What is Line: Definition and 1000 Discussions

I am reading Mathews and Howell's book: Complex Analysis for Mathematics and Engineering. I am currently reading Section 1.6 - "The Topology of Complex Numbers". I have a problem with an aspect of Example 1.22 on page 38. My problem is a simple one related to algebraic manipulation of a couple...

Homework Statement Evaluate the line integral ∫^{(1,0)}_{(0,1)} (x^2-y)dx + (y^2+x)dy along (a) a straight line from (0,1) to (1,2); (b) the parabola x=t, y=t2 + 1; (c) straight lines from (0,1) to (1,1) and then from (1,1) to (1,2). Homework Equations Equation of line: y = mx + c The Attempt...

Homework Statement i have this problem and need your help. I tried to solve the first 2 question but don't know ho to solve the third one

Homework Statement Can I measure the probability of a person being at a certain end location after n steps using the binomial distribution if, probability student goes x=x+3 is 0 <= p <0.5 , x=x-1 is 0<= 0.5 p <1.Homework Equations x=x+3 is 0 <= p <0.5 x=x-1 is 0<= 0.5 p <1 The Attempt at a...

Go to 1:24 of this video: He recalls some integral he wrote at a young age: " ... times the sixty-fourth power of ... what?" and looks confused. At 1:44 Neil Degrasse Tyson says, "By the way, the answer to your little calculation is i." Can someone explain the historical reference to me...

Homework Statement Recall that a flow line, c(t), of a vector field F has c'(t)=F(c(t)) at all times t. Show all work below. a.) Let c(t) be the flow line of a particle moving in a conservative force field F=-grad(f), where f:R^3->R, f(x,y,z) >=0 for all (x,y,z), represents the potential...

Homework Statement (2 part problem) a) A plane passes through the point P(3,1,4) and is orthogona to the line (x-1)/2 = (2-y)/-7 = z-3 b) Find the point on the line closest to point (3,1,4) Homework Equations Symmetric equation --> (x-x1)/t = (y-y1)/t = (z-z1)/t ( anyway i think that's what...

Dear All, Please help me clear some doubts about Theorem 3.3.1 in the 1st attachment. The condition ## |a| = |b| ## has only 8 cases right? ## { x+iy. x - iy, -x + iy, -x - iy, y + ix, y - ix, -y + ix, -y - ix } ## so for the condition ## |a| = |b| ## and ## b \bar c = \bar a c...

Homework Statement Use Green's Theorum to evaluate the line integral ∫c (x^2)y dx, where c is the unit circle centered at the origin. Homework EquationsThe Attempt at a Solution Taking the partial derivative with respect to y and subtracting it from zero(I'm taking the dy in the original...

Homework Statement We are given a wedge configuration with three sections. There are two conducting planes held at zero potential that make an angle of ##2\beta## with each other. They are connected by a portion of a conducting cylinder with radius ##a##. An infinite uniform line charge of...

Why line spectrum of hydrogen includes no X-ray frequencies?

Homework Statement Find the line integral of f(x,y,z) = x+y+z over the straight-line segment from (1,2,3) to (0,-1,1). Homework Equations ∫ f(x,y,z)ds = ∫ f(g(t), h(t), k(t)) |v(t)| dt The Attempt at a Solution I arrived at the correct solution, but I'd like some clarity on the result...

Homework Statement I understand the setup for finding the slope, but always get confused whether I've fully simplified when trig identities get involved. [/B] Homework Equations My dy/dx is [/B] 4sin(θ)cos(θ) -2csc2(θ) which I simplified to just (-2sin(θ)cos(θ))/(csc2(θ) Does that...

Homework Statement Evaluate the line integral over the curve http://webwork.math.ttu.edu/webwork2_files/tmp/equations/33/92ca0e3b907f876e5a974ad1457d1f1.png from to http://webwork.math.ttu.edu/webwork2_files/tmp/equations/6f/bccf9dd59b9c22450c590a042bb77d1.png . ∫-ydx+3xdy (over the curve C)...

