# equations Definition and 57 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. ### Explanations On Entering Various Equations Into Mathematica?

I've had Mathematica for a long time, but up until now, I just used to use the free-form input. I'm trying to learn the language so that I'm able to do more with the software. However, the information I gather from the Wolfram site is worthless for a lot of things, as I don't understand what...
2. ### Mathematica 3D Graphing (3D Plot) Issue

I'm trying to graph two equations to compare the two visually. For some reason, one of them isn't showing up, even though I'm in a range to where it should be. See the screenshot below. The "3x - y = 4" is graphing fine, but for some reason, "x + y + z = 5" isn't showing up. At first, I...
3. ### Problem with dimensionless quantities in an equation requiring M^2 (Super Hamiltonian Formulation for Geodesic Motion)

I've worked my way through this exercise but I am a bit puzzled by the last line "What do the choices ##\mathcal H = -½, 0, -½\mu^2, +½ ## mean for the geodesic and the choice of parameterisation?" I've worked to produce: ##\big (\frac {dr}{d\lambda} \big ) ^2 = E^2 - \big (1- \frac {2M}{r^2}...
4. ### Engineering Determine the flight time and heights of 2 balls thrown vertically

To find the time of this problem, I used the equations 3 + (10 * x ) = 13.5 *x. 3 = 3.5*x. Therefore x was 0.857. To start off with child A was already three feet above ground and I got the answer to the time. However I couldn't find the height.
5. ### I Claude Naiver work on Navier-Stokes equations

I am interested what are main differences/news in two Claude Navier works "Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molecules"- memoire 1 and "Sur Les Lois du Mouvement des Fluides" memoire-2? Are both works written(not published) in 1821? Does memoire 1...
6. ### Find the possible values for ##a## and ##b## where ##a## and ##b## are integers

I noted that, ##lcm(a,b)=2048## Letting ##a=2^x## and ##b=2^y##, ##⇒\dfrac{1}{2^x}+\dfrac{1}{2^y}= \dfrac{3}{2^{11}}## ##⇒\dfrac{2^{11}}{2^x}+\dfrac{2^{11}}{2^y}= 3=[4-1]## ##⇒\dfrac{2^{11}}{2^x}+\dfrac{2^{11}}{2^y}=2^2-2^0## My intention being to write all the numbers to base ##2##...
7. ### Diophantine equations and physics

Hello, can anyone tell me about applications of Diophantine linear equations to physics?The only example that comes to mind is that of a series of weights. I have a measuring rod that is 40cm long and hinged in the middle. If I put a 40g weight at one end, how can I place 5g, 7g, 11g, 13g, 17g...
8. ### Correct Derivation of the Adiabatic Condition? (PV Diagram)

By the First Law, Definition of an Adiabatic Process, and Definition of Work: ##\Delta E = Q - W = - W = - P \Delta V ## (because ##Q = 0##) (Equation 1) By the Equipartition Theorem: ##\Delta E = \frac{3}{2} Nk \Delta T ## (Equation 2) By Setting Equation 1 equal to Equation 2 ## \Delta T...
9. ### Magnus Effect Equations and Mechanics

Ok I need to clear up a few things. First, in (Figure 1), a soccer ball (the circle in the photo), would have the magnus force towards the lower pressure because the universe favors high entropy? Also what are the forces are active in figure 2? Lastly what to the variables in Figure 3 mean...
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### Solving inexact ODE

For this problem, Does someone please know how they combined the two equations for H to get the finial equation ##H(x,y) = .... = c##? Thanks!
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### Coupled system of differential equations

For this problem, Would it not make sense to use for ##x' = -sx - gx - ry## as a better version of ##x' = - gx - ry## since the ##sx## term connects the two DEs to form a coupled system (from what the author explains the ##sx## term represent insulin glucose transformation). Thanks!
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### Solving system of differential equations using matrix exponential

For this problem, The solution is, However, can someone please explain to me where they got the orange coefficient matrix from?It seems different to the original system of the form ##\vec x' = A\vec x## which is confusing me. Thanks!
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### Complex Eigenvalues of system of DE

For this problem, Can someone please explain to me how they got from the orange step to the yellow step? I am confused how the two expressions are equivalent. Thanks!
14. ### Praise Issues with LaTex

Hello, can anyone give me a hand? I am trying to make a post but the LaTex engine doesn't work properly. I Try the four dollars´ and the four hashtag´ method on, but the equations dont appear when I click the Preview button. The LaTex engine doesn't do anything. I have posted several threads...
15. ### A Equations of Motion for Torsional Inverted Pendulum on a moving cart

Hello I am trying to figure out the equations of motion for the following scenario: a mass m is held upright on by a massless rod mounted on a cart that is being pulled by a linear force. The caveat is that the rod is mounted on the cart via a torsional spring which causes a restorative torque...
16. ### Cables, pulleys, 2 weights

