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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

What is the best statistical method for choosing an element who has Multiple properties?

The method will depend on what the population comprises. For example, if every element in the population has multiple properties then simply random selection will suffice.

Why do the inside of triangles add up to 180 degreass?

because a circle is 360 degrees which means a full turn in a circle. if you get up and spin around one time that is called a 360 turn. if you spin half way that is called a 180 turn.

a squares inside angles are 90 degrees each. since there are four angles they add up to 360 degrees.

a triangles insides angles vary but always equal 180 degrees. it is just the nature of the triangle.

a straight line will always be 180 degrees.

Why is it that the null set is a subset of all sets?

-- The null set is a set with no members.

-- So it has no members that are absent from any other set.

Is every complex number a pure imaginary number?

No. For example the number 1+i.

Pure imaginary complex numbers are of the form 0 + a*i, where a is a non-zero real number.

What are facts about the number 52?

There are 52 cards in a deck and 52 weeks in a year. Some people also think there are 52 states in USA but that isn't true.

In how many ways can you arrange of the letter PHILIPPINES?

Assuming the Ps and Is are indistinguishable:

There are 10! / 3! / 3! = 100800 ways

If the Ps and Is are distinguishable, then there are 10! = 3628800 ways

What is geographic differentiation?

Geographic differentiation is the identification of foods by where they have been grown. Geographic differentiation is important because fruits and vegetables grown in different locations may vary in flavor or texture.

Why is set theory so hard?

Set theory is difficult for some people, because it is approached much differently than most other areas of mathematics. Where we are used to taking a great deal of intuitive assertions for granted, such as arithmetic, or even having numbers to work with, in set theory, this is abandoned in favor of trying to build everything from the very bottom up, by beginning with only the most essential propositions about collections of objects. It's essentially the most abstract of the major fields, and the least friendly to outsiders.

What is difference between partial differentiation and total differentiation?

We use differentiation to find the rate at which a function changes as its input changes. This can give us information about the rate at which a physical process is occurring, or about how a physical quantity changes with position, for example. Partial differentiation gives us an extra facility: it is a way for us to find out about the change in a function that depends on more than one input. In real problems, physical quantities very commonly depend on more than one physical variable and we need to know how the quantity changes as we change any of these variables. For example, the sediment build-up on a river bed may be described by a function representing the thickness of the sediment. This function will depend on one or more spatial coordinates (i.e. whereabouts on the bed we look) and will also depend on time. That means we can ask two quite different questions about the sediment thickness: how rapidly does the sediment thickness change as we move over the bed, at any particular time, or how rapidly does the thickness change in time, at any particular point on the bed. Notice that these questions are about two totally different physical characteristics of the sediment build-up. The main point to remember about those two questions is the following. When we are concerned about how the thickness changes as we change one of the variables, we want to keep the other variable fixed. So if we look at different positions we do it at a particular time and if we're looking at different times we do it at a fixedposition. That idea is at the heart of the process of partial differentiation.

What is the area of the square if the side length is 36cm?

well, area is length times width. If all the side lengths are 36cm and formula is length times width. Then its 36 times 36 which equals 1296

How many inches are in 1yard 9 inches?

1 yard =36 inches

1 yard 9 inches = 36 + 9 = 45 inches

What is 6.9 x 104 out of scientific notation?

I think you might have entered the question wrong.

6.9 x 104 = 717.6

However, I think you might have intended to write like this:

6.9 x 104

with the 4 in the superscript position to mean 10 to the 4th power.

This is in scientific notation.

The answer would be to do this:

Write down 6.9

Move the decimal place four places to the right. Of course, you need to fill in the blank spaces with zeros.

So the answer is:

69000

How do you change the oxygen sensor in a 2000 Chevy Metro step by step?

there are two sensors on a 2000 metro one right after the exhaust manifold and one after the convertor they unscrew like a spark plug if you cant get them out with an adjustable wrench there is a special socket you can get at any auto parts store. then they just unplug at the connector rout the new ones just like the old ones

What is a number with 16 digits?

A number with 16 digits will be somewhere between 1,000,000,000,000,000 (either a quadrillion or a billiard, depending on where you are from - see related link below) and 9,999,999,999,999,999 (1 less than 10 quadrillion)

Is 238 divisible by 6?

238 is not divisible by 6. It is not also divisible by 3. However, it is divisible by 2.

How can I use a proportion to convert 3.5 tons into pounds?

Well think of it this way. Each ton is 2,000 pounds. so multiply 2,000 by 3.5 tons

Can two parabolas of the form with different vertices have the same axis of symmetry?

The form is not specified in the question so it is hard to tell. But two parabolas with different vertices can certainly have the same axis of symmetry.

Why are data oraganized into tables and graphs?

Tables and graphs are used to present data in an easier to view and analyze format.

What is the distributive property when multiplying polynomials?

You just multiply the term to the polynomials and you combine lije terms