Lines Definition and 1000 Threads

Homework Statement Find a differential equation whose solution is a family of straight lines that are tangents to the circle x^2+y^2=a^2 where a is a constant. The Attempt at a Solution So actually I'm stuck on the first part, coming up with such an equation. After some work I came up with...

How are power lines connected over canyons? Are they simply laid out on the canyon floor and then hoisted up and stretched to the towers? Just wondering. Thanks.

So I ran across this problem on the 'net and I can't determine "x". The arc length of the circle is 360. I added some other variable and took what I know about a circle and intersecting lines. I wound up with four variables and four equations. x = 1/2 (y + 67) w = 1/2 (z + 147) y +...

Here is the problem: http://postimage.org/image/1jy6nol5w/ Method 1: Steps 1. Calculate V(T1)=12*10=120V, V(T2)=10*10=100V 2. Since V(3)=10V and I(3)=1A, P(T3)=10W 3. Since not otherwise stated, Assume transformers are perfect. 4. So P(T3)= P(T2) = 10W 5. known...

Hi all, I am not sure if this is the right place to ask but I have two problems which I require enlightenment. The questions are, 1) Show that the intersection of two lines can be computed by rational operations. 2) Show that the intersection of a line and a circle can be computed by...

Homework Statement So I'm studying for my test. doing even and odd problems from the book. I wanted to see if this answer is right. Q: find an equation for the line in the xy-plane that is tangent to the curve at the point corresponding to the given value of t.Also, find the second derivative...

Homework Statement x1 = (0,0,4) + s(2,0,-1) x2 = (-4,2,2) + t(-5,1,1) Homework Equations The Attempt at a Solution First of all I find the common perpendicular (vector cross product) Make it unit Find a arbitrary line joining the two 2 lines (set s = t= 0) Then scalar...

Hi, I really tried to find some explanation about this notation S(x)-S(y), but I couldn't find any! I am reading a paper about Excitation of H_2 in Photodissociation regions, and it all the time say something like: "we find that the model can account for the first low H2 rotational line...

What determine the relative heights of the k-alpha, k-beta peaks in the X-ray production curve?

Homework Statement Yeah that always confuses me, why do books sometiems refer lines implicitly?

So I know that we can use absorption or emission lines from a star or object emitting light to determine the composition of that object. But what methods are used to confirm that? We've been doing this in class and it seems rather primitive to eyeball the lines and compare them with example...

Homework Statement <\body> <with|mode|math|\<b-phi\><rsub|B> = <big|oint>><with|mode|math|\<b-B\> \<cdot\> \<b-d\>\<b-A\>>\ \; magnetic flux is proportional to the number of field lines passing though the surface \; </body> <\initial> <\collection>...

Find the characteristic lines for the equation: 2 du/dx + 8x du/dt = 16x Here's my attempt a = 2 b = 8x c = 16x Using dt/dx = b/a = 8x/2 = 4x t = 2x2 + C C = t1 -2x12 Hence the characteristic is: t = 2x2 + t1 - 2x12

Homework Statement Two planes have equations 2x-y-3z=7 x+2y+2z=0 Find a vector equation for their line of intersection The Attempt at a Solution I haven't learned the vector product in class but read it and attempted it and got the direction vector 4i-7j+5k. However, I don't...

The lines (AC) and (BD) intersect at the point P(3,K) Show K=1. AC=(4,2) or (x,y)=(5,2)+s(4,2) BD=(3,-6) or (x,y)=(1,5)+t(3,-6) A(1,0), B(1,5), C(5,2), D(4,-1) [PLAIN]http://img840.imageshack.us/img840/6263/1894869.jpg

Hi, all: Say we have a bare-bones Vector Space v, i.e., V has only the basic vector space layout; no inner-products, etc., over a finite field . I think then , we can still define a line in V as the set {fvo: vo in v, f in F}, i.e., as the set of all F-multiples of a fixed...

