What is Line: Definition and 1000 Discussions

The slope of a fitted line = Cov(X,Y)/Var(X). I've seen the derivation of this, and it is pretty straightforward, but I am still having trouble getting an intuitive grasp. The formula is extremely suggestive and it is bothering me that I can't quite see its significance. Perhaps, my mental...

I studied Taylor series but I would like to have an answer to a doubt that I have. Suppose I have ##f(x)=e^{-x}##. Sometimes I've heard things like: "the exponential curve can be locally approximated by a line, furthermore in this particular region it is not very sharp so the approximation is...

This is the line: read(A, *) B The variable A is defined earlier in the code. I searched around the internet, and the 'read' syntax requires an input from the keyboard. However, the syntax I saw is read(*, *) var, so the two arguments are both asterisks. What if the first asterisk is defined...

Homework Statement for the line segment c2 , why did the author want to differentiate dx with respect to dy ? and he gt dx = 0 ? I'm curious why did he didnt do so for C3 , where dy= 0 ..Why didnt he also differentiate dy with dx ? dy/dx = 0 ? Homework EquationsThe Attempt at a Solution is...

I am re-piping a oil line use for burning reclaimed oil and currently the oil returns to the tanks to the bottom of the tanks. I want to have them return to the top of the tanks to increase the mixing of the oil. My only problem is that their are two tanks that will fill up by the same oil line...

Let us see how the line element transforms under conformal transformations. Consider the Minkovski metric gij, a line element ds2=dxigijdxj, and a conformal transformation δk(x)=ak + λ xk + Λklxl + x2sk - 2xkx⋅s We have δ(dxk)=dδ(x)k=λ dxk + Λkldxl + 2 x⋅dx sk - 2dxkx⋅s - 2xkdx⋅s And so the...

(Sorry for my bad English.) I was reading about the Green's theorem and I notice that the book only shows for the case where the function is a vector function. When learning about line integrals, I saw that we can do line integrals using "ordinary" functions. For example, the line integral of...

So I just learned that in a spectrum like this one: (For now, let's concentrate on the graph given below.) The longer the dip is in the graph, the more the corresponding element is present. However, if each individual color corresponds to a different element, then how can a larger dip mean...

This is not a homework question. School year has ended for me and I'm doing some revision on my own. I want to proof the following because in an exercise I had to find the equation of the line that passed through a given point and 2 given lines. If a line r intersects with 2 given crossing...

Hi (I hope this is the right place to post this - sorry if it's not) Say I have a line (in the graphic is shown a 10mm but it could be any length) and it rotates around a point at one end. What is the formula to get the length along the x-axis directly under the other end of the line. In the...

http://www.space.com/33410-star-snow-line-seen-for-first-time.html From there, For the first time, astronomers have caught a glimpse of the water snow line around a star — the point in the young star's orbiting disk of debris where snow and ice first appear. Normally, that boundary huddles...

Homework Statement i'm not sure what is line integral... Homework EquationsThe Attempt at a Solution Does it mean total length of line under the curve?

Hello, If someone takes two segments, one longer than the other, it is naturally assumed that the longer one is most definitely longer than the other. However, if the longer segment is put at an angle with the other to make a triangle, suddenly someone can draw a one to one correspondence...

If I have n dots, how many configurations exist for lines that connect them, including no connections? For example, if I have 0, or 1 dots I believe this should be 0 since no connections are possible (or perhaps I should consider the single dot as having a single connection to itself?) If I...

Homework Statement An infinitely long line of current $I_1=6[A]$ is following along the positive z-axis in the direction of +$\hat{a_z}$. Another current is following a triangular loop counter clockwise from the points A(0,2,2), B(0,6,2) and C(0,6,6). Homework Equations To start I applied...

I'm looking to build an Arduino that is capable of following a line depending on a colored strip on the ground, either black or white. I think I might use a LDR, but not quite sure where to even start to be honest. My office is having an Arduino contest, and I just want the Arduino to carry...

Homework Statement We've got a line element ds^2 = f(x) du^2 + dx^2 From that we should find the geodesic equation Homework Equations Line Element: ds^2 = dq^j g_{jk} dq^k Geodesic Equation: \ddot{q}^j = -\Gamma_{km}^j \dot{q}^k \dot{q}^m Christoffel Symbol: \Gamma_{km}^j = \frac{g^{jl}}{2}...

