Using math logarithms

Welcome to math tutors online,
We need to talk about logarithms. Say you have 2^x = 64
(2^x is my way of saying "2 raised to the x power"), and you want to
solve for x.

Well, we know that
64 = 2*32 = 2*(2*16) = 2*2*2*8 = 2*2*2*2*2*2 = 2^6, so x = 6.

How about 2^x = 5? There we're stuck, because 2^2 = 4 and 2^3 = 8
so x should be somewhere between 2 and 3 to make 2^x = 5.

There's another way of saying what x should be, and this is called the
logarithm of 5 to the base 2. examples on free math; That is, x = log[2](5); (the 2 should be
a subscript, like a power but typed a bit below the log, so it isn't
log 10). In general, the solution to b^x = n for some given b and n is
x = log[b](n). b is called the *base* of the logarithm.
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Engineering calculations

Greetings from math tutor online free,

Engineers really do carry out some of these types of calculations, but
the mathematics textbooks tend to simplify the problems quite a bit
(which is not necessarily a bad thing; examples on free math; this type of problem really
does illustrate how specific mathematical concepts are applied to
other fields.)

For engineers in the world, the support column
mentioned above might also need to hold 28 tons after it is eighty
years old, has been crashed into by three cars and a truck, and has
survived four earthquakes and one flood. Now how would you calculate
the diameter? By the way, don't forget that the concrete at the
bottom of the column also needs to hold the weight of the column
itself in addition to the 28 ton 'load'. learn more on math helper.

Math in applied science

Welcome to free math tutoring,

Actually, there are some common misconceptions about the use of mathematics in
the applied sciences, like engineering: most engineers actually spend
a very small portion of their time carrying out mathematical
calculation. But that does not mean that mathematics is not important
to engineering. In fact, mathematics is indispensable.

Let me expand my answer into four different areas, because I have
thought of four different ways in which civil engineers (and other
engineers) use mathematics. online math forum; I'm sure there are many others. These
are just the first four that come to mind:

1. To help them understand the chemistry and physics fundamental to
the construction of civil engineering projects;

2. To carry out the technical calculations necessary to plan a
construction project;

3. To help them with modeling and simulations to predict the
behavior of structures before they are actually built; and

4. To help them with business decisions and other 'non-technical'
aspects of their jobs.

Now let us study more on math forum.

Right Calculations

Welcome to free math help,
It's unfortunate that your teacher doesn't seem to
have a gift for making math come alive. On the other hand, this is an
opportunity for you to learn a very valuable lesson, which is that you
don't need to wait around for teachers to teach you math - or anything
else - in order for you to learn it.

My advice to you is to take charge of your own education in math. So,
how do you do that?

You'll never go wrong by starting at the beginning! I would suggest
starting with your present textbook and working through it. examples on math tutors online, Read each section, and work the problems for that section until they seem too
easy. Then go to the next section. more examples on math helper.

Learning Math

Welcome to free math tutoring,
you've been able to learn other
things easily because you've been able to instantly form lots of
connections to things that you already know. If you've worked with
wood a lot, then you already have a feel for much of what you'd learn
in a class on trigonometry.

If you've worked with pottery, or
sculpture, then you already have a feel for much of what you'd learn
in a class on integral calculus. free math ;That is, you'd be learning new
syntax, but you'd already have a handle on the semantics.

The best way
to understand _anything_ that you're told in a math class is to come
at it from the direction of something that you understand intuitively.
That way, each new pattern or formula isn't a new, isolated fact to be
memorized, but just a new way of looking at something you already
know.
more examples on online math forum.

Math Zonogon

Welcome to free math help,
The introduction of the idea of a zonogon (all pairs of opposite sides
parallel and congruent) looked as if it might make the term Calligram
superfluous until we found the hexagon created by lopping off the
corners of a regular triangle. math helper; Parallel opposite sides then did not
imply equal opposite sides, and the Calligram (or whatever someone
already named it) is preserved as a unique set.

Still, it surprises me, after reading the definitions for things like
'open', 'closed', 'bounded', etc. that 'opposite' wouldn't show up in
a glossary. Especially when you think of all the geometric theorems
that use the term - "the side opposite the largest angle in a
triangle..." etc. If a published formal definition pops up, please let
me know. learn more on online math forum.

Importance of Math

Welcome to free online math help,
One thing you're learning together is why mathematicians have to
define all their terms before they can state, and especially prove,
conjectures. If you can all agree on some definition of "opposite,"
that would work fine for your purposes. I don't see anything wrong
with my definition, free math; though it's probably one of those things that we
tend to assume we all understand.

Certainly your definition that
opposite means parallel makes your whole conjecture circular, and to
count a pentagon as fitting your definition when by your definition
any sides that aren't parallel simply don't have opposites seems
really odd.
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Geometry History

Welcome to math tutoring,

Let us study the History of Geometry on free math help,

look in the front of your textbook. Each
geometry course is organized a little differently, and the authors of
the book developed this particular course. But all geometry courses
more or less follow the trail blazed by Euclid, before 300 BC.