(from my limited understanding) In our observable universe a photon could travel say, 5 billion light years in a straight line if unperturbed. Call the points X and Y traveling down-up. If point X was moved one Planck length to the left, would it still be able to travel exactly to point Y?

So we're using NXT 2.0 and MATLAB to program a robot to follow a white line through a maze. I'm using a light sensor, color sensor and an ultrasonic sensor in the process. Any programming/Coding ideas of how i should start? This is the maze...

Homework Statement Let \Delta be a line and A a point in space. [itex ] B [/itex] is a point on \Delta ans H is a point on \Delta such that \newcommand{\vect}[1]{\vec{#1}} \vec{AH} \perp \Delta . a) Show that \| \vec{AH} \| \leq \| \vec{AB} \| (a geometric reasoning should be used)...

Hi, I was wondering if it would be possible for someone to help me clarify a few things regarding transmission lines and transformers? For a Power Transmission line, what exactly is the mutual coupling between phases of a 3 phase line? Is this the same as the shunt capacitance and if not...

Hi, if I simulate a three phase transmission line operating with a fault across two of the phases, would the mutual coupling have any effect on the current through each of the lines, as I have calculated the fault current values using symmetrical component analysis and the values are...

Homework Statement In Exercises 45-46, show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. 45. The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t Verbatim from Poole - Linear Algebra: A...

If there was no Sun then the Earth would move in a straight line with constant velocity. This is because the space has vacuum and there is no friction in space. This is because if you observe on Earth where there is friction we need to apply force against this friction. But in space there is...

In the problem attached, why is the integral become just the length of line cf?

< Mentor Note -- thread moved from EE to the Homework Help forums > I'm studying for a Level 3 Diploma in Electro technical science. My tutor had a hard time teaching me what I need to know in order to answer this question; Calculate the phase and line current when three resistors each having...

Homework Statement Determine whether or not f(x,y) is a conservative vector field. f(x,y) = <-3e^(-3x)sin(-3y),-3e^(-3x)cos(-3y) > If F is a conservative fector field find F = gradient of f Homework Equations N/A The Attempt at a Solution Fx = -3e^(-3x)(-3)cos(-3y) Fy =...

I need to figure out if my companies pulling equipment can handle a 795 drake conductor (about 1 lb/ft) double bundled (times 2). The pulling equipment has a safe working load of 4000 lbs. We are pulling it across 16 spans with a average span of 674 feet. the towers are 115' tall. Max sag...

Homework Statement I've been given the line element given below in the relevant equations section and I need to prove that the space it represents is just the same as the 2-D Euclidean plane. Homework Equations ds^2 = a^2 \frac{d\eta ^2 }{cosh^4(\eta)} + a^2 tanh^2(\eta) d\theta ^2 Where...

Hi PF! I am very new with Latex and was building a resume using a downloaded template. What I would like to do is create a vertical line down the page. Can anyone help? The line of code that seems to create a horizontal line is...

Homework Statement Hello I was given the vector field: \vec A (\vec r) =(−y(x^2+y^2),x(x^2+y^2),xyz) and had to calculate the line integral \oint \vec A \cdot d \vec r over a circle centered at the origin in the xy-plane, with radius R , by using the theorem of Stokes. Another thing, when...

Hi, When calculating a line-line fault, I understand that the Positive and Negative Phase Sequence networks are placed in parallel with each other as shown in the first attached image, and that the zero phase sequence is excluded. Although this is connected in parallel, does it not produce a...

Homework Statement The input range of a particular sensor is from 0-6 units and it's output is modeled by the equation O = ƒ(I) = 1+2I+0.005I^2-0.00833I^3 Ideally the output should be relate to the input by the straight line equation (ISL) if the form O=kI+a A) give the law if the ideal...

Homework Statement Attached here is a diagram. My questions are, how to compute for the value of the chord? How to compute for the value of the tangential line? Please help.. Thank you in advance.

Hi guys, Here is a little puzzle I have been wondering about. I can't solve it, perhaps you can help. We know there are infinitely many real numbers on the number line. Indeed, already between 0 and 1 there are infinitely many real numbers. So if a real number is a point on the number line...

