Line Definition and 1000 Threads

Hi, In my calculus book,I found this vector form of line equation in space (bold means vector): Given point (x1,x2,x3) lies on line L & v=<a,b,c>, then equation of line is : r = <x1,x2,x3> + t <a,b,c> with t any number. Now, my question if I plug any number for t, then result will be vector...

We have trams in Melbourne, and this weekend I watched a pigeon on the tracks fly up and along the route as the tram came along, being hit by the windscreen (it survived, no worries). Yet it could of flown up and across and escaped because the tram was higher than it was wide. It prompted the...

I'm having some trouble getting my head around the scale at which capillary flow and contact line dynamics are important. In the simple case of liquid rise in a capillary tube, a smaller tube will allow for greater rise since a larger height is required to achieve an equal weight of the liquid...

Hi All, I am trying to solve what I think should be a simple problem, but I must be missing something because I am struggle to solve it. The situation is shown below: So to summarise: A body starts at Point A It moves in a straight line to Point B, covering a distance of 10m The time taken...

What is the prerequisite of "the length of world line equals proper time"?C=i?orC=1?If metric is-+++: ##ds^2=-c^2d\tau^2\Rightarrow whenC=i,s=\tau## If metric is +---: ##ds^2=c^2d\tau^2\Rightarrow whenC=1,s=\tau## So,which one?

I don't have any idea to answer these questions. I am working on it by searching the reference books where similar questions have been solved by authors. Meanwhile, any member of Physics Forums may help me in answering these questions.

I don't have any idea to answer this question. So, any math help will be accepted. I know ##\nabla fg = f\nabla g + g\nabla f \rightarrow (1) ## But I don't understand to how to use (1) here?

I don't have any idea about how to use the hint given by the author. Author has given the answer to this question i-e F(x,y) = axy + bx + cy +d. I don't understand how did the author compute this answer. Would any member of Physics Forums enlighten me in this regard? Any math help will be...

. Let C be a smooth curve with arc length L, and suppose that f(x, y) = P(x, y)i +Q(x, y)j is a vector field such that $|| f|(x,y) || \leq M $ for all (x,y) on C. Show that $\left\vert\displaystyle\int_C f \cdot dr \right\vert \leq ML $ Hint: Recall that $\left\vert\displaystyle\int_a^b g(x)...

Hi, I was experimenting , after doing some reading, with 'Net Share' in my Windows 10 Command Line, on my PC, which I'm not using as a server, i.e., I'm not running ( nor do I have installed) Windows Server nor other server software. The output was: Share name Resource...

ok I am actually trying to plot $f(x)=5x^2-2x$ with the tangent line going thru $(1,3)$ which is $8\left(x-1\right)+3$ I thot I could just change this from an example but does seem to like it stack exchange had some samples but they got very complex with other features added anyway mahalo...

This thought came to me while I was trying to fill my MTB bike tire a while ago as an exercise in laziness to not "check" the tire pressure with a separate gauge! Mostly, my mind just wanders... If I have some very large tank filled with compressed air at gauge pressure Ptank. The hose runs...

Question: Equations: My solution: Could someone verify my answer?

Hi PF! I have a vector valued function ##f(s) = r(s)\hat r + z(s)\hat z## that plots a line in the ##r##,##z## plane when I use ParametricPlot. I'd like to plot this line into a surface, so that it revolves around the ##z## axis, but in a sinusoidal fashion. Basically I'd like to revolve it...

I am having trouble with the spacing and positioning of some number line. Sorry for any format problems. \usepackage{tikz} \usepackage{parskip} \subsubsection{Graphing Real Numbers on Number Line} We can graph subsets of real numbers on the number line. The number lines continue forever...

Homework Statement:: I go back to the line to finish the previous line in MCNP cell card but I had the error message shown in the photo. Please make a solution to my problem Relevant Equations:: c ********************* BLOCK 1: cartes des cellules **************** 1 2 -1.184 -40 #3 #19 #18...

Visualize a lid to a toddler snack cup. Making an entry into an object which is to be placed in nature which can be used by humans but not easily by animals, would the curves used in some toddler snack cups be more durable and flexible without being floppy, or would straight line radii from the...

can someone tell me what is the meaning of the horizontal line in the sentence ? thanks .

From Stokes we know that ##\iint_{\textbf{S}}^{}curl \textbf{F}\cdot d\textbf{S}=\int_{C}^{}\textbf{F}\cdot d\textbf{r}##. Now, we can calculate the surface integral of the curl of F by calculating the line integral of F over the curve C. The latter ends up being 0(I calculated it parametrizing...

Swing - Shim Sham - at Carnation Plaza at Disneyland:

Find the question here; My interest is on question ##3(c)## only. My approach, Let the co ordinates of ##C##= ##(x,y)## then considering points ##B## and ##C##. We shall have the gradient given by; ##\dfrac {y-4}{x-1}##=##-2## also from straight line equation, considering points ##A## and...