There were others who contributed to geometry centuries earlier in Greece,
and even farther back, the Babylonians and Egyptians had some practical
geometrical knowledge. But Euclid is the one who systematized geometry
- set it up as a collection of definitions, postulates, and theorems,
all logically following from one another.
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Math Arithmetic

Once, while I was still a child in school, I heard that
'minus times minus is plus'. How strange it seemed that
negatives could cancel out -- as though two wrongs could
make a right. math helper; I wondered if there could be something else,
still like arithmetic, but having yet another sign. Why
not make up some number things, I thought, that go not
just two ways, but three? I searched for days, making up
new little multiplication tables. Alas, each system ended
either with impossible arithmetic (e.g., with one and two
the same), with no signs at all, or with an extra sign.
Eventually, I gave up. If I had had the courage to persist,
as Gauss did, I might have discovered the arithmetic of
complex numbers, or, as Pauli did, the arithmetic of spin
matrices. But no one ever finds a three-signed imitation
of arithmetic because, it seems, it simply doesn't exist.

Try, for example free online math tutor, to make a new number system that's like the
ordinary one except that it skips some number -- say, 4. It
just won't work. Everything will go wrong. You'll have to
decide what 2 plus 2 is. If you say that this is 5, then 5
will have to be an even number, and so also must 7 and 9.
Then, what's 5 plus 5? Is it 8, or 9, or 10? You'll find that
to make the new system at all like arithmetic you'll have to
change the properties of all the other numbers. Then, when
you're done, you'll find that you have changed only those
numbers' names and not their properties at all. more examples on math forum.

Ancient Egyptian Numbers

Let us study free math Egyptian Numerical,

In 3000B.C the Egyptians had a numerical writing system based on hieroglyphs. Hieroglyphs are represented in the form of pictures. The Egyptians had a bases 10 system of hieroglyphs for numerals.

They standardized separate numerical symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million.
I hope the above explanation was useful in this math forum, continue reading i'll help you with free online math tutoring.

Introduction to Ellipse

Let us study Ellipse formula,
An ellipse is the locus of a point which moves so that its distance from a fixed point is in a constant ratio, less than one, to its distance from a fixed line.
The fixed point is called the focus of the ellipse. The fixed line is called the directrix of the ellipse. The constant ratio is called the eccentricity of the ellipse and is denoted by e.
Equation of an Ellipse
Let S(h,k) and ax+by+c=0 be the focus and directrix of an elipse respectively. Let e be the eccentricity of the ellipse.
Let P(x,y) be a general point on the ellipse.

I hope the above explanation was useful, now let us study maths symbols

What is Graph Theory

Let us study What is Graph Theory,

Graph Theory:
In learn online representations, the graph theory is used. The selected area shows the isomerism’s common area between graphs and other forms. In spectral graph theory, the graphs can be denoted by algebraic structures.
Order Theory:
In learn online representations, the order theory is also used. From the experiments, each graph is shaped by the intersection of the graphs in an ordered set called as containment or inclusion relation. The containment instructions for a class of normal objects are Boolean pattern of dimensional order n.
I hope the above explanation was useful.

Explain Solution set

Let us study about Solution set,

The set of ordered pairs (x,y), which satisfy the given inequation, is called the solution set of the inequations.
Graphical representation of linear inequations on the real number line

A real number line can be used to represent the solution set of an inequation (Linear).
The convention is that O (a hollow circle) marks the end of a range with a strict inequality (i.e. <>) and (a darkened circle) marks the end of a range involving equality as well as inequality.

Examples:



I hope the above explanation was useful.

What do you call a six sided shape

What do you call a 6 sided shape ?

Hexagon is one of the polygon type. In polygon different shapes contains different sides. Each of the polygon shape is named as different based on the shape and size. One of the six sided shape is the hexagon. Hence, the polygon contains the 6 sided and 6 vertices. Schlafli symbol present in the regular hexagon. The interior angle of any degree is 720 degree. Let we see about many information about hexagon.

Properties of Six Sided Shape Hexagon:

From the above definition we can define many properties.

Property 1: Amount of triangles used in hexagon

Property 2: Amount of diagonal used in the hexagon

Property 3: Total number of the internal angles used in the hexagon shape.

I hope the above explanation was useful.

Learn Sine Rule

Let us study about sine rule in Trigonometry,

Introduction :

An equation containing the trigonometrical functions of an unknown quantity is termed as a trigonometrical equation, which holds for some values (and not for all values) of the quantities involved.
Co-terminal Angles

The angles (2p + A), (4p + A)......have the same initial and terminal arm as the angle A and so these angles are called co-terminal angles. For all such angles, the value of any trigonometric ratio is the same. Thus, all co-terminal angles are trigonometrically equivalent.

Theorem 1
General solution of sin q = k.

Theorem 2
General solution of cos q = k.

Theorem 3
General solution of tan q = k.

Theorem 4
General solution of acosq + bsinq = c.

I hope the above explanation helped you, now let me explain Cos.

