Line Definition and 1000 Threads

I know that for two points, the difference between them is a line segment lets say these two points are 'a' and 'b' respectively, so b-a = "new vector represent the line" In my textbook b-a=d*t -- where 'd' is a vector along the directon of 'b-a' and t is a parameter. does 'd' actually...

Hello! (Wave) I am writing a text in LATEX. Since the equalities I wrote are longer than the paper's size, I tried to break the line as follows, but it failed. \begin{multline} y'=y+4 \pi \cos(4 \pi t)y \Rightarrow y'=(1+ 4 \pi \cos(4 \pi t))y \cap \Rightarrow \frac{dy}{dt}=(1+ 4 \pi \cos(4...

Homework Statement Consider the vector field F(r) = Φ^ (a) Calculate ∫ F⋅dl where C is a circle of radius R (oriented counterclockwise) in the xy-plane centered on the origin. Homework Equations maybe Φ^ = -sinΦx^ + cosΦy^ The Attempt at a Solution not really a solution. i am just stuck at...

Homework Statement If i have a system with one linear conductor and point, it's not problem to determine magnetic field at point, nut what happens if i have to determine the magnetic field at the straight line parallel to the linear conductor. Homework EquationsThe Attempt at a Solution For...

Homework Statement An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.5*10^4 kg, and the force causes its speed to change from 7100m/s to 5500m/s. (a) What is the work done by the force? (b) If the...

Homework Statement http://www.sumoware.com/images/temp/xzlknterambqmokp.png How to calculate the Magnetic Force of THE "Right Triangle" influenced by a Line when the magnetic field isn't constant B=u0*I/2piR? Homework Equations B=u0*I/2piR F=iLB The Attempt at a Solution I can use F=iLB to...

Hello, So I have a circuit where I input a square pulse with a source impedance and load impedance (which are just pure resistors) each of which can be varied and a transmission line circuit connecting them which is made up of resistors, capacitors, inductors in a lumped element model. I set...

Hey! :o Let $\overrightarrow{\sigma}$ a curve in $\mathbb{R}^3$ with zero acceleration. Show that $\overrightarrow{\sigma}$ is a straight line or a point. Let $\overrightarrow{\sigma}(t)=(x(t),y(t),z(t))$ be the curve. We have that...

Homework Statement Find an equation of the tangent line to the curve at the given point. Homework Equations y=x¼ Point = (1,1) The Attempt at a Solution [/B] Derivative of y is y' = ¼x-¾ Plugging in the derivative to the equation for a line: y-1=¼(x-1)-¾. My book's answer is Y=¼x+¾, but I...

Homework Statement My textbook says that the slope of the tangent line at a point can be expressed as a limit of secant lines: m = \underset{x \rightarrow a}{\lim} \, \frac{f(x) - f(a)}{x - a} \, . If x > a and we approach a from the right, why do we have to insist that this limit exists...

Homework Statement A bullet fired straight upwards experiences an acceleration due to air resistance of 1m/s2 during its entire flight. If it leaves the barrel of the gun at 300m/s, with what speed does it hit the ground? Homework Equations None given The Attempt at a Solution integral of a=t...

In my EM book, Wentorth, he used the example of a transmission line as an infinite line of charge. The book states "...a test charge placed a couple of centimeters from an elevated transmission line will see what appears to be an infinite length line (of charge)." I'm confused why this would...

I was reading textbook and felt confused about this-- when trying to deal with inner inductance of transmission line, only the fraction (x/r)^2 of total current, which interlock with magnetic lines should be considered. However, isn't the inductance or even flux linkage an intermediate...

I have a spike guard that is showing line and neutral reversed. Those 2 Leds glow. This wasnt happening before the wiring was changed of the house. Now when i connect a mobile charger(with 2 pins) then the mobile gets charged, but when i connect a three pin hard drive power cord to it, then the...

I did some data analysis with excel fitting some linear, zero intercept data with trend line and the regression analysis tool. The slopes generated by the two methods were different by about 10%. The regression line seemed to be weighted differently, are these two methods different for some...

hi pf! So I'm drawing a picture in tikz and when I use the \shade command my lines are changing from black into the color. anyone know how to prevent this? Thanks so much!

can you do load line analysis on a bjt with just a knowledge of algebra or is calculus required?

