equation Definition and 105 Threads

After collision energy is mgh/2. I am having trouble in writing the energy equation after this.

Let's denote ##\sqrt[3] r =t##. The three expressions above can be written as $$x_1=2t \cos \frac {\phi} 3, x_2=t (-\cos \frac {\phi} 3 -\sin \frac {\phi} 3), x_3=t (-\cos \frac {\phi} 3 +\sin \frac {\phi} 3)$$ The Vieta's formulae for the given equation are $$x_1+x_2+x_3=0$$ $$x_1 x_2+ x_2 x_3...

If the laws of physics say that nothing can move faster than the speed of light, how can we square it in Einsteins equation? It dosent make synce to me. How does Einsteins equation work can someone break it down for me and explain it in layman’s terms please. How can we warp spacetime just by...

TL;DR Summary: Exponential VS Logarithmic Regression (using the TI-84 Plus graphing calculator) Here is the question: A scientist examines the growth of bean plants under different growing conditions. The results of one trial are as follows: Day...

Proof: Consider the equation of ## a^2-x^2=\epsilon\sinh x ## for ## 0<\epsilon<<1 ##. Let ## \epsilon=0 ##. Then the unperturbed equation is ## a^2-x^2=0 ##. This gives ## a^2-x^2=0\implies (a+x)(a-x)=0\implies x=\pm a ## with the root ## x=x_{0} ## such that ## x_{0}(a)=a ## because ## x\geq...

a) Proof: By definition, the potential energy ## V(x) ## is given by ## F(x)=-\frac{dV}{dx} ##. Note that ## \ddot{x}=-\frac{dV}{dx} ## where ## \ddot{x}=-x-\epsilon(\alpha x^2\operatorname{sgn}(x)+\beta x^{3}) ##. This gives ## \frac{dV}{dx}=x+\epsilon(\alpha x^2\operatorname{sgn}(x)+\beta...

I've tried a few things. I did one method to try to accomplish the removal of the -70 in the derivative boundary condition. It came out as below. When plotting it however it gave a solution that didn't make sense.

(Yes, I'm guilty of passing along something incomplete and of utterly unknown provenance that someone saw somewhere and didn't understand. I feel dirty.) ∀t(T(x,t)⟹(¬H(x,t)∨H(x,t+Δt))) Certainly, without specifying any of the variables, it's got to be useless. At least we can assume t and Δt...

Was the approach used by the referenced tutor correct? In my understanding, the set up equation ought to be, ##s=-h, u=16## as the stone is being thrown upwards and ##g=-9.8## giving me, ##-h = 64 - \dfrac{1}{2}×9.8 ×16## ##-h=-14.4##m ##h=14.4##m , or it does not really matter.

I need an idea. Thank you.

The paper follows (free): https://arxiv.org/abs/2111.03203v2 I was trying to read it, but couldn't understand where equation 2 comes from (page 3). Is this just a standard diffraction or interference equation? Could anyone provide a reference that explains that equation?

My attempt and solution : $$2^x=3^y+509\Longrightarrow 2^x-512=3^y+509-512\Longrightarrow 2^x-2^9=3^y-3$$ $$\Longrightarrow 2^9(2^{x-9}-1)=3(3^{y-1}-1)$$ $$\Longrightarrow (x,~y)=\boxed{(9,~1)}$$ İs there any solution?

Would we also use Newton's method, or are there more powerful methods? Are there general methods for solving equations with fractional exponents? The solution to this problem is; https://www.wolframalpha.com/input?i=solve+x%5E%2817%2F6%29+%2B+x%5E%2821%2F25%29+%3D+15

Is there a better way of solving this, My steps, ##5(x+1)^{1.5}-4x-28=0## ##(x+1)^{1.5}=\dfrac{4x+28}{5}## ##(x+1)^3=(\dfrac{4x+28}{5})^2## ##x^3+3x^2+3x+1=\dfrac{16(x+7)^2}{25}## ##25x^3+75x^2+75x+25=16(x^2+14x+49)## ##25x^3+59x^2-149x-759=0## Letting ##f(x)=25x^3+59x^2-149x-759=0## and using...