Introduction of coordinate Geometry

Let us learn about coordinate Geometry,

The use of geometry dates back to before the beginning of history. However, it was often used in a very practical manner. It wasn't till about 600 BC that mathematicians began using formal logic and reasoning.

Coordinate plane--a two-dimensional surface on which a coordinate system has been set up; invented by Rene Descartes; also called Cartesian plane, graph, coordinate grid

Coordinates--the numbers in an ordered pair that locate a point in the coordinate plane

Ordered pair--a pair of numbers, written as (x,y), that represents a point on a coordinate grid

Line segment--the part of a line between two points on the line, including the two points

X-axis--the horizontal number line on a coordinate grid

Y-axis--the vertical number line on a coordinate grid

Quadrants, Origin

To plot points, always write the x value first and then the y value.

Ex. (2, 3) (3, -1) (-2, 3) (-3, -2)

Postulates and Theorems

Let us study about postulates and theorems,

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates.

* Postulate 1: A line contains at least two points.

* Postulate 2: A plane contains at least three noncollinear points.

* Postulate 3: Through any two points, there is exactly one line.

* Postulate 4: Through any three noncollinear points, there is exactly one plane.

* Postulate 5: If two points lie in a plane, then the line joining them lies in that plane.

* Postulate 6: If two planes intersect, then their intersection is a line.

* Theorem 1: If two lines intersect, then they intersect in exactly one point.

* Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point.

* Theorem 3: If two lines intersect, then exactly one plane contains both lines.

I hope the above explanation was useful

Comparing Statistical Results

Let us study how to do comparing statistical results,
Making predictions is only one use of statistics. Suppose you have recently developed a new headache/pain remedy that you call Ache-Away. Should you produce Ache-Away in quantity and make it available to the public? That would depend, among other concerns, upon whether Ache-Away is more effective than the old remedy. How can you determine that?

One way might be to administer both remedies to two separate groups of people, collect data on the results, and then statistically analyze that data to determine if Ache-Away is more effective than the old remedy. And what if the results of this test showed Ache-Away to be more effective? How certain can you be that this particular test administration is indicative of all tests of these two remedies? Perhaps the group taking the old remedy (the control group) and the group taking Ache-Away (the treatment group) were so dissimilar that the results were due not to the pain remedies but to the differences between the groups.

It's possible that the results of this test are far off the results that you would get if you tried the test several more times. You certainly do not want to foist a questionable drug upon an unsuspecting public based upon untypical test results. How certain can you be that you can put your faith in the results of your tests? You can see that the problems of comparing headache remedy results can produce headaches of their own.
Hope the above explanation was useful to you.

algebra of complex numbers

Let us study algebra of complex numbers,
A complex number is an ordered pair of real numbers with addition defined
by
(a, b) + (c, d) = (a + c, b + d)

and multiplication defined by
(a, b) × (c, d) = (ac − bd, ad + bc),

where a, b, c, and d are any real numbers.
We will let i denote the complex number (0, 1). Then, by our definition of multiplication,
i2 = (0, 1) × (0, 1) = (0 − 1, 0 + 0) = (−1, 0).



Geometric representation of a complex number

If we identify the real number a with the complex number (a, 0), then we have
ai = (a, 0) × (0, 1) = (0 − 0, a + 0) = (0, a).
Then for any two real numbers, we have
(a, b) = (a, 0) + (0, b) = a + bi.

That is, a + bi is another way to write the complex number (a, b). In particular, with this
convention, becomes
i2 = −1,
that is,
i = p−1.
Moreover, we may write as
(a + bi) + (c + di) = (a + c) + (b + d)i
and (7.1.2) as
(a + bi) × (c + di) = (ac − bd) + (ad + bc)i.
In fact, we may view the latter as a consequence of the ordinary algebraic expansion of
the product
(a + bi)(c + di)
combined with the equality i2 = −1. That is,
(a + bi)(c + di) = ac + adi + bci + bdi2 = (ac − bd) + (ad + bc)i.
It also follows from this formulation that if r is a real number, which we identify with
r + 0i, and z = a + bi is a complex number, then
rz = r(a + bi) = (r + 0i)(a + bi) = ra + rbi.
Hope the above explanation helped you.

Exterior Angle of a Triangle

Let us learn what is Exterior Angle of a Triangle,
An exterior angle of a triangle is formed when one side of a triangle is extended. The nonstraight angle (the one that is not just the extension of the side) outside the triangle, but adjacent to an interior angle, is an exterior angle of the triangle (Figure 1 ).





Figure 1 Exterior angle of a triangle.

In Figure 1 , ∠ BCD is an exterior angle of Δ ABC.

Because m ∠1 + m ∠2 + m ∠3 = 180°, and m ∠3 + m ∠4 = 180°, you can prove that m ∠4 = m ∠1 + m ∠2. This is stated as a theorem.

Theorem 26: An exterior angle of a triangle is equal to the sum of the two remote (nonadjacent) interior angles.

Example 1: In Figure 1 , if m ∠1 = 30° and m ∠2 = 100°, find m ∠4.

Because ∠4 is an exterior angle of the triangle,

Hope the above explanation helped you.