Suppose we have a cosmological model where condensed objects of characteristic mass ##m## occupies some fraction ##\Omega## of the critical density ##\rho_c##. Take a QSRS to be at cosmological distance ##L \sim 1/H_0## (##c=1##). Its easy to the that the average distance between the condensed...

The question word for word : "Write the equation satisfied by all of the points P(x, y, z) that are at the same distance from the point F(0, 0, 4) and the plane z = 0." I figured I could maybe start by finding the distance between point F and the plane z = 0 but I can't figure out how to...

Homework Statement The mechanism in the attached photo contains two masses, each treated as particles. When released from rest, the 4-kg block falls and the 6-kg sphere rises. Initially, the angle between the two rigid, massless linkages is θ = 60° What is the velocity of the sphere when θ =...

Homework Statement The new earth-Pluto SuperShuttle line boast that it can take you between the two planets (which are about 5.0 h apart in distance) in 2.5 h according to your watch on board the shuttle. Assume that the shuttle travels at a constant velocity. a.) What time interval must the...

Homework Statement Mass M is distributed uniformly along a line of length 2L. A particle of mass m is at a point that is a distance a above the center of the line on it's perpendicular bisector. For the gravitational force that the line exerts on the particle. calculate the components...

I would appreciate very much if you could help me with a puzzling question that seems a paradox to me. Every excited state of an atom (every line of the characteristic spectrum) has a “width”: the higher the width, the shorter the lifetime of the state, and when the atom de-excitates we get...

Homework Statement F(x,y) =(x2y,xy2) Homework EquationsThe Attempt at a Solution I wrote the function as a differential equation dy/x2y = dx/xy2. After integration I got C+y2=x2. This gave me that the line of force is a hyperbolic paraboloid. The function is not conservative. ∂F1/∂y = x2 ...

Homework Statement I am trying to graph the flux density field between two infinite line charges located at y = 1 and y = -1 Homework Equations I am trying to do it using the equation for a line charge that I got from lecture notes. The above equation is derived from this: Here is the...

Hello! :o Find the equation of the line that passes through $(1, -2, -3)$ and that is perpendicular to the plane $3x-y-2z+4=0$. Can we formulate it as followed?? The perpendicular vector of the plane is $\overrightarrow{v}=(3, -1, -2)$. Since the line that we are looking for is also...

I was reading "The foundation of the general theory of relativity" by Albert Einstein. I faced some difficulty to understand his derivation of "geodetic line", stated in "The equation of the geodetic line. The motion of particle" headed section. I will try to describe my problem clearly and in...

Homework Statement [/B] Find the coordinates of the point P on the surface of the paraboloid z=6x2+6y2-(35/6) where the normal line to the surface passes through the point (25/6, (25√22)/6, -4). Note that a graphing calculator may be used to solve the resulting cubic equation. Homework...

Homework Statement A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis. Homework Equations E = kQ/r^2 The Attempt at...

Homework Statement (a) A transmission line has a length, ℓ, of 0.4λ. Determine the phase change, βℓ, that occurs down the line. (b) A 50Ω lossless transmission line of length 0.4λ is terminated in a load of (40 + j30) Ω. Determine, using the equation given below, the input impedance to the...

Homework Statement Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)? Homework Equations R = R0 + tV (for each line) The Attempt at a Solution If the lines are parallel, then the V for the two equations will be proportional to each other...

Why is the function: y = f(x) = a(x-1)(x-2)(x-3) symmetrical about the line x = 2? I mean how can we be sure that it is? Is there any method to check it?

A line in 2-dimensional euclidean space can be determined by the coordinates of any two particular points on the line. Hence four "parameters" are required. Now let’s consider a line given by the usual equation y = mx + c. c, being the intercept on the y-axis, is related to the point (0,c) which...

I have set of date with error bars of different length on my y values. I want to know what the error is on the slope and intercept of my line of best fit through this data. Is there a numerical way to calculate this that takes into account the fit of the regression line and the y error bars?

Homework Statement http://postimg.org/image/lb6hsi843/ I am trying to draw an energy and hydraulic grade line for this system. The gauge pressure is supposed to be 0 at the points shown and those are centrifugal pumps. What I don't know is how flow and pressure vary throughout Homework...