Homework Statement Consider a uniformly charged half spherical shell. The total charge is Q and the radius is R. a) Calculate the electric field as a function of z for – 5R < z < 5R. b) Draw equipotential curves in the xz-plane for – 5R < x, z < 5R with at least 8 equallyspaced curves...

Homework Statement Take the Earth for instance, if I were to draw field lines, would it be field lines coming out of the mass or into the mass? I initially thought it would be going out because we could look at it as a "positive charge", but then I thought that was silly because gravity is...

Hi, I have a matrix V, which is a 5-by-2 matrix, where each row represents a point in the xy-plain. How can I connect these points together in MATLAB, please? Thanks in advance

some lines are called "resonant" Hi, I would like some explanation on a topic for which I do not find detailed literature online or in books. In photon absorption/emission processes by atoms, some lines are called "resonant" (for example, the 2P1/2 (or 2P3/2) to 1S1/2 transition of...

FIGURED IT OUT, PLEASE DISREGARD Homework Statement Find the shortest wavelength of the Lyman series for a triply-ionized beryllium atom (Be3+). Express your answer in nanometers using four significant digits. Homework Equations Rydberg's Formula: 1/\lambda=RZ2(1/n12 - 1/n22) The Attempt...

shining white light through a gas of a vapourised element causes absorbtion lines to be created in the white light spectrum ie. there are dark lines running through the otherwise continuous spectrum and the position of these lines are unique to particular element. Why is it though that we...

Homework Statement The lines r=(2+2t)i+(3-3t)j+(4-2t)k and v=(4+2s)i+(1-6s)j+(5-3s)k are skew. Find the perpendicular distance between them at the point(s) where they cross over each other. Homework Equations The Attempt at a Solution Does this seem right...

The electric flux around a charge is represented by electric lines of force. But it is said that the electric lines of force is purely an imaginary concept to visualize a field. In the Gauss' law, using the formula q/epsilon we calculate the total number of lines of force. For a charge of 1...

Linear Algebra - Find the value of "a" such that 2 lines lie in a plane Homework Statement Consider the lines L1 and L2 with the following equations: L1: (x y z)=(7 4 −4)+t(2 2 −2) L2: (x y z)=(a 4 −4)+s(−3 2 −2) Find the value of a such that L1 and L2 lie in a plane. They also gave...

I understand why a ball's velocity vector is reflected across the line normal to the wall when it hits the wall. Why does this happen with light and a mirror? What is happening atomically for an atom to take in a photon and spit it out across the normal line?

Homework Statement Let f:\mathbb{R}^2\to\mathbb{R} be continuous everywhere except, possibly, at the origin. Furthermore, for any point p\in\mathbb{R}^2, let s_p:\mathbb{R}\to\mathbb{R}^2 be defined by s_p(t) = tp. Now assume that f\circ s_p is continuous, as a function...

Two tangents to an ellipse meet at a point T, find the coordinates of T. The two equations are (bcosΘ)x + (asinΘ)y= ab (-bsinΘ)x + (acosΘ)y= ab This has been really frustrating me as I feel it should be simple, but with the trigonometric...

Hi everyone, My data consists of road accidents and spatial covariates. Originally i wanted to apply an inhomogenous Poisson process with covariates. Then I realized that the accidents cannot occur everywhere in space, but only on roads. I found an example, that is quite similar to mine. it...

Where is it writ that forces must act in straight lines?

I am unable to comprehend the proof for tangent line to conics. Here is the proof as per the book (Multiview Geometry by Hartley and Zisserman). Everything is in homogeneous coordinates. The line l = Cx passes through x, since lT x = xT Cx = 0. If l has one-point contact with the conic...

I have a multi-lined coloured plot in which I need some lines represented by dashed lines ('linestyle', ':') and I also need my plot to be quite a high resolution (dpi) for publication reasons (print -r600 -dtiff myfile.tif). So this works fine but when I open the tiff file with high resolution...

Homework Statement Determine the magnitude and direction of the electric field at point 1 in the figure. Homework Equations E=\frac{QK}{r^2} V=-\frac{QK}{r} The Attempt at a Solution \int E dr=-V When I take the derivative of both sides of this relation wrt to R, I get...

