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.
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...
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...
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}...
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.
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...
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##...
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...
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...
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...
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!
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!
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!
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...
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...
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...
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...
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...
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...
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...
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 ##Tcosθ+N=mg
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?
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 ...
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!
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...
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...
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)
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...
I have the matrix relationship $$C = A^{-1} B^{-1} A B$$ I want to solve for ##A##, where ##A, B, C## are 4x4 homogeneous matrices, e.g. for ##A## the structure is $$A = \begin{pmatrix} R_A & \delta_A \\ 0 & 1 \end{pmatrix}, A^{-1} =\begin{pmatrix} R_A^\intercal & -R_A^\intercal\delta_A \\ 0 & 1...
Can anyone guide me how can I find ##C_P## and ##C_V##?
There are two equations in my book which I think can help but I'm not sure if I can use them to find ##C_P## and ##C_V## of a vander waals gas.
I know equation of state of this gas.
Been dipping my toes into maths by examining how equations work on the most basic level, and I love encountering equations that turn out to model similar aspects in nature, for example the inverse square law is apparent in equations for gravity and for electromagnetism.
In the thumbnail of...
Just going over some basic equations to help someone out and i have noticed that i get 2 different answers when using 2 different but very similar equations for impulse.
first eq. I=F*t
lets say that i have a small rocket motor that has a force of 5.95 newtons and a impulse of 2.5 n-s...
I tried using these equations, but it's not clear if we should hold y_1 = y_2. A transverse velocity vector would produce a flow at some angle to the horizontal, but How do they known there's such a vector?
I am having a difficult time finding papers that derive the equations of motions of the Restricted Three Body Problem using Newtonian mechanics. I have found some (barely) for the CRTBP, but there are none on the ERTBP.
Does it depend on what is being studied within the problem that the...
and
Can someone explain how they made these equations like this?
How did the radius become that equation?
What formulas from algebra did they applied?
I'm looking at these formulas and I don't understand how r=z+1/2*d
If I reason this as follows, I run into problems. Please help me understand what is wrong with reasoning like this.
a) I start with the left hand side of the equation and let that x be -2.
b) I square it. This gives me 4. So I now have the square root of 4.
c) The square root of 4 is +/- 2. The...
TL;DR Summary: solve linear systems of equations
Hi,
I am supposed to solve the following problem with Mathematica
This is the tutorial we received on how to solve linear systems with Mathematica:
I then tried the whole thing for the task, but unfortunately Mathematica doesn't give me any...
I have observed that one cannot use colour here while typing something in ##\LaTeX##.
Let me try : ##\text{Let's see if this can be \color{blue} {coloured}?}##. Nope, I type, via an edit after posting. Of course I can use colour from the panel above, but that will have to work for the entire...
I was given a problem to use an array, not a matrix, to solve a system of equations. I have not heard of doing this and can not find any reference to how to do it.
like... 2x+3y = 12, and 3x-4y = 14 How is this solved using an array or grid?
In circuit analysis, everything seems to work out when you set i*cos = sin. But thats not a legitimate equation, so why does that work? Is there a proof that this is a real equation?
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...
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?
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.
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...
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)