Homework Statement We are giving to lines: r1(t)=<1-t,4,5+2t> r2(s)=<2,1+s,-s> 1. Find an equation perpendicular to the two lines and passing point P(1,1,1) 2. Find Coordinates of points of intersection of the line found in #1 with planes x=-1, xz-plane 3. Parametrize the line segment joining...

$\textbf{Problem}$ The line segment from $\textbf{p}$ to $\textbf{q}$ is the set of points of the form $(1 - t)\textbf{p} + t\textbf{q}$ for $0 \le t \le 1$ (as shown in the figure below). Show that a linear transformation, $T$, maps this line segment onto a line segment or onto a single point...

$\textbf{Problem}$ Given $\textbf{v} \ne \textbf{0}$ and $\textbf{p}$ in $\mathbb{R}^n$, the line through $\textbf{p}$ in the direction of $\textbf{v}$ is given by $\textbf{x} = \textbf{p} + t\textbf{v}$. Show that linear transformation $T: \mathbb{R}^n \rightarrow \mathbb{R}^n$ maps this line...

Textbooks tell us that a four vector under time reversal changes as ##x^\mu \to \tilde x^\mu = x_\mu##, and ##i \to -i##. The gluon field changes as ##A^\mu(x) \to A_\mu(-\tilde x)##. My question is how does the following integral (the wilson line in the perpendicular direction) change unter...

Homework Statement Three charges, Q1, Q2 and Q3 are located on a straight line. The charge Q3 is located 0.169 m to the right of Q2. The charges Q1 = 1.56 μC and Q2 = -3.03 μC are fixed at their positions, distance 0.268 m apart, and the charge Q3 = 3.18 μC could be moved along the line. For...

Homework Statement Find a set of parametric equations for the line of intersection of the planes. 6x-3y+z=5 and -x+y+5z=5[/B]Homework Equations The cross product formula The formula for the parametric equations of a line in three dimensional space: x=x1+at, y=y1+bt, z=z1+ct Knowing the fact...

I'm currently trying to determine the error on the slope of a regression line and the y-intercept. My y values are: My y error is: My x values are: 27.44535013 0.03928063 136 29.78207524 0.07836946 44 27.4482858 0.0385213 143 27.27481069...

hi! in the first page of the attached pdf, after the title " 't hooft double line notation", he says that we have to consider the gluon as NxN traceless hermitian matrices to convince ourselves about the double line notation. there is my question: if you want the indices a,b to run from 1 to...

Hello, Some years ago I have heard from the brazilian physicist, Constantino Tsalis, that the DNA molecule, if unfolded and made to lay in a line, will be close to one meter long. But he said that thermodynamically this configuration could be taken as an impossibility, for no such long and...

Homework Statement Figure shows a 50 Hz, high-voltage, transmission line. The relationships between the sending and receiving end voltages and currents are given by the complex ABCD equations: where 'S' stands for sending-end and 'R' stands for receiving-end (a) Given the parameter...

ds2=guvdxudxv Why is the invariance of ds2 as shown above? Why can't it be something like ds2=guudxudxu or ds2=dxudxu ? Isnt it based on Pythagoras theorem? Why must it have 1 u and 1 v instead of just 2 u or 2 v? Forgive me for such dumb question as I just started.

Hi, If we start humidifying an unsaturated air for some dry-bulb temperature, can we move up to dew point for that processes also moving up to saturation line? In other words, Can we make a process in which process line goes up with 90 degrees up to saturation line? Thank you.

Pardon me if I stated the title incorrectly/ informally. I just want to say about the title is about the 220 V, 60 Hz source (present in our outlets also) in our house by which comes from nearby electrical post. I have four questions in this post/thread so kindly tell me if I need to edit this...

Sorry for the confusing tittle but I could not explain it better. Here is what I am trying to ask: When you have 2 axis(x and y) such as the image below, the sum of the two angles, a and b will always be equal to 90 degrees. a + b = 90degrees However when you add a 3rd axis(x, y and z, making...

Homework Statement Hi, An equation of the form Ax + By + C = 0 is a standard equation of a line in 2D. An equation of the form Ax + By + Cz + D = 0 is an equation of a plane. Is it possible to: Describe a plane in space, written in standard form, such that one variable is missing from the...