When calculating the electric field from a point above a line of charge using coulomb's law, the integral that comes up is of the form \int { \frac { dx }{ { x }^{ 2 }+{ a }^{ 2 } } } . But if the point we were asked for is right in the middle, the horizontal (cosine) components cancel out...

Homework Statement I need to find the work done by the force field: $$\vec{F}=(5x-8y\sqrt{x^2+y^2})\vec{i}+(4x+10y\sqrt{x^2+y^2})\vec{j}+z\vec{k}$$ moving a particle from a to b along a path given by: $$\vec{r}=\frac{1}{2}\cos(t)\vec{i}+\frac{1}{2}\sin(t)\vec{j}+4\arctan(t)\vec{k}$$ The Attempt...

Homework Statement Hi everybody! I have a crazy problem about Lagrangian on which I've been working on for two days without being able to figure it out. I have a solution, but I think there is a flaw in it. First here is the problem: A line rotates with constant angle velocity ##\omega##...

Hello people, I have a serious design problem for designing a sprocket-chain system. I want to know that can three sprockets as in picture (in attachment) can be rolled by a chain? The main concern is for middle sprocket it have few teeth above and few teeth in bottom connected to chain. The...

Hi PF! I'm plotting a line in TikZ using the following code \draw[domain=0:25,samples=100,color=blue,variable=\x,line width=1.5] plot (\x,{0.9924686128641765 - 0.023406305144575135*\x - 0.0006942621866861979*\x^2 - .000001925581045950128*\x^3}); The largest zero is 24.0699 but latex is...

This is part of a larger question, but this is the part I am having difficulty with. I have had an attempt, but am not sure where I am making a mistake. Any help would be very, very appreciated. 1. Homework Statement Let C2 be the part of an ellipse with centre at (4,0), horizontal semi-axis...

If a line intersects both points (2, 2) and (6, 7), determine its slope.

Homework Statement Evaluate ∫c (x + y) ds, where C is the circle centred at (1/2, 0) with radius 1/2. Homework EquationsThe Attempt at a Solution parametrise x=1/2cos(t) y=1/2sin(t) 0≤t≤2π ds=√dx2+dy2 =√(1/2)2-sin2(t)+(1/2)2cos2(t) =√-(1)2(1/2)2sin2(t)+(1/2)2cos2(t)...

Homework Statement I'm doing quite a strict proof in school. Where we should proof something and use mathematical language and symbols. Homework Equations The Attempt at a Solution To proof what I have to proof I need to draw some help lines. As for instance the "red" one I did from A to B...

I'm working on re-designing a restaurant by the sea. I'm a interior decorator so I know very litle about physics. Here's my question: let's say you're in the back of a room with 90 meters of floor in front of you. You are 7 meters above ground but your eyes are only 10 cm above the floor. I've...

Dear Experts, I want to put new feature for my hydraulic pressing station (capacity:-350TON). present it existing with dial type pressure indicators. and directional propositional valve 3/4 for pressure lines. here value are made DAIKIN (JSO-G03-2CB-10) this model top side Alean key thread...

Hi there, Wifi uses either 2.5 GHZ band or 5 Ghz band and these bands lie in Microwave in EM spectrum. As i read in books, Microwaves are propagated using line of sight (LOS) technique, so sending and receiving antennas should need to be aligned accordingly. But WiFi signals are broadcasted...

Homework Statement "Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates." ##7.##...

Homework Statement Hi everybody! I would like to make sure I properly solved that problem because I find the result strange: Given a force field ##F_x = axy^3##, ##F_y = bx^2y^2##, ##F_z = cz^3##. Calculate the work with the line integral ##\int_{C} \vec{F} \cdot d\vec{r}## from point...

Hi can anyone help me with this question on inertial forces in gears? Cheers Ali :)

For a flat layout sheet metal part, is the bend line located directly in the middle of the bend allowance section, or is it inset from one side by a distance of the bend radius? So for a U-channel with an opening of approx. 4.56" (distance between inside of legs), would the distance between the...