I would like a program to read in a file entered by the user via the command line, which is then used in the main body of the code. See example code below: #include <iostream> #include <fstream> struct run_t { std::string file; }; run_t run; const POINTER* ptr = toy(run.file,0); int...

Hi all, I need some help with this one:There are 3 shapes of pasta: 1,2,3. In a box there are 3 packages of pasta of shape 1, with different weights: 300 gr, 400 gr, 500gr. In addition, there are 5 packages of paste of shape 2, with weights: 300gr, 350gr, 400gr, 500gr, 600gr, and 4 packages...

I wonder if someone please could explain what the relationship between a spectral line strength and gravity is? Does the equivalent width of e.g. Ca II decrease with increasing gravity? what kind of processes affects the strength of a line if we change the gravity of a star? Hope you can help me

I have tried solving this question, but I am not even sure where to start from and how to specify a state space for this question where it has a trick stating that a worker works overnight. However, for part a, is it the case that there are only 2 states to consider which are: {machine working...

This is the question ... I have it's solution ... My problem : I can't understand why dx=R/cos^2(teta) dteta I have thought many hours but I couldn't find it's reason ... Can anyone please help with this ?!

I have two line equations representing two temperatures: Temperature 25C: y= 0.7479x + 0.6586 Temperature 33C: y= 1.050x + 1.601 I am tasked with using these to work out the difference in development rates of a particular species under each temperature. Y= development time and x=Time. I am...

Hi PF! At the bottom of a transparent cup full of water is a hole where water drains. The cup is sloshed, so the gas-water interface is not flat. Are there any techniques you're aware of that implement machine learning to track the interface? My current technique not using ML is: 1) splice...

I have a formula y=log(x)/log(0.9) which has this graph: I want to find the intersection of this curve and a tangent line illustrated in this rough approximation: The axes have very different scales, so the line isn't actually a slope of -1, it's just looks that way. How can I figure out: 1)...

Imagine a ball floating in space, and there is an observer at rest next to it. Then the observer goes for a trip at high speeds and returns to be at rest with the ball once again. Would the world line of the ball be curved because of the frame of reference of the observer, or would the world...

Find the problem below; My approach, if##x=0##, then ##y=b## and if ##y=0##, then ##x=a##, therefore our co-ordinates are ##(a,0)## and ##(0,b)##. The gradient will give us, $$-3=\frac {b-0}{0-a}$$ It follows that, ##b=3a##, therefore $$20=\sqrt {(3a-0)^2+(0-a)^2}$$ $$400=9a^2+a^2$$ ##a=2\sqrt...

Find the question here ( this one is a pretty easy question). I have attempted this in the past using varied approach, this is in reference to part(b) of the question... i have previously used pythagoras theorem to finding co-ordinates of ##B## and ##D##... Anyway find my current approach on...

Find Parametric eq for line segment from (-2,18,31) to (11,-4,48) ok not sure how to start on this the book example is in the spoiler

This is a textbook problem (Mechanics). Attached find the question and respective solution. This is fine with me, i like trying different ways of solving math related problems. My approach is as shown below. Using the graph sketch It follows that, ##s##= ##(35×12)##+##\frac...

Then might be regarded as continuation of discussion https://www.physicsforums.com/threads/impedance-matching-when-the-transmitter-line-and-load-impedances-are-different.1009266/ where unfortunately it's not more possible to post further replies (why?). So I would like to continue it here, since...

Summary:: Two parallel lines (same slope) - one intersects the y-axis, and the other doesn't. Trying to find the intersection of either with a given geometric sequence. The lines are: y=mx y=mx+1 The values on one or the other of the lines - but not both simultaneously - are to be completely...

I found this problem, which I thought was interesting and somewhat original: Calculate the volume of the solid of revolution of the area between the line ##y = x## and the parabola ##y = x^2## from ##x = 0## to ##x = 1## when rotated about the axis ##y = x##.

Question: My attempt: Could someone please confirm my answer?

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I tried using hamilton method but i don't think that's correct

Problem statement : As a part of the problem, the diagram shows the contour ##C##above on the left. The contour ##C## is divided into three parts, ##C_1, C_2, C_3## which make up the sides of the right triangle. Required to prove : ##\boxed{\oint_C x^2 y \mathrm{d} s = -\frac{\sqrt{2}}{12}}##...

Assume we have a general rf system where source with impedance ##Z_S## transfers a signal to a load with impedance ##Z_L## through a transmission line with impedance ##Z_T##. We want to match this system in order to maximize it's effiency: In https://en.wikipedia.org/wiki/Impedance_matching...

Problem : We are required to show that ##I = \int_C x^2y\;ds = \frac{1}{3}##. Attempt : Before I begin, let me post an image of the problem situation, on the right. I would like to do this problem in three ways, starting with the simplest way - using (plane) polar coordinates. (1) In (plane)...

I asked this from a number of people but no one knew what to do about this exponential with iota infinity in the power,in Eqtn 5.7 