Math graphed equation

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If you've graphed equations, look at the graph
of y=1/x. If you look at the region enclosed by y=1/x, the line y=0 (the
x-axis), and the lines x=1 and x=e, it looks like a rectangle but with one
curved side. What is the area of this shape? In fact, it is exactly 1. examples on math help;
Mathematically speaking, we say "the area under the curve y=1/x from 1 to e
is 1," or even better, "the *integral* of 1/x from 1 to e is 1." This is
because if we replaced the line x=e with some line x=b for some b>1, the
area of the region is the natural logarithm of b.

Note the natural logarithm
of e is 1, because e^1 = e; that is, 1 is the exponent for which the base
(e) is equal to e.

And finally, for something I hope someone else will explain,

e^(i*Pi) = -1, where i is the square root of -1.

Solving the math equations

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The equations that describe what happens to any one part are not very
difficult to write down, but solving the equations for all of these
parts at the same time would be extremely time-consuming. That is why
this type of modeling is almost always done using a computer.

The computer solves the mathematical equations, the computer scientists
programmed the equations into the computer, examples on free math;
but (pay attention here) the engineers had to write down the equations in
the first place. For that, they needed to know a lot of mathematics, especially calculus
and differential equations. learn more on math forum.

Math related construction

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suppose you were designing a concrete freeway over-pass.
One of the things you would need to understand is how the concrete
cures as a function of time. similar exercise on free math
How long does one 'batch' need to cure
before construction can continue? When does it need to be tested?
How long until the bridge can be opened to regular traffic? (Concrete
appears to 'dry' in a day or two, but actually does not reach its full
strength for over a month!)

Well, it turns out that the strength of
the concrete as a function of time is described by an equation of the
form S=c(1-e^-kt) where S is the strength at time t and c and k are
constants specific to the type of concrete you are using. (How strong
is the concrete at time t=0? How strong is it as t approaches
infinity? How long will it take to get to half of its final
strength?) more examples on free math help.

Math practice

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One final thing you need to learn is the importance of _practicing_
what you've learned. The more you practice the material at each stage,
the more quickly you'll be able to learn the material at the next
stage. Think of practice as a pain management game. free math; A little pain up
front is often the key to avoiding a lot of pain later on. (If you
think about it, the main task of becoming an adult is learning, and
applying, that lesson.)

I know this advice sounds almost too simple to be useful. But I can
assure you that almost everyone who has become any good at math has
learned it in this way.

And whenever you come across a particular problem that you can't
solve, write to Dr. Math, and we'll see what we can do to help you get
past whatever's blocking you. more explanation on math forum.

Math Interesting

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We get this question all the time, and here are a few of the answers
that I've given in the past. I'm sorry if they seem long, but it's an
important question, and I've put a lot of thought into the answers. I
hope you can get something out of at least one of them.


1) Here is one of my favorite stories (from _The Little, Brown Book of
Anecdotes_):

At Columbia University, the young professor Raymond Weaver gave his
first class in English literature their first quiz. more examples on math tutoring;
The young men,
who had been trying to make things hard for the new instructor,
whistled with joy when Weaver wrote: "Which of the books read so
far has interested you least?" They were silent, however, when he
wrote the second, and last, question: "To what defect in yourself
do you attribute this lack of interest?"

Math _is_ interesting, and once you've figured out that it's
interesting, it's the easiest thing in the world, and more fun than
baseball or video games or going to the movies. more on free math.

Math Regular polygon

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Now move to a regular polygon. We lose just a little bit of
generality, because we see that only with an even number of sides can
we call one SIDE opposite another; but otherwise all the definitions I
can see yield the same result. We haven't clarified the definition at
all.

Now make the polygon slightly irregular, and we're forced to make some
decisions. There probably won't be any parallel side, so that's out.
Halfway around the perimeter, or cutting the polygon into equal
halves, may give you an intuitively "opposite" side, but may also give
a vertex, help in math ; leaving the choice uncertain - and both ways would be very
hard to calculate. Actually, once the sides have different lengths,
such a definition applies only to points not sides; and that's the key
to our choice. Since we're talking about sides, our definition ought
to relate to sides.

So we go back to the most basic possible
definition, one that relies only on counting sides - count half the
sides, and you're at the opposite side. This is the "topological,"
rather than "metric" definition - one that doesn't depend on
measuring any distances, but only on how the sides are connected. For
some special purposes a different definition (especially for 'opposite
point') might be useful, but since we're accustomed to thinking of
polygons topologically, this feels so natural to most mathematicians
that we don't bother mentioning it. more on math forum.

Polygon opposite sides

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Let us study about Polygon opposite sides on math help com,

It might help to know the context in which you have seen the phrase;
but I would say that, in a polygon with an even number of edges, the
side opposite a given side is the side that is separated from that
side by the same number of sides in each direction. Perpendicularity
or convexity is not required, only an even number of edges. You could
define it a bit more formally by saying that, for a 2n-gon, more examples on help in math;
the
opposite side is the nth side counting from the given side in either
direction.

In a pentagon, there is a vertex opposite each side, but not a side
opposite a side.

Math analogy

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To use an imperfect analogy -- don't try to push this too far -- when
you have an attractive melody, there are lots of other 'similar'
melodies that aren't attractive at all. It appears that attractive
melodies -- and useful mathematical systems -- are little islands
surrounded by seas of unattractive -- and useless -- ones.

The question that Minsky is addressing in his article is: Why should
this be the case?

In a sense, then, a mathematician is like an explorer looking for
islands in the Pacific, examples on free math homework help ;
back in the days before airplanes and
satellites. There's no way to know where they'll be, or just what
they'll be like, but -- to an explorer, at least -- there's nothing
quite as exciting as finding one. math forum.

True Math

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Let us study what is mathematics with math helper,

Mathematics can be defined as the construction and exploration of
formal systems. The advantage of this definition is that it emphasizes
the somewhat subtle point that mathematics IS formal -- which is just
another way of saying that it has no NECESSARY relation to anything in
'the real world'.

What all this means is that what is 'true' in mathematics depends
entirely on what axioms you start with, and what rules you use to
combine them. To take your example of 'proving' that the product of
two negatives is positive -- your result is true given the system you
set up, but it may be false in other systems.

I hope the above explanation was useful, now let us study more examples on math forum.