What is equation: Definition and 67 Discussions

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. A

    I Adiabatic Processes: Why does this equation use constant volume and not constant pressure?

    Why is this equation (red sign) written in constant volume and not in constant pressure?
  2. PLAGUE

    I Why do the lines m and l coincide in the proof of the parallelogram rule?

    I was going through this book called "A Course in Mathematics for Students of Physics Volume 1 by Paul Bamberg and Shlomo Sternberg". There in a part they said something like this: ...if we start with a point P and write ##R=P+u## ##Q=P+v## and ##S=P+(u+v)## then the four points ##P,Q,S,R## lie...
  3. chwala

    Find the value of ##k^2## in the problem involving trigonometry

    In my working i have, ... ##\cos C = 2\cos^2 \dfrac{1}{2} C -1## ##c^2= a^2+b^2-2ab(2\cos^2 \dfrac{1}{2} C-1)## ##c^2= a^2+b^2+2ab(1-2\cos^2 \dfrac{1}{2} C)## ##c^2= (a+b)^2 (1-2\cos^2 \dfrac{1}{2} C)## Now from here, ##k^2 =2## but text gives different solution. I am still checking...
  4. lukegxhycj

    SUVAT equation question: When will the car collide with the lorry?

    s1=-u1^2/2a1 s2=-u2^2/2a2 s2>s1+d (If distance the car stops is bigger than the distance the lorry stops plus the initial distance then they will crash) (sub s1 and s2 in) -u2^2/2a2 > -u1^2/2a1+d Switch 2a2 with whole left side of equation. -u2^2/(-u1^2/2a1)+d > 2a2 Make the (d)a fraction by...
  5. chwala

    Solve the equation: ##\tan x ⋅\tan 4x = 1##

    I saw this link; is the approach here correct...
  6. T

    MTW Box 21.1 - What can "add and subtract" do for Equation (12)?

    I haven't posted for a while and I am still (!) working through some of the things I didn't quite get in MTW Chapter 21. Here is my latest puzzle. I want to work out how to get from Equation (12) in the attachment, to Equation (15). I've tried the "add and subtract" ##\{\frac...
  7. L

    I Finding the equation of a curved line

    Ok, so i have done many math classes, as i am an engineer, however, a theory class and proof class i h ave not done, except maybe one haha. here is my question, if i draw some sort of curved line by hand, how do i find an equation for that? for example, i draw half of a tear drop but along...
  8. W

    Attempting to teach this: Momentum and Impulse

    For question 1. I am stuck. I know that the equation involves time and possibly rate, should solve for distance. But not sure how to set it up with information given. 2. Ft= m 🔺️ v F(3)= (100kg)(30m/s) 3 s= 3000 kg m/s Same applied to question 3. 3. F(2)= (100kg)(-30m/s) F(2) = -3000 kg m/s...
  9. FlowiwGhar

    Physics problem - Salmon jumping waterfall

    m * g * h + (1/2) * m * v² = m * g * y Simplifying the equation: g * h + (1/2) * v² = g * y Substituting the values: g * 0.614 + (1/2) * v² = g * 2.73 * sin(26.7°) Now, let's solve for v: (1/2) * v² = g * 2.73 * sin(26.7°) - g * 0.614 v² = 2 * (g * 2.73 * sin(26.7°) - g * 0.614) v = √(2...
  10. al4n

    B How to find an integer solution to a nonlinear equation?

    given something like: an = c where c is given and a, n, and c are only allowed to be integers. how would one find the value of say n or a?
  11. H

    A Proving an equation in a book about Periodic Structures

    Hello everyone, I am reading some book titled: Periodic Structures: Mode-Matching Approach and Applications in Electromagnetic Engineering. In Chapter 2, there is an equation as follows: where . Here the electric field is along the transverse x − y plane like the propagation vector kt. Now it...
  12. jamesbrazil

    Maple Finding the solution of this long equation using Maple

    I need help solving an equation. I started using Maple, but had no success. Could someone explain to me which command to use? I need to find a very small value of ##x##, that is, ##x \ll 1##. The equation is $$434972871000000000.0+{\frac {\sqrt {6} \left( { 1.488388992\times 10^ {-36}}\,\ln...
  13. Q

    I What is the distinction between invariance and covariance?

    What is the difference between these two concepts? An equation is said to be "invariant" under some operation if the form of the equation doesn't change. However, isn't that exactly what "covariance" in physical laws means—that the form of the laws remains unchanged when applying an operation to...
  14. pairofstrings

    I Adding 'z' to 2D graph equation

    Hi. If I write any random equation in 2D then the graph undoubtedly shows up on that 2D graphing system. Equation example: ##x^2 y^2 + x^2 y + x y =1## My question is: if I take the same equation: ##x^2 y^2 + x^2 y + x y =1## and if I manipulate the equation by including another variable...
  15. JMFernandez

    Question about this Capacitor voltage integral equation

    Hi. I don´t know if this question should be in the maths forum, but as it´s related with circuit analysis, I will post it here. I just would like to know how you get: v(t) = 1/C ∫tt0 i(τ) dτ + v(t0) From: v(t)=1/C ∫t-∞ i(τ) dτ I just know the basics of calculus and I don´t know how to...
  16. PhysicsTest

    Capacitor equation to be used in electrical analysis

    I am confused with the equation to be used for capacitor in electrical analysis The standard equation we have is Q=CV -> 1 the other equation is is V = Z*I ohms law Z is the impedance of the capacitor. Both are giving me voltage, which one to use ?
  17. P

    A Exploring a QM particle in Motion with GR

    I encountered a problem in reading Phys.Lett.B Vol.755, 367-370 (2016). I cannot derive Eq.(7), the following snapshot is the paper and my oen derivation, I cannot repeat Eq.(7) in the paper. ##g^{\mu\nu}## is diagonal metric tensor and##g^{\mu\mu}## is the function of ##\mu## only...
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