I’ve found that when I use g(x)= (x+3)(x-1)2 You get everything except the maximum x=-1 I just cannot get that last one

I figured since ## dr/dt ## is simply the velocity of the target mass, the velocity ##u_x## would simply have to be changed by the Lorentz transformation. Since the rest mass doesn't change, I think this should be as simple as taking the Lorentz transformation for velocity, and substituting the...

Proof of kinetic energy work done equals a change in kinetic energy in a mechanical system. δW = F.ds W = ∫F.ds W = m∫a.ds W = m∫(dv/dt).ds W = m∫v.dv here if v and dv are in the same direction the change in kinetic energy will be the usual equation. what happens if both are in different...

I'm currently taking Math Methods in Physics, and we're working on infinite series right now. In one of the examples, in order to find the limit, they do what you can see below in "Example 3" As you can see, they turn the original equation into a ln equation, so that they can bring the...

I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading...

I initially thought about the different forms of energy present at each of the points: Total energy at starting point: PEA+ KEA= mgH at point D: KE_D = 1/2mv2f PED= mgD Energy at point D: PED+ KED D = mgD + 1/2 mv2f because EA= ED mgH = mgD = 1/2 mv2f mg(H-D) = 1/2 mv2f g(H-D) = 1/2...

Proof: Let ## x=\sqrt[3]{18+\sqrt{325}}+\sqrt[3]{18-\sqrt{325}} ##. Then ## x^3=(\sqrt[3]{18+\sqrt{325}}+\sqrt[3]{18-\sqrt{325}})^3 ##. Note that ## (a+b)^3=a^3+3ab(a+b)+b^3 ## where ## a=\sqrt[3]{18+\sqrt{325}} ## and ## b=\sqrt[3]{18-\sqrt{325}} ##. This gives ##...

I can imagine x + y = 1 to be line in xy - plane but how can x + 2y + z = 3 be a line, not a plane? Thanks

Where can I find detailed derivation of Field Equation of Teleparallel Gravity from variation of Action ?

I've seen a lot of people use implication and equivalence logic incorrectly. For example, when solving equations (i.e. ##x - 2 = 3 \implies x = 5##). Implication is not reversible, thus it only works in one way. By saying, ##x - 2 = 3 \implies x = 5##, you are essentially saying that it is...

Balancing the complete combustion of acetic acid equation to carbon dioxide and water is straightforward if you remember hydrogen is always +1, elemental oxygen is zero and combined oxygen is always -2. just balance the exchange of electrons between oxygen and carbon. But how do you balance...

Who and when first time introduced below equations(dont have to be in same notation, content is important)? If this formula is always the same, what is contribution of Navier, what of Stokes, what changes all these years?

For this problem, The solution is, However, I have a question about the solution. Does someone please know why they write out ##\frac{dF}{dx} = \frac{\partial F}{\partial y}y' + \frac{\partial F}{\partial y'}y''## since we already know that ##\frac{dF}{dx} = 0##? Thanks!

$$(b-a)^2-4(b-c)(c-a)=0$$ $$b^2-2ab+a^2=4(bc-ab-c^2+ac)$$ $$b^2-2ab+a^2+4ab=4bc-4c^2+4ac$$ $$(b+a)^2-4ac=4c(b-c)$$ $$b-c=\frac{(b+a)^2-4ac}{4c}$$ I don't know how to continue and not even sure what I did is useful. Thanks

Hi; given the equation ydy/dx=x^2 how is the chain rule applied to result in ydy =x^2dx? Thanks

I have having trouble understanding Maxwell's Equations. Can anyone recommend some good book or website that can help me to understand these Equations? How can electric and magnetic fields travel perpendicular to each other? What causes electromagnetic waves to first radiate from its source? I...

This is a question from the MIT Open courseware website. (1). d = vt + ut let t = time it takes d = (u + v)t t = d / (u + v) (2). d = vt + ut d - vt = ut. Substitute t with d / (u + v) d - v*(d/(u+v)) = u*(d/(u+v)) d - v*(d/(u+v)) = “distance...

This question is from the MIT Courseware. I’m having difficulty finding the general equation to solve the problem (1). d = vt + ut d = (u + v)t t = d/(u + v) (2). d = vt + ut d - vt = ut sub t with d/(u+v) d - (v*d)/(u+v) = (u*d)/(u+v) I’m done with the...

