. Angles are measured in degrees. One complete rotation is measured as 360°. Angle measure can be positive or negative, depending on the direction of rotation. The angle measure is the amount of rotation between the two rays forming the angle. Rotation is measured from the initial side to the terminal side of the angle. Positive angles (Figure 1 a) result from counterclockwise rotation, and negative angles (Figure 1 b) result from clockwise rotation. An angle with its initial side on the x-axis is said to be in standard position.

Figure 1 (a) A positive angle and (b) a negative angle. Angles that are in standard position are said to be quadrantal if their terminal side coincides with a coordinate axis. Angles in standard position that are not quadrantal fall in one of the four quadrants, as shown in Figure 2 . Hope the above explanation helped you.