Fx = 0 = ABcos(a)+BCcos(b)-BDcos(30) Fy = 0 = ABsin(a)+BCsin(b)-BDsin(30) == Fx = 0 = ABcos(a) + 3.2737cos(b) - 3.738 Fy = 0 = ABsin(a) + 3.237sin(b) - 2.158 But i cant find a third equation to use. I've tried a+b = 90 but that produced a number of errors. Thank you. Edit: angle b is the...
17. ### Show that the system of equations has no unique solution

solution; @Mark44 we discussed this sometime back on the forum. The approach of using determinant or echelon form of a matrix was sufficient. Would i be correct to use this approach, ##x+2y+3z=4x+5y+6z## ##3x+3y+3z=0## and ##7x+8y+9z=x+2y+3z## ##6x+6y+6z=0## Then, it follows that the...
18. ### My Website For Creating Interactive Visuals Linked To Equations

I recently finished a website and I'd like to share it in case it would be useful, as well as to get feedback. The URL: equationvisuals.com The website uses a basic computer algebra system (CAS) I built to solve systems of equations and show its steps. These equations can then be linked to...
19. ### LaTeX Possible name of the software used to type equations in a video

Video Link Many thanks if you can guess what the name of the software is. It can be very useful for teaching. Let me also confess that, till date, I haven't found a software that can type ##\rm{LaTeX}## equations in real time on to the computer screen. LyX is the only one I know of, but the...
20. ### I Lorentz Transformations Confusion

Two simple equations, yet I can't find any sources that explains it very well. If you have any suggestions on where I could find this then please link them! $$\Delta{t'}=\gamma(\Delta{t}-\frac{v}{c^2}\Delta{x})$$ Does it matter if S' is moving away to the right, or to the left, of S? I...
21. ### The ratio between two horizontal speeds in this pendulum arrangement

From the forces equation I can only understand from it that the forces' equations are:##N=Mg## and ##T\sin \theta=m\ell \ddot{\theta}##. But I don't know how to find the Torques' equations. Any help is appreciated. N=Mg ##Tcos⁡θ+N=mg
22. ### I Why Do Some Theorists Claim Cosmic Inflation Dilutes Magnetic Monopoles?

So if Maxwell's Equations state that Div B = 0 which is a statement that there are no magnetic monopoles why do some folks claim that Cosmic Inflation "dilutes" magnetic monopoles?
23. ### Work out the amount that Arjun paid in rent in 2019

I am interested in a more direct linear equations approach...to solve, which i know is possible... A. My initial thinking was along the lines, let ##x## be the amount that Arjun paid in 2018 and let ##y## be the amount that Gretal paid in 2018 where A was the total amount paid in 2018 ...
24. ### Simpliying this partial differential equation

Does this equation mean that: ## x+y =z ##, and ## x = y##? I mean ## \delta_{ij} ## terms in the LHS of the eqaution equal those at the RHS ? with knowing that ## \partial_i \partial_j x ## term dose not vanish for ## \delta_{ij}=1 ## Any help is appreciated!
25. ### Solve for all angles x: cos(2x) + cos(x) = 0, where 0<x<2pi

I'm not sure how to go about solving this mathematically? In just using what seems obvious, I know the angle pi would work, because pi = -1, and 2pi = 1. However, as far as manipulating the equations in a way where it can solve itself without me having to look at a chart where cos for both x...
26. ### I Heisenberg Equations of Motion for Electron in EM-field

Consider the Heisenberg picture Hamiltonian $$H(t) = \int_{\textbf{r}}\psi^{\dagger}(\textbf{r},t)\frac{(-i\hbar\nabla+e\textbf{A})^{2}}{2m}\psi(\textbf{r},t)$$ where ##\psi(\textbf{r},t)## is a fermion field operator. To find the equations of motion that ##\psi,\psi^{\dagger}## obey. I would...
27. ### I Solve the system of linear equations

This is fine but i have my own approach as follows; ##\begin{pmatrix} -7 & -6 & -12 & -33 \\ 5 & 5 & 7& 24 \\ 1 & 0 & 4 & 5 \end{pmatrix} ## → Row 1 times 5 and row 2 times 7... ##\begin{pmatrix} -35 & -30 & -60 & -165 \\ 35 & 35 & 49& 168 \\ 1 & 0 & 4 & 5 \end{pmatrix}## →...
28. ### Basic Simultaneous Equations Problem

I got c=13, but I'm using an app that, at the 'diagnostic' stage, doesn't tell you if you're correct or not (I multiplied the first equation by 4, and the second by 2, then subtracted the second from the first)
29. ### Derivation for modified sine curve equations

Hello, I am looking for a detailed derivation of the equations used to generate the modified sine curve. I found one in Cam design handbook by Harold A. Rothbart but I didn't understand how we get certain equations. My end goal is to combine the modified sine curve with constant velocity and get...

47. ### 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?
48. ### 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.
49. ### 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...
50. ### 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)