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Mathematical Analysis

Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.

2,575 Questions

Scientific and mathematical tools in chemistry?

For example statistical analysis of data, mathematics of spectral data processing, rational experiments design, VSEPR, LCAO, etc.

What is understanding the message in communication?

Perfect understanding is called message in the communication. i.e., the sender has to give correct information about what he wants and receiver should go hand in hand with what he receives from sender.

How hard is it to turn a set toilet 90 degrees to face a different direction?

It depends on the flange used and how hard it is to move the supply line. Without looking at the job it is impossible to tell. Some toilet flanges have a second mounting point 90 degrees apart, others can have the screws taken out and the mounting ring can then be turned 90 degrees, some have no provision for movement. You would have to remove the toilet to see what you have. If the flange cannot turn or it is in too bad condition (rusted out) you will have to replace it or use a flange repair ring. it depends on the circumstances. If there is room to put an extention flange on it would be easy. if not it depends on your pipe size running to the toilet, if the bottom of the flange is accessable or many other factors.

How do you multiply?

== Ex: 321 x 10 first you multiply 0 with the numbers on top Ex: 0 x 321== 000 and 1 times 321 = 321 but you have to add a 0 and the back Ex: 3210.....then you add 000+3210= 3,210........... That's all. ===
im NT that good on my 7s but on my 2s and 12s i use whats half of dat number for excample if i want 2 figure out 6x6= i use 3x3= and double the asnwer which gives me the answer for 6x6=

If 1 mole of gas occupies 224 dm cubed then how many m cubed would 2263000 tons be?

There is one critical piece of information missing in the question, i.e. which gas are we talking about since different gas will have different molecular weight. In addition 1 mole of gas occupies volume of 22.4 dm3 at stp. This is equivalent to 22.4 L or 0.0224 m3 per mole of gas. Assuming the molecular weight of the gas Y is x g/mole, then the general solution is as followed: 2263000 tons of gas Y equal 226300*1016*1000g/(x g/mole)*(0.0224 m3/mole) equal 5.15022592e9/x m3 of gas Y

How many basic geometric shapes are there?

Geometric shapes formed from three or more straight lines (polygons) include:

3 sides

triangle

4 sides (quadrilaterals)

square (4 equal sides, right angles)

trapezoid (4 sides with only 1 set of parallel lines)

rectangle (4 sides with 2 sets of parallel lines)

rhombus (4 sides, 2 parallel pair)

5 sides - pentagon

6 sides - hexagon

7 sides - heptagon (rarely septagon)

8 sides - octagon

9 sides - enneagon (classically - nonagon)

10 sides - decagon

11 sides - hendecagon (classically - undecagon)

12 sides - dodecagon (classically - duodecagon)

13 sides - tridecagon or triskaidecagon

14 sides - tetradecagon

15 sides - pentadecagon

16 sides - hexadecagon

17 sides - heptadecagon

18 sides - octadecagon

19 sides - enneadecagon (nonadecagon)

20 sides - icosagon

*For a list of some other basic shapes, see the related link.

How can I generate a declining function with constraints on the x and y intercepts so that the integral of the curve is constant?

The integral of a given function between given integration limits will always be a constant. The integral of a given function between variable limits - for example, from 0 to x - can only be a constant if the function is equal to zero everywhere.

What Mayan innovation is still important in mathematics today?

It is the usage of the zero symbol that is still essential in mathematics even today.




How did Charles Fourier try to the ills of industrialization?

One way Charles Fourier tried to correct the ills of industrialization was by advocating for socialism. He wanted the factors of production to be owned by the citizens.

What is 0.8009 in word?

You can pronounce all the digits after the decimal point, like this: zero point eight zero zero nine

What ways are there of arranging 35 students so that there are an equal number of students in each row?

Either 5 rows of 7 students - or - 7 rows of 5 students.

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or 1 row of 35 students

or 35 rows of 1 student (like in an exam hall)

How many hour in 6000 miles?

Obviously you can't convert between hours and miles, since they measure different things. If it is a speed problem, use the formula:

distance = speed x time

What are the smallest and biggest whole numbers that round to 170000 to nearest 10000?

When rounding to the nearest whatever, half the number round up and half round down.

→ the numbers that round to 170000 to the nearest 10000 are 170000 ± (10000 ÷ 2) = 170000 ± 5000

However, if a number is exactly half way, the convention is to round them up, so the numbers in the range:

170000 - 5000 ≤ number < 170000 + 5000

→ 165000 ≤ number < 175000

will round to 170000 to the nearest 10000

→ smallest number is 165000

→ biggest [whole] number is 175000 - 1 = 174999

What are the electronics and communication engineering applications of vector calculus?

The theory of radio waves and waveguides is explained in terms of equations in the form of vector calculus. Examples are Maxwell's equations.

What is the next term of the sequence jfmamjj?

a

[months in order]

a = august

after j-une and j-uly

[last four are therefore... sond]

Why is zero raise to zero undefined?

By definitions,x^0 = 1 for any non-zero number x

also

0^x = 0 for any positive x


So, if 0^0 was defined, then the first definition would say it was equal to 1 and the second that it was equal to 0.


There is a more detailed but complicated explanation which relies on limits but I hope this will suffice.

How long would it take you to count aloud to 1000000?

Let's assume that all syllables take equal time.

One, Two, ..., Nine->10.

Ten, Eleven, ..., Nineteen->20

Twenty, Twentyone, ..., Ninetynine->10*Twenty, Thirty, ..., Ninety+8*One, Two, ..., Nine->10*17+8*10=250.

One, Two, ..., Ninehundredninetynine->100*Two-, ..., Nine-+100*9*-hundred-+10*One, Two, ..., Ninetynine->100*9+100*9*2+10*(10+20+250)=5500.

One, Two, ..., Ninehundredninetyninethousandninehundredninetynine->1000*Two-, ..., Ninehundredninetynine-+1000*999*-thousand-+1000*One, Two, ..., Ninehundredninetynine->1000*5499+999000*2+1000*5500=12997000 syllables. Figure out the time from your personal opinion on time per syllable.

Are rational numbers closed under division multiplication addition or subtraction?

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Why is slopes and linear function so important?

First of all, many relationships are inherently linear. For example, distance travelled is a linear function of time where the slope is speed.

Beyond that, linear functions are extremely simple. Because of this they can be used to model pieces of more complicated functions in a simple way. Thus, you can study the properties of the complicated function by studying a piece of it at a time, in a sense.

Many mathematical objects can be said to behave as linear operators. This means that a firm undertstanding of lines, slopes and linear functions transfers to these objects.

Linearity is fundamental to a great deal of mathematics.