Line Definition and 1000 Threads

I'm getting really stuck with understanding this example: (Source: page 98) What is a line vortex, and how do we derive those equations of motion? All I can tell is that the velocity of a given vortex depends on a contribution from every other vortex in the plane, but I wondered if someone...

Assuming the line element ##ds^s=e^{2\alpha}dt^2-e^{2\beta}dr^2-r^2{d\Omega}^2 ##as usual into the form ##ds^s=e^{-2\alpha}dt^2-e^{-2\beta}dr^2-r^2{d\Omega}^2##, I found that the ##G_{tt}## tensor component of first expression do not reconcile with the second one though, it fits for ##G_{rr}...

i'm trying to find what sort of 2-d geometry this system is in, I've been given the line element 𝑑𝑠2=−sin𝜃cos𝜃sin𝜙cos𝜙[𝑑𝜃2+𝑑𝜙2]+(sin2𝜃sin2𝜙+cos2𝜃cos2𝜙)𝑑𝜃𝑑𝜙 where 0≤𝜙<2𝜋 and 0≤𝜃<𝜋/2 Im just not sure where to start. I've tried converting the coordinates to cartesian to see if it yields a...

I copied and pasted some code from another thread on this forum, and it has worked, however I am unsure how to change the length of the line. On the attached image, the line is the one labelled H(X,T). I want the line to be perpendicular to the plane- to pass through the blue node labelled (dfd)...

Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks

I couldn't find any information on this but I do wonder, what was the average CRT raster scan line thickness in terms of pixels illuminated in each full scan from left to right? Did the electron beam illuminate a line that is just a single pixel width on each pass or did it hit multiple pixel...

$\textbf{xy-plane}$ above shows one of the two points of intersection of the graphs of a linear function and and quadratic function. The shown point of intersection has coordinates $\textbf{(v,w)}$ If the vertex of the graph of the quadratic function is at $\textbf{(4,19)}$, what is the value of...

From Newton's second law: $$T_{x} = F_{turn}$$ So $$T \sin \theta = ma$$ $$T_{y} = F_{y}$$ so $$T \cos \theta = mg$$ Equate the two equations to get: $$ \frac{T \sin \theta}{a} = \frac{T \cos \alpha}{g} $$ and the angle is given by: $$tan (\theta) = \frac{a}{g} $$ where ##r = \frac{v}{w}## and...

I want to find the probability that the two points ($x_1, y_1$) and ($x_2, y_2$) lie on the opposite sides of a line passing through the origin $o = (0, 0)$ and makes an angle $\psi$ that is uniformly distributed in $ [0, \pi]$ with the $x$ axis when the angle is measured in clockwise direction...

Hi I'm very stuck on what to do for these 2 questions I got wrong Can someone please help me on what triangle I need to sketch out in order to find the 2 components of forces for F1 and F2. I'm assuming you have to make use of the sine or cosine rule here I'd be grateful for any help given...

Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.

Hi, I was recently attempting a question about transmission lines and I don't seem to really understand how the voltages travel through the line. Question: If we send a voltage pulse of amplitude ## V_0 ## through a lossless transmission line, what does the voltage at the output look like when...

I need some help resolving the follow problem. I really don't know where to put the "twice as large as the resultant force on Q3" in order to build an equation. Thank you !

Hi, I apologise as I know I have made similar posts to this in the past and I thought I finally understood it. However, this solution seems to disagree on a technicality. I know the answer ends up as 0, but I still want to understand this from a conceptual point. Question: Evaluate the line...

This is the second quadrant of the equipotential line. I think this would be symmetry but I'm not sure what to do. Is this going to be the symmetry of both the x-axis and y-axis and the symmetry of the y-axis is ( - )? Sorry for the bad English! feel free to leave comment if you can't...

what I've done so far? -i've determined the vector between the point (4, 0, 0) and the point P. (4, 6, 8) - (4, 0, 0) (0, 6, 8) -The norm of this vector is the radial distance of the line to point P (the value of “ρ” in the formula) √(0^2 + 6^2 + 8^2) = 10 -> ρ = 10 -and its unit vector is...

F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so...

Hi PF! Do any of you know a good way to detect the meniscus of the attached image (in MATLAB)? I have a very ghetto method, and would like something more automated. Thanks for your help!

Sorry - I wish I had some way of writing equations in this forum so the "relevant equations" section is easier to read. The answer to the first part is (a) so the rest follows from using the electric field given in B. If anyone is interested this question comes from Griffith's 3rd edition...

What is the best and fastest way to remove the inside weld line of pipes with 16mm outside diameter and 1m thickness so a piston can reciprocate easily inside it? I have two options in mind. one is to have the inside of LSAW pipes machined, which might be laborious. The other option is to cold...

I'm making a robot the will follow a black line and I need some assistance does anyone here have experience with python and line sensors.(IR) If anyone does I can elaborate on my issues more. Thanks

I know that on an alternating current circuit, you have to have both a line 1 and a line 2 to have a circuit. Here is a pictorial diagram of an alternating current circuit: In a previous thread, I asked why would an AC circuit like in Diagram 2 not work? Here is a photograph of diagram 2...

