equations Definition and 62 Threads

In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with 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 well-formed formula consisting of two expressions related with an equals sign 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.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.

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  1. D

    I Dimension and solution to matrix-vector product

    Let $$ X \in R^{m*n} $$ where m=n with rank(X)<m then there is at-least one equation which can be written as a linear combination of other equations. Let $$ \beta \in R^{n} $$. $$ X\beta=y $$ Suppose we have x<m independent equations (the equations are consistent) formed by taking the dot...
  2. Connor123

    A Level: Rearranging Equations into Y = mx + c

    c = fλ, where the dependent (y) variable is λ, and the independent variable (x) is f. λ = c/f c * 1/f = λ Are you able to leave 1/f as equavalent to simply 'x', where the gradient would be c, or do you have to ensure 'x'/independent variable is actually f?
  3. SwetS

    A How is eq. 1.5.3 written using three-vectors and how does it lead to eq. 1.5.4?

    I am going through https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf, here I don't understand how we wrote eq. 1.5.3 with the help of three-vectors to get eq. 1.5.4.
  4. J

    B Question about Euler's formula

    Euler gave us the below equations: But this doesn't actually give me a number value for where the y value is when you plug in a number for x. For example, if i plug in 2pi for x, i know cosx should be 1. But that equation gives me (e^2i*pi +e^-2i*pi)/2. This doesn't give me 1. So what really...
  5. D

    What is the Resultant Force from adding these two forces?

    when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations: R^=f1^2+f2^2+2f1f2cos(theta) squart3*R=f1^2+f2^2-2f1f2cos(theta)
  6. pairofstrings

    I Questions about these Trigonometry Graphs involving sin() and cos()

    Hi. I have two trigonometric equations whose graphs I am trying to understand. Here are the equations: 1. a sin(x) - b cos(y) = y; a = 2, b = 2 2. a sin(x) + b cos(y) = 1; a = 1, b = 1 My question is why the graphs are the way they are. What should I do to understand them? Can anyone...
  7. JD23

    A Stimulated emission/absorption - which equations act on external targets?

    Stimulated emission-absorption have two symmetric equations for population (N_1 - number of ground state atoms, N_2 - of excited) written below, at heart of lasers: https://en.wikipedia.org/wiki/Stimulated_emission#Mathematical_model We assume that both equations act on the central target inside...
  8. chwala

    Find the area of the quadrilateral OCBAO

    My challenge was on trying to determine the angles: My approach; came up with a number of equations: ie ##m+n=70^0## ##r=p+40^0## ##q-2r=100^0, ⇒ r=50^0 + \dfrac{1}{2} q## then it follows that, ##2q+100^0=180^0## ##⇒q=40^0, r=70^0, p=m=30^0, n=40^0## ##m+40^0+t=180^0, ⇒t=110^0## and...
  9. Slimy0233

    [Kinematics] Calculating the maximum height reached by the ball

    I realize I can solve the other way too. But I want to solve using the equations ##v = u +at## ##S = ut +0.5(at^2)## and I don't know why I didn't get the right answer. Thank you for your help!
  10. Edy56

    Engineering Confused about defining unique current loops when using the node voltage method

    Please only respond if you know the node voltage method. I need to write equations for this circuit. My problem is that 1 has two paths towards 3, so when I write equations do I write both of those paths or only one. U30(1(-jXc1)+1/(jXl1+R1)+1/(jXl2)-U10((1/(-jXc1)+1/(R1+jXl1))-U20.... (the...
  11. Edy56

    Engineering Power dissipation of 2 diodes (1 is a Zener diode)

    Are my equations correct? And my process of how I should solved this problem?
  12. M

    Direct proportionality equations

    For this, Can a the equation ##x = vt + x_0## not be considered a direct proportionality between ##x## and ##v##? If so, is it because there is a constant ##x_0##? Many thanks!
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