I was able to solve with a rather longer way; there could be a more straightforward approach; My steps are along these lines; ##\sinh^{-1} x = 2 \ln (2+ \sqrt{3})## ##\sinh^{-1} x = \ln (7+ 4\sqrt{3})## ##x = \sinh[ \ln (7+ 4\sqrt{3})]## ##x = \dfrac {e^{\ln (7+ 4 \sqrt{3})} - e^{-[\ln 7+ 4...

Hello there, I am trying to solve the Following equation for r, $$2 a Q^4+5 r^4 \left(3 c (\omega +1) r^{1-3 \omega }-2 r (r-3 M)-4 Q^2\right)=0$$ Clearly this is unsolvable. But if we substitute a=0 and c=0 we get one of the solution, ##r=\frac{1}{2} \left(\sqrt{9 M^2-8 Q^2}+3 M\right)##. Can I...

Thanks a lot in advance!

Solve the given PDE for ##u(x,t)##; ##\dfrac{∂u}{∂t} +10 \dfrac{∂u}{∂x} + 9u = 0## ##u(x,0)= e^{-x}## ##-∞ <x<∞ , t>0## In my lines i have, ##x_t = 10## ##x(t) = 10t+a## ##a = x(t) - 10t## also, ##u(x(t),t)= u(x(0),0)e^{-9t}## note this is from, integrating ##u_t[u(x(t),t] =...

Solve the given PDE for ##u(x,t)##; ##\dfrac{∂u}{∂t} +8 \dfrac{∂u}{∂x} = 0## ##u(x,0)= \sin x## ##-∞ <x<∞ , t>0## In my working (using the method of characteristics) i have, ##x_t =8## ##x(t) = 8t + a## ##a = x(t) - 8t## being the first characteristic. For the second...

My confusion refers to this question above. If I were to ask you, what is the equation of the radial line, what would you say? I know that the general equation the radial line with cartesian gradient of m has an equation of θ = arctan(m). Clearly here the angle between the radial line and...

Hello. I registered today. Maybe you can help me. How do I use LaTex in the forum for to write equations?

Hi there, I am going through a book on multi-storey steel structures and I have come to a chapter that gives approximate methods to calculate rotations at the joints (The intersecting members) of a rigid frame. There is a recurrence equation that computes the rotations and this is given below...

Can someone please explain me the steps of calculation of X1:X2 after putting in the lower value of W^2 in equation 9.9 in "Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 2006 - pg 319"? I have attached the page as a PDF file. Thank you.

For this problem, I am confused by the term below. I get all their terms, expect replacing the highlighted term by ##e^{3t}##, does someone please know whether this is yet another typo? Thanks!

hb=54 2h+2b=33 h=54/b therefore, 2(54/b)+b=33 108/b + b = 33 I’ve got a feeling I’ve gone down a blind alley here. Any hints?

In my line i have, ##\dfrac{∂r}{du} = \vec{i} +\dfrac{1}{2}u \vec{k} = \vec{i} +1.5 \vec{k}## ##\dfrac{∂r}{dv} = \vec{j} -\dfrac{1}{2}v \vec{k} = \vec{j} -0.5\vec{k}## The normal to plane is given by, ##\dfrac{∂r}{du}× \dfrac{∂r}{dv} = -\dfrac{3}{2} \vec{ i} + \dfrac{1}{2}\vec{j}+\vec{k}##...

So basically i am vary green when it comes to equations/formula Well to the point i don't even know if proper name for what i'm looking for is called equation or formula but let's stick to equation So going as simple as i can I want to throw boomerang creating boomerang like ellipse trajectory...

This is the general suggested approach given in a textbook. My question is why can I not directly write it in vector form? E1 vector + E2 vector =0 should be valid no? Why are they choosing to write E1 mag + E2 mag=0 Then find a vector form Then convert the magnitude equation into a vector...

For this problem, Does someone please know where the term highlighted in blue came from? Thanks!

Need help solving this question. Can't seem to get the right answer using PV/T=constant P1V1/T1 = P2V2/T2 Patm = 75.23cmHg T1+20+273=293K STP: P=1.01 x 10^5 N/m^2 Pabs=41cmOil P1 = density x g x h = (810 kg/m^3)(9.8 m/s^2)(75.23-41)x10^-2 mOil=2717.18 N/m^2...