0
Abstract Algebra
Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.
1,849 Questions
What are the kinds of sets according to number of elements?
One possible classification is finite, countably infinite and uncountably infinite.
y - 2 = 0
What is the expression to 3b-1?
The expression is 3b - 1. Not very helpful, but that IS the answer to the question!
People use polynomials in their everyday life . People use polynomials for modeling of various buildings and objects , used in industries , used in construction . They are even used in marketing , finance , stocks . etc.
The Legendre polynomials are used for the simulation of the scattering sound field in a multilayered elastic shells. an engineer designing a roller coaster would use polynomials to model the curves, while a civil engineer would use polynomials to design roads, buildings and other structures.
an example of polynomial and rational function
function f(x)= (3x-2)(x+2)^2
y intercept:
f(0)= {3(0)-2}(0+2)^2
= (-2)(4)
= -8
y intercept of the graph of y=f(x) is(0,-8)
x intercept:
0= (3x-2)(x+2)^2
3x-2=0 , x=2/3
(x+2)^2=0 , x=-2
x intercepts of the graph of y=f(x) are (2/3,0) (-2,0).
Now find the end behavior
f(x)= (3x-2)(x+2)^2
f(x)= (3x-2)(x2+4x+4)
f(x) = 3x^3+12x^2+12x-2x^2-8x-8
f(x) =3x^3+10x^2+4x-8
The end behavior of function f will be the same as the end behavior of 3x^3.
How do you get the difference?
to get the defference you have to subtract the number and the answer is the derrerance!!!!!!!!! thanks
What is the value of a1946 dime?
8-13-11>>> Although 1946 is the first year of issue for the Roosvelet dime, all are considered common. Average retail values for cirulated coins are $3.75 to $4.60 regardless of mintmark.
What does the rule position to term mean in maths and algelbra?
It means changing the postitioning of a number into the place of the tern number x
Why maths are important in eng?
The important of Math to language is the same as Math to Language. In particular to English.
First Math is just a method of conveying thoughts, it's another language. Sometimes, regular words cannot be used to describe things (how much money your earned today? I earned "k" dollars), we need to use a different language, namely Math. Same vice versa (Hey, what's are you typing on? 5 + 9 = 14!) It's a tool.
secondly, not as important or as obvious, is that Math is a practice of critical thinking. While it certainly won't help you write a better article right away (use induction to prove your essay!), it will help you think critically on what to write about and how to make it better (logically speaking, we cannot "assume" A, but we can easily see that the author's choice of word here "implies" it)*.
* "assume" and "implies" are commonly used math language in analysis and abstract math. THey are basically logic courses with balls instead of events.
9 (and 15)
What is the time when it is half past noon?
12:30 pm (Latin ; post meridian ; After noon).
or 1230 hours (military etc).
Casually 'lunch time'.
On the Analogue Clock, the small finger/hand is half way between '12' & '1' and the large finger/hand is pointing directly at '6'.
Well honey, if you wanna know what percent 168 is of 224, just divide 168 by 224, which gives you 0.75. Then multiply that by 100 to get the percentage, which is 75%. So, 168 is 75% of 224. Math can be a real hoot, can't it?
What are the example of the numerical coefficient?
In mathematics, a numerical coefficient is a constant factor in a term of an algebraic expression. For example, in the term 5x, the numerical coefficient is 5. In the expression 2y^2, the numerical coefficient is 2. Numerical coefficients can be positive, negative, integers, fractions, or even irrational numbers.
When does a set of hypotheses become a theory?
Hypotheses are statements which may or may not be true. If there is overwhelming support for such a set, it becomes a theory. In science a theory can be disproved but it can never be proven: you can only add to the weight of evidence in its support.
Mathematics is somewhat different. Although Kurt Godel proved that any non-trivial axiomatic system must contain statements whose truth or falsehood cannot be proven from within the system, most statements can be proven to be true or false. A set of hypotheses becomes a theory if every statement in it can be shown to be true, starting from the system's axioms and using any theorems already proven to be true.
What are nearly level area that has been eroded called?
A nearly level area that has been eroded is called a peneplain. It is a landform characterized by extensive, low-relief surfaces that result from prolonged erosion and weathering processes.
What is the median of the set of numbers 1 4 9 15 25 36?
First of all , place the numbers in rank order. Already done in this case.
1,4,9,15,25,36
Since there are an even number of terms, we take the absolute middle two terms, '9' and '15'.
Add together and divide by '2'
Hence ( 9 + 15) / 2 = 24/2 = 12
12 is the median.
What is the formula for exponential growth?
It can vary , but it is something along the lines of
G(t) = Ae^(xt)
Where
'G' is growth at time 't'
'A' is a constnt
'e' is the exponential 2.7818....
'x' is the variable factor
't' is the time.
e^(xt) is the exponential raised to the power of 'variable factor multiplied to time'.
Who developed the modern portfolio theory?
The modern portfolio theory was developed by Harry Markowitz in 1952. His work revolutionized the field of finance by introducing the concept of diversification and the importance of balancing risk and return in investment portfolios.
Is a negation another term for axiom?
No, a negation is not another term for an axiom. A negation is the logical operation that expresses "not" in a statement, while an axiom is a self-evident or universally accepted truth that serves as a starting point for reasoning in a mathematical system or a logical argument.
Laboratory method refers to a systematic approach used to conduct scientific experiments and investigations in controlled environments such as laboratories. This method involves following a set of procedures, utilizing specialized equipment and tools, and recording data to analyze and draw conclusions based on the results obtained. It is widely used in various scientific fields to study and understand phenomena under controlled conditions.
Derivation of an expression for eigenvalues of an electron in three-dimensional potential well?
The eigenvalues of an electron in a three-dimensional potential well can be derived by solving the Schrödinger equation for the system. This involves expressing the Laplacian operator in spherical coordinates, applying boundary conditions at the boundaries of the well, and solving the resulting differential equation. The eigenvalues correspond to the energy levels of the electron in the potential well.
