What is Math equation: Definition and 25 Discussions
In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=". The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any equality is an equation.Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables.An equation is written as two expressions, connected by an equals sign ("="). The expressions on the two sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation. Very often the right-hand side of an equation is assumed to be zero. Assuming this does not reduce the generality, as this can be realized by subtracting the right-hand side from both sides.
The most common type of equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials.
The sides of a polynomial equation contain one or more terms. For example, the equation
A
x
2
+
B
x
+
C
−
y
=
0
{\displaystyle Ax^{2}+Bx+C-y=0}
has left-hand side
A
x
2
+
B
x
+
C
−
y
{\displaystyle Ax^{2}+Bx+C-y}
, which has four terms, and right-hand side
0
{\displaystyle 0}
, consisting of just one term. The names of the variables suggest that x and y are unknowns, and that A, B, and C are parameters, but this is normally fixed by the context (in some contexts, y may be a parameter, or A, B, and C may be ordinary variables).
An equation is analogous to a scale into which weights are placed. When equal weights of something (e.g., grain) are placed into the two pans, the two weights cause the scale to be in balance and are said to be equal. If a quantity of grain is removed from one pan of the balance, an equal amount of grain must be removed from the other pan to keep the scale in balance. More generally, an equation remains in balance if the same operation is performed on its both sides.
In Cartesian geometry, equations are used to describe geometric figures. As the equations that are considered, such as implicit equations or parametric equations, have infinitely many solutions, the objective is now different: instead of giving the solutions explicitly or counting them, which is impossible, one uses equations for studying properties of figures. This is the starting idea of algebraic geometry, an important area of mathematics.
Algebra studies two main families of equations: polynomial equations and, among them, the special case of linear equations. When there is only one variable, polynomial equations have the form P(x) = 0, where P is a polynomial, and linear equations have the form ax + b = 0, where a and b are parameters. To solve equations from either family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.
Differential equations are equations that involve one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model processes that involve the rates of change of the variable, and are used in areas such as physics, chemistry, biology, and economics.
The "=" symbol, which appears in every equation, was invented in 1557 by Robert Recorde, who considered that nothing could be more equal than parallel straight lines with the same length.
Hi all,
I want to know if a second solution exists for the following math equation:
Ce^{At} ρ_p+(CA)^{−1} (e^{At}−I)B=0
Where C, ρ_p, A and B are constant matrices, 't' is scalar variable. I know that atleast one solution i.e. 〖t=θ〗_1 exists, but I want a method to determine if there is...
I don't understand the extra - in the second part of the equation, before the 2.
From my understanding, the squaring of the first part of the first equation is so that the equations consist of magnitudes. I'm just not quite sure where the negative came from. If I had to guess, it would be, w...
Summary:: Question: a car of mass 800kg, 3600N driving force experiences resistive forces of 120v Accelerates from rest. Form equation and show max speed is 30 ms^-1, assuming driving force does not change.
my attempt at a solution -I can not see how to rectify it as I don’t think I did...
Okay so I recently found out that in official canon, the Galactic Republic of Star Wars was founded 25,000 years before the first original movie. Hyperdrives were presumably invented around 25,000 BBY. By the time of the Phantom Menace which is in the year 32 BBY, Technology has stayed basically...
Homework Statement: what is the mathematical explanation for fresnel lenses
Homework Equations: No equations were provided
I'm going to post a link to one article I found that I think has the answer, but I couldn't understand because of my lack of knowledge in physics and math...
I posted this link a couple years ago, but just in case you need to draw a Christmas Tree:
https://tex.stackexchange.com/questions/39149/how-can-we-draw-a-christmas-tree-with-decorations-using-tikz
There are a lot of interesting variations posted, maybe PF could have our own contest!
Here's...
Hi I’m looking for someone who could help me with this little problem of mine... My sister studies math at a university she is on her 3rd year and her birthday is coming up i would like to make her a Tshirt with a print that says “I am (long mathe equation) years old... so i need a math equation...
Homework Statement
cos2x + cos x = 0 (0 <= x <= 360)
Homework EquationsThe Attempt at a Solution
cos2x + cos x = 0
2cos(3x)/2 cos(x)/2 = 0
3x/2 = 90 degrees
x = 60 degrees
x/2 = 90
x = 180
3x/2 = 270
x = 180
x/2 = 270
x = 540 (not qualified)
is there any more possibility (answers) for x?
Homework Statement
Homework EquationsThe Attempt at a Solution
2x - 1 >= 0
x >= 1/2
x - 2 >= 0
x >= 2
for x <1/2
then 2x - 1 and x - 2 are negative
solve : -(2x-1) - (x-2) = 2
-3x + 3 = 2
x = 1/3
for 1/2 <= x < 2
the (2x - 1) positive, (x-2) negative
solve : 2x -1 -x + 2 = 2
x = 1
for...
Homework Statement
my book shows:
(-1/(1-((b+acosx)/(a+bcosx))^2)^1/2) * ((a+bcosx)(-asinx)-(b+acosx)(-bsinx))/(a+bcosx)^2
=
(a^2+b^2cos^2(x)-b^2-a^2cos^2(x))^(-1/2)
*
((a^2-b^2)sinx/(| a+bcosx |))
I'm having a hard time understanding how they did this.
What software is used to create a text editor, math graph, and math equation such as below image?
It seems the math graph is a vector illustration (not pixel), the math equation is not Latex, and they are integrated with the text editor.
What software to create such as book?
Homework Statement
Solve for A
27 = 81/√3a-3
Homework Equations
The Attempt at a Solution
Im not sure where to begin with this question. Can someone go through all the steps into solving for A. Thanks
Hello everyone, longtime reader, first time poster.
A friend and I discovered this piece of math graffitied on an obscure laneway wall in Melbourne. I find it a bit mindblowing that someone would go to all this effort, particularly in a place where very few people are going to see it. As you...
Homework Statement How would I solve for L in this expression:
sintheta=L/sq.rt(x^2+L^2) ?
Homework Equations
sintheta=L/sq.rt(x^2+L^2) ?
The Attempt at a Solution
and if they have the same angle between them would solving for L create an equal answer using...
Hi, I wish to do math equations electronically.
Can someone help me to find a good software?
I heard there is such a thing called latex. Where can I find it?
Thanks
Hey guys i have been attempting this problem for days. If you can help me with it and explain how to solve it, I would be extremely grateful. I wrote my answer on the right. Thanks!
I've already done the Physics part, but now I am stuck with the equation 2h = vt + gt^2
It's just a variable problem, so no numbers are involved, just variables. Now I just need help solving for t.
hi, I've been searching around the site and found it pretty useful but I'm having a pretty tough time with a few questions i have
its pretty much the same as This
but the coefficient values are different, the problem I'm having is with the coefficients for the bends, could someone please...
One mathematical sum is harassing me since a few days the problem is;:-
a^2+b^2=25 and a^3+b^3=91. find the value of a and b.
Now here we cannot take that into consoderation that as a^2+b^2=25 , a=3 and b=4. But we have to find the answer without any assumtions.May i please get the...