Hi everyone. I ran into a minor problem while trying to solve a problem on line integral. I suspect this question to be very straight-forward as it gave the parametric equations of the curve C. However, I am still unable to get the answer for some reason. May I have someone to point out where I...

So I am kind of confused about the role of force when calculating work. Specifically, when defining work using a line integral. There is a paragraph in my calculus book that is really throwing me off and its really bugging me so much I can't continue reading unless I fully understand what's...

Given the function f(x) = 3x / (x - 2), determine the coordinates of a point on f(x) for 3 < x < 6 where the slope of the tangent line is equal to the slope of the secant line passing through A(3, 9) and B(6, 9/2). So I found that the slope of the secant line is -1.5 (therefore slope of tangent...

Does anyone know a good algorithm for calculating the closest points/distance between two line segments? I use some pretty general code: http://geomalgorithms.com/a07-_distance.html which works in most cases but fails horribly when line segments are nearly parallel. I've been messing with the...

At what point on the curve $$y = e^x$$ is the tangent line parallel to the line $$y = 2x$$ The derivative of y is $$\frac{dy}{dx} = e^x$$ But I'm unsure how to proceed from here.

Can I perform line operations on a matrix product? For example the matrix product ABC and I know that A and C are invertible, can I row reduce to get ICI? Will the product be conserved?

Hi, I was doing a L.A question and a question arose. ( well I will write the question now, I found the answer I just can't visualize what I am doing which bothers me greatly) Find the equation of the plane that contains the line (x,y,z)=(1,0,0)+t(1,3,2), and is parallel to the line of...

Hey everyone, so for fiber optic networks we can either (in analogy) increase how fast the cars or photons move or add more lanes to increase the amount of data. What if now we use the color of the light to interpret several times more data?

I have just finished a junior-level lab assignment in which we used X-ray diffraction to determine the lattice constants of unknown materials. In the theory section of the lab write-up, it briefly explains the K-alpha doublet of the characteristic spectrum. I understand that it is the result...

Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

Homework Statement Show that (Grad dot E) =0 in the dielectric of a coaxial line. (Hint: apply the divergence theorem to a portion of the dielectric.) Homework Equations Divergence theorem The Attempt at a Solution I think I need to show that grad dot E = p/epsilon = 0 I don't know - I'm...

Homework Statement refer to the question Homework EquationsThe Attempt at a Solution from figure b , moving to the right, we know that the wavelength increases. since e= hc/λ , so the energy diffrenece should be increases as going to the right, so i consider line 1,2 and 3 is in a specific...

Given the force (derived from a potential in planar polar coordinates) F(p,w) = 2p+sin(w)e_p+cos(w)e_w Where e_p and e_w are unit vectors How do I calculate the line integral over a circumference that is defined as: p = 2 0 ≤ w ≤ 2pi Using the definition of a line integral \int_0^{2pi} \...

Homework Statement Let F be a vector field F = [-y3, x3+e-y,0] The path in space is x2 + y2 = 25, z = 2. My parametrization is r(t) = [5cos(t),5sin(t),2] Homework Equations Line integral is the integral of F(r(t)) * r'(t) dt, where here the asterisk * is for the dot product, not normal...

I would like to install a vent stone on a 3/4" vent line. The line vents upwards of 1500 psig of stored gasous nitrogen in under 1 second. The vent stones are only rated for 300 psig, so I'd like to add an orifice just upstream to limit the exit flow rate to a point where it can handle the...

In tightening a bolt whose center is at point O, a person exerts a 180-N force on the ratchet handle with his right hand. In addition, with his left hand he exerts a 90-N force as shown in order to secure the socket onto the bolt head. Determine the equivalent force–couple system at O. Then find...

Homework Statement This is the point: (6,0,-2) Homework Equations x = 4-2t y = 3+5t z = 7+4tThe Attempt at a Solution Do I just plug in the points and see if I get matching values of t? If not, how do I go about this?

Homework Statement Birds can be seen perched on a high voltage power line yet seem unaffected by the high voltage. This is due to... A) Low resistance of the birds compared to the wire, minimizing current through the birds B) birds keeping only one foot on the wire, thus not completing a...