Fine the word done in moving a particle in the force field F=<2sin(x)cos(x), 0, 2z> along the path r=<t,t,t2>, 0≤t≤π To do the line integral, I need to find F(r(t)), but I don't understand how to express it. For example I looked at the online notes provided here...

Homework Statement In the picture above, line y = c intersects with parabola y = 6x-x^2 in the first quadrant. If the gray area below line y = c and the gray area above line y=c are equal, then value of c is ... A. 19/4 B.21/4 C.23/4 D.25/4 E. 27/4 Homework Equations Area under parabola =...

I think we can say that a straight line is a triangle in which sum of two side equals third side in which two angle equals 0° and the middle angle equals 180°, but can we say that a striaght line is a triangle with two angle equals 90°, I am saying this because my sister is not beliving that...

I have an odd, yet intriguing question. I want to describe a particle that is constrained to move along a straight line in the x direction. The location of the particle can be described with theoretically infinite parametric parameters, d, along the line. For example: R = [d 0 0]T R = [d2 0 0]T...

Homework Statement Evaluate ∫C < −y, x − 1 > dr where C is the closed piecewise continuous curve formed by the line segment joining the point A(− √ 2, √ 2) to the point B( √ 2, − √ 2) followed by the arch of the circle of radius 2, centered at the origin, from B to A. 2. The attempt at a...

The curve y=x^4-2x^3-2x^2-2x has a bitangent. I need to find the equation of this line. First, I started off by computing the slope. Since it touches two points on the curve, their slopes should be the same. So, I have the equation 4x^3_1-6x^2_1-4x_1-2=4x^3_2-6x^2_2-4x_2-2 I got up to the point...

This should be easy but I'm totally stuck here. So I'm calculating the Kβ line (emitted energy) of Molybdenum (Mo 42). I'm using Moseley's law and am moving from the M-shell to the K-shell. Recall Moseley's law is E = 13.6 eV (Z-σ)2 *1/n2. The effective formula for the energy emitted is thus...

Homework Statement A thin insulating rod with charge density lambda=+5nC/m is arranged inside a thin conducting cylindrical shell of radius r =3 cm. The rod and the shell are on the same axis, and infinite in length. What is electric field at point p? 6cm from the central axis. Homework...

Homework Statement identifying the slope of the line?[/B] Homework Equations y2-y1/x2-x1 The Attempt at a Solution i chose two points on the line, the first point is (8,-3) and the second point is (-6,4). Are these points accurate? i used the slope equation to solve for the slope of the line...

Homework Statement I am trying to determine the x- and y-intercepts of the line 3x – 5y + 15 = 0. Homework Equations standard form The Attempt at a Solution :[/B] To find the x-intercept (where the line crosses the x-axis), substitute 0 in for y: 3x + 5y + 15 = 0 (substituted 0 in for y)...

Question: Determine the equation of a line for the following: a) The line that has an x-intercept of 6 and that passes through the point (2, –2) b)The line that never intersects 5x – y + 3 = 0, and which is five grid squares lower than that line Relevant equation: y= mx+b Attempt at a...

Homework Statement You wish to determine the electric field magnitude along the perpendicular bisector of a 230-mm line along which35 nC of charge is distributed uniformly. You want to get by with a minimal amount of work, so you need to know when it is sufficient to approximate the line of...

Homework Statement Use a line integral to find the area of the surface that extends upward from the semicircle ##y=\sqrt{9-x^2}## in the ##xy##-plane to the surface ##z=3x^4y## Homework Equations Parametric Equation for Circle: ## x = rcos(t) ## ## y = rsin(t) ## Line Integral: ## \int_c...

Hi, I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another...

I think its a defination to have infinite longitudnal lines , if line are not perpendicular than the infinite point will not add up to give the circumferance of equator, please help

Given a cube, choose a vertice and draw 2 of the three possible diagonals. What is the measure of the angel between those two diagonals? Proposed answer: We can say that both diagonals touch vertice A, to give it a name. We can also call the endpoints of both diagonals B and C. If we imagine...

Disclaimer: I'm not exactly sure that this topic would belong in this thread but I don't think it would fit better anywhere else. I'm working on writing a paper for my grad research project and my PI wants me to model the plots after another paper that our lab published in the past, but I'm...