Homework Statement You are given the two lines with the following parametric equations: L1: x = 4 + 2t y = 4 + t z = -3 - t L2: x = -2 + 3s y = -7 + 2s z = 2 - 3s Both s, and t are elements of a real number. Determine the coordinates of P1 that lies on L1, and P2 that lies on...

Homework Statement A very long (infinite), straight line of charge runs parallel to another very long (infinite) straight line of charge. Both lines are uniformly charged, one with +1*(lambda) and the other with -2*(lambda). The distance between them is d. Find (if any) the location(s) where...

When objects are heated they produce blackbody radiation which varies with their temperature, and when the electrons in the orbitals of atoms are given energy they produce radiation at specific frequencies known as spectral lines. My question is this. When an object, say a piece of mental is...

Homework Statement Rotate the area bound by the following lines around the x-axis. y = x^2+1, y = -x^2+2x+5, x = 0, x = 3 Homework Equations None that are uniform enough to put here considering I'm fairly sure it's not washer... The Attempt at a Solution

Homework Statement ABCD is a quadrilateral with AB=CD P,Q,R,S are the midpoints of AD,AC,BD,BC respectively Prove that PS is perpendicular to QR Homework Equations The Attempt at a Solution I've tried a bunch of different avenues, but I think that the most promising one is...

hello forum, I am trying to read and learn about balun. Some transmission lines are said balanced while other unbalanced... In a balanced transmission line the voltage on one wire is always as big as the voltage on the other wire but 180 out of phase. For example wire 1 is at 50 V while...

Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...

Complex numbers - "parallel lines meet at infinity"? What does it mean? We started learning about complex numbers last week. One of the first things my teacher said was that "We learned that parallel lines never meet. But as it turns out, they meet at infinity." I'm willing to accept it...

Hi, I a question related to an equation for a magnetic field vector, B, from a dipole in cylindrical coordinates. This is the equation I found for the B field (thought I'm not 100% certain this is correct). B = (u0*m/4*Pi*r^2)* {2 Cos[theta] , Sin[theta]} where the first index is the...

Homework Statement Draw the electric field lines and equipotential lines for the electrode configure. Assume one of the parallel plate is at a positive potential and the other one is grounded. Homework Equations The Attempt at a Solution I know the electric field lines and...

Hi, I've been trying to work out exactly why the t=const and r=const lines look like they do in the Minkowski conformal diagram. I started with the usual Minkowski metric in polar coords (t,r) then go into null coords, then pull in the infinities by using arctan transformations, finally I then...

We've all seen Carl Sagan's Pale Blue Dot picture, taken by Voyager [PLAIN]http://www.humanistsofutah.org/images/PaleBlueDot.jpg My question is: What are those huge red, green, and orange lines?

Can anyone explain to an ignorant layperson, with as little mathematics/geometry as possible, whether field lines in expanding space become "farther apart". I view this question as being closely related to the concept of quantum foam distribution in expanding space... do virtual point particles...

Homework Statement The adjacent figure shows the E-field lines (with arrows) and equipotential contours for a certain charge configuration. Determine for each of the following statements whether it is true or false. Assuming that these contours are those of a point charge at the origin...

Magnets "lines of force are" electrons? So I understand that a magnetic field is defined by the lines of force that go from the north to the south pole...what are these forces? The flow of electrons back and forth...?

I'm supposed to find the equation of a line perpendicular to and intersecting another line. The original line was parameterized in t. I got the answer as L = (0, 1, 2) + s <3/2, -1/2, -1> The book gave it as L = (0, 1 ,2> + t <3, -1, -2> Since both equations describe the same...

Homework Statement L1 pass through the points (-2,36,9) and (-8,44,12) L2 pass through the points (55,-31,7) and (41,-16,13) Find a point P on L1 and a point Q on L2 so that the vector \vec{}PQ is orthgonal to both lines. Homework Equations Dot product/ Cross product The Attempt at a...