Line Definition and 1000 Threads

Homework Statement Let γ : [0, L] → Rn be arclength parametrized. Show that the distance between the endpoints of the curve can at most be L, and equality can only hold when γ is a straight line segment. Thus, the shortest path between two points is the straight line segment connecting them...

Homework Statement The potential difference between the surface of a 2.2 cm -diameter power line and a point 1.9 m distant is 3.8 kV. What is the magnitude of the line charge density on the power line? Express your answer using two significant figures. Homework Equations V =...

Homework Statement so I have this text file that I'm reading line by line and here is an example of a line: root pts/1 01-19 13:41 (10.0.0.48) Homework EquationsThe Attempt at a Solution How can I extract the terminal and timeframe only? I tried echo $line | cut -d : -f2, 4 and...

Pick any three points on the line y = (x/2) + 3. 1. Reflect each point in the line y = x. Do I simply exchange the x and y coordinates of the chosen 3 points? 2. Show that the 3 reflected points all lie on one line. I need one or two hints here. 3. What is the equation of the line for part...

Show that the points (a, b) and (b, a) are symmetric about the line y = x. Solution: Let m = slope m = (a - b)/(b - a) I know the slope of y = x is 1. Must I now show that the line y = x passes through the midpoint? If so, how is this done when the slope is not a number (as in this example)?

The point P is located on line segment AB in such a way that AB/AP = AP/AB. In words: P divides line segment AB into two segments such that the ratio of AB to the longer segment is equal to the ratio of the longer segment to the shorter segment. (A) Show that this ratio is equal to (1/2)(1 +...

The slope of y = x is 1. Why is this the case?

Show that the slope of the line passing through the two points (x, x^2) and (x + h, (x + h)^2) = 2x + h. Must I use m = delta(y)/delta(x)?

This link is yet another detection of a 3.5 KeV line in long exposure X-ray astronomy observations. It seems that this line is really there, since it has been seen in multiple objects with multiple instruments. I haven't seen any convincing explanations of this line as being due to atomic...

I'm not proficient here, nor skilled, but it is it one of most important calculations in sport. Every point on Mile start line means all run 1609.344m by hitting tangent at various points on 1st bend Every guy has to hit a tangent at assumed different parts of bend ( 36.80m is shortest...

Homework Statement [/B] This question was raised on the 11th January 2015 but that thread appears to be no longer active now. There are 2 parts to the question (a) and (b). Initially I am only trying to work on (a) Figure shows a 50 Hz, high-voltage, transmission line. The relationships...

Homework Statement Find the Electric field a distance z above one end of a straight line segment of length L that carries a uniform line charge λ Homework Equations Complicated formula due to lack of font for the notation used by the author of the book. so I wrote it out. I did my best to...

Homework Statement A transmission line has the primary coefficients as given below. ##R=2\Omega/m## ##L=8 nH/m## ##G=0.5 mS/m## ##C=0.23 pF/m## Determine the lines secondary coefficients ##Z0##. ##\alpha## and ##\beta## at a frequency of ##1 GHz## Homework Equations [/B] In my notes I am...

Homework Statement [/B] a ##50\Omega## lossless transmission line of length ##0.4\lambda## is terminated in a load of ##(40+j30)\Omega##. Determine, using ##Zin=Z0\frac{ZL cos \beta l+j Z0 sin \beta l}{Z0 cos \beta l +j ZL sin \beta l}## the input impedance to the line. ##Z0=50\Omega##...

Homework Statement A line of charge with a non-uniform charge density lambda=ay, where a=−34.00 nC/m^2 lies along the y axis in the region 0≤y≤2.90 m. Calculate the electric potential of this line of charge at point P on the x axis a distance 0.80 m from the origin. Assume the potential...

Homework Statement (a) A transmission line has a length, ##l##, of 0.4λ. Determine the phase change, ##\beta l##, that occurs down the line. Homework Equations ##\beta=\frac{\omega}{f\lambda}## or ##\beta=\frac{2\pi}{\lambda}## The Attempt at a Solution This question was posted a couple of...

Hi guys, I've another exercise... 1. Homework Statement Determine the equilibrium internuclear distance ##R_M## of HCl molecule, knowing That some contiguous lines of the rotational spectrum of 2H35Cl are observed at the wavelengths: 234.1, 186.8, 156.4, 134.1, 117, 5 ##\mu m##. If the...

Homework Statement A cyclist rides along a road up an incline at a steady speed of 9.0 m s–1. The mass of the rider and bicycle is 70kg and the bicycle travels 15 m along the road for every 1.0 m gained in height. Neglect energy loss due to frictional forces. Calculate the component of the...

I'm trying to plot 5 periodic functions on the same graph in MATLAB and I can't seem to figure out how to do it correctly. The following code will work, except that I still need to change the line style for each line so that they are easy to tell apart. k = 1; %spring constant w0 =...

1. Homework Statement An infinite line of charge with linear density λ1 = 6.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.5 cm and outer radius b = 4.8 cm. The insulating shell is uniformly charged with a volume density of ρ = -667 μC/m3. 1) What is λ2...

1. Here is the Problem: A line passes through A(2,3) and B(5,7). Find: (a) the coordinates of the point P on AB extended through B to P so that P is twice as far from A as from B; (b) the coordinates if P is on AB extended through A so that P is twice as far from B as from A. Homework...

Homework Statement Pls refer to the second photo , the red line part ...I don't understand the meaning of when 1 unit load move at C , the unit load is inclusive in the right system... I can understand the FBG sin45 + 1 = RE Homework EquationsThe Attempt at a Solution When the in unit load move...

If a line in space has no thickness, how can I distinguish the line from its surroundings when I look at the line such that I can't see its length? After all, in three dimensional space, you can look at a line from different angles.

Homework Statement For the highlighted part , why we need to replace the support at A with a roller guide ? We could see at A , it's a pinned support , right ? Homework EquationsThe Attempt at a Solution Pinned support will resist horizontal and vertical reaction , why the author said it...

Hi All, This question is about vector calculus, gradient, directional derivative and normal line. If the gradient is the direction of the steepest ascent: >> gradient(x, y) = [ derivative_f_x(x, y), derivative_f_y(x, y) ] Then it really confuse me as when calculating the normal line...

Hello Forum, I understand that an electron inside an atom/molecule has many possible transitions that it can make from a higher energy state (once it is excited there) to a lower energy state (possibly the ground state but not necessarily). For example, the electron can jump directly from...

Homework Statement Compute the work of the vector field ##F(x,y)=(\frac{y}{x^2+y^2},\frac{-x}{x^2+y^2})## in the line segment that goes from (0,1) to (1,0). Homework Equations 3. The Attempt at a Solution [/B] My attempt (please let me know if there is an easier way to do this) I applied...

Field at End of Line of Charge 2 A charged rod of length L=7.10 m lies centered on the x axis as shown. The rod has a charge density which varies according to λ=ax^2 where a=−20.2 μC/m^3 . What is the x component of the electric field at a point on the x-axis a distance of D=3.70 m from the...

$\tiny{231.12.3.63}$ $\textsf{ Determine the smallest distance between point P and the line L through the origin}\\$ $\textsf{$P(-8,4)$ L is $y=6x$ }$ \\ $\textsf{$\therefore A=6, B=-1, m=-8, n=4$}$ \begin{align*}\displaystyle d&=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}\\...

Homework Statement http://cereference.com/book/structural-analysis/influence-lines-beams In the example , i don't understand the moment in the part of beyond AC . I don't understand why we don't have to consider the momenty due to unit virtual load in the part beyond AC , just like what we did...

1. Homework Statement An air coaxial transmission line has a solid inner conductor of radius a and a very thin outer conductor of inner radius b. Determine the inductance per unit length of the line. Homework Equations the book states the methodology to find the inductance as follows: 1)...

Homework Statement In part a , the author state that at the roller , it will restrain the beam from moving vertically , so the beam wouldn't deflect at roller at part a ... But at b , the author showed that the beam will deflect at roller , why is it so ? Homework EquationsThe Attempt at a...

Homework Statement why at C . the shear force V change from -0.5 to 0.5 ? We wantg to determine the shear force at different location , and a unit force is applied at arbitary location ( measured from A) ... Homework EquationsThe Attempt at a Solution IMO , there's no upwards force of 1...

Hey! :o I want to draw the contour line of the function $\displaystyle{y=f(x_1, x_2)=-0,1x_1^2-0,4x_2^2}$ at $y=-2,5$ and at the point $(3,-2)$ I want to draw the gradient. We have the following: \begin{equation*} y=-2,5 \Rightarrow -0,1x_1^2-0,4x_2^2=-2,5 \Rightarrow -10\cdot \left...

Homework Statement find equation of plane P that is perpendicular to line L which passes through the point (-2,-2,3) Homework Equations ... The Attempt at a Solution [/B]line L passes through the points (1,2,1) and (0,0,-3) I have worked out the parametric equations of line L to be x=1-t...

I realize that in a spectrometer the spectral line being viewed will be the result of the actual spectral line plus an instrument line function as well (as seen in the linked image). What I don't understand is how this is produced? Someone tried explaining this to me once before but their...

Can someone explain how this is possible? it makes no sense to me. You wouldn't walk along the track surrounding a soccer field if you wanted to get to the other end... you would walk straight across the grass to reach your destination. Why did Einstein propose this?

So I'm reading the first page of Rudin. This is right after proving that there is no rational solution to x^2=2. How does this show that the rational number system has gaps? All it shows is that A has no upper bound and B has no lower bound. Is it really necessary to have two sets A&B perfectly...

I've been looking all over the internet for the line element of the Misner solution to the Einstein Field equations, but I can't find it. Can someone please post the line element? Thank you.

Homework Statement p(x) = 0.2*(x-1)^5, q(x) = 4x-6 The Attempt at a Solution I took the diffrence h(x) = p(x) - q(x) h'(x) = ((x-1)^4) - 4 got two solutions for h'(x)=0.

What is the x-intercept of the graph of y = x2 – 4x + 4? How would you foil this?

Dear Forumers, This question is about load-line analysis for loudspeaker driver magnetic circuits in FEMM 4.2 (Finite Element Method for Magnetics), I can't seem to get an answer from the mailing lists. I would like to get the permeance coefficient for random points inside the magnet. I have...

Homework Statement The following point (x0,y0), is on the curve sqrtx +sqrty = 1Show that line equation of the tangent line in the point. (x0,y0) Is x/sqrtx0 + y/sqrty0 = 1 I've found the slope which is -sqrty/sqrtx. So slope of the point is -sqrty0/sqrtx0 Homework EquationsThe...

Homework Statement Let ##f(x,y)=(xy,y)## and ##\gamma:[0,2\pi]\rightarrowℝ^2##,##\gamma(t)=(r\cos(t),r\sin(t))##, ##r>0##. Calculate ##\int_\gamma{f{\cdot}d\gamma}##. Homework EquationsThe Attempt at a Solution The answer is 0. Here's my work. However, this method requires that you are...

Homework Statement I am having question with part c , for both c1 and c2 , here's my working for c1 , i didnt get the ans though . My ans is -5 , but the given ans for c1 and c2 is 27 , is the ans wrong ? Or which part i did wrongly ? Homework EquationsThe Attempt at a Solution

Homework Statement An infinite line of charge with charge density λ is parallel to and a distance d above an infinite grounded conducting plate. What is the charge density σ that is induced in the plate? For simplicity, consider the line of charge to lie along the line x = 0. Homework...

Real analysis shows that the real line is complete. All the gaps between the rationals are filled. It is perfectly continuous. Of course, all of this is based off of certain axioms that make it work mathematically. Are those axioms now sound? According to quantum, the plank length is the...

This is a fiction project, but the question is about 3D geometry (a bit beyond my HS math skills). Given two points on a sphere (oh say, hypothetically, the Earth), draw a line from point A through the Earth to Point B. If I were to stand on point A and point directly at point B, what...

Sorry where is pi/4 coming from in the line integral(section 3)? because i think it should be 1/2=tan(theta) which theta is 26.5651... it is impossible that the angle is pi/4? where is pi/4 coming from inside the circle? thank

Homework Statement Sisyphus is pushing a boulder up a 100-ft tall spiral staircase surrounding a cylindrical castle tower. a) Suppose Sisyphus's path is described parametrically as $$x(t)=(5\cos3t, 5\sin3t, 10t)$$, $$\space 0\leq t\leq10$$. If he exerts a force with constant magnitude of 50 Ib...