AB and DC not parallel line., AB=55,BC=65,DC=76,DA=48 Ax=28,xD=20,By=37,yC=28 How to find length of xy?

Let $P$ be a real polynomial of degree five. Assume that the graph of $P$ has three inflection points lying on a straight line. Calculate the ratios of the areas of the bounded regions between this line and the graph of the polynomial $P$.

Preface to thread: I am darn well aware of the fact that on an AC circuit, there has to be a line 2 after the load to bring current back to the power source. This thread is about WHY does there have to be a line 2 after the load to bring current back to the power source. I hope that I don't...

I know that I need to find the equation of the line of motion of the two particles, the dot product of which with one of the options will give 0. I began with founding the coordinates of center of mass: R = (m1r1+m2r2)/(m1+m2) = (2a/3, 0, a/3) and velocity of the center of mass: V =...

if ## \gamma (t):= i+3e^{2it } , t \in \left[0,4\pi \right] , then \int_0^{4\pi} \frac {dz} {z} ## in order to solve such integral i substitute z with ##\gamma(t)## and i multiply by ##\gamma'(t)## that is: ##\int_0^{4 \pi} \frac {6e^{2it}}{i+3e^{2it}}dt=\left.log(i+3e^{2it}) \right|_0^{4...

I think that we can say that PPR = α*PRPS where PR and PS are the points where occurs the intersection on the line R and S. Obs: line r and s are found by knowing that the straight line intersection of two planes are n1 X n2 [cross product] Lr = (0,1,-2) + y(-1,1,1) Ls = (0,1,-1) + u(1,2,1)...

∈Was wondering if anyone here could help me with an explanation as to how Axler arrived at a particular step in a proof. These are the relevant definitions listed in the book: Definition of Matrix of a Linear Map, M(T): Suppose ##T∈L(V,W)## and ##v_1,...,v_n## is a basis of V and ##w_1...

Not homework, just trying to understand a statement in the book. On page 158 in Fisher, the following statement is made: In these applications of the Residue Theorem, we often need to estimate the magnitude of the line integral of e^{iz} over the semicircle = Re^{i\theta}, \; 0 \le \theta \le...

Summary:: For finding the electric field at P in the photo below, may I select a gaussian surface circular? [Mentor Note -- thread moved to the schoolwork forums, so no Homework Template is shown]

The vector field F which is given by $$\mathbf{F} = \dfrac{(x, y)} {\sqrt {1-x^2-y^2}}$$ And the line integral $$ \int_{C} F \cdot dr $$C is the path of $$\dfrac{\ (\cos (t), \sin (t))}{ 1+ e^t}$$ , and $$0 ≤ t < \infty $$ How do I calculate this? Anyone got a tip/hint? many thanks

A trapezoid with a base of 100m and 160m is divided into 2 equal parts by a line parallel to the base. Find the length of dividing line.

Find the equation of the line which forms with the axes in the second quadrant a triangle of area 4 and whose intercepts differ by 5.

Please can you have a look at the file at point me in the right direction if I'm wrong. Thank you

I feel like i am spinning my wheels at the start here. so I figured that i would start with some type of wire loop that I could change its diameter. This would allow there to be a change in flux through the loop creating a current through the wire. i could then read the current through the...

How do I algebraically prove how many times the line y=-5 intersects the circle (x-3)^2 + (y+2)^2 =25?

Hi all, I'm finding it difficult to start this line integral problem. I have watched a lot of videos regarding line integrals but none have 3 line segments in 3D. If someone can please point me in the right direction, it would help a lot. I've put down the following in my workings: C1...

What I've done so far: From the problem we know that the curve c is a half-circle with radius 1 with its center at (x,y) = (0, 1). We can rewrite x = r cos t and y = 1 + r sin t, where r = 1 and 0<t<pi. z stays the same, so z=z. We can then write l(t) = [x(t), y(t), z ] and solve for dl/dt...

Hi friends How exactly do we change the general equation of a line in space( given two intersecting planes) into the canonical form Thanks

Hi PF! I'm trying to edit two lines from files in different directories, U and controlDict. I want to change the lines with numbers from two other .dat files, VEL.dat (vector of numbers) and VEL_t.dat (single scalar number). Below is my attempt, but I know at least two things that are wrong...

An old puzzle that was given to me long ago. I don't know how to approach this problem, any help is appreciated. I'm removing some specifics because I don't want it solved for me, I want to know how to approach it. Feel free to solve a simplified version if that helps you explain it to me...

Van der Waals EoS is a cubic EoS that can represent the transition between gas and liquid phase. If you plot a P-V graph you end up with something like this The part I underlined in red are said to be metastable equilibria (i.e. superheated liquid and supersaturated vapor). I don't understand...

a) 99.5% B) 577.4 A c) 692.88 V

In Hartle's book Gravity: An Introduction to Einstein's General Relativity he spends chapter 2 discussing some basic aspects of differential geometry. For example, he derives the expression for a differential line element in 2D Euclidean space: dS^2 = (dx)^2 + (dy)^2 in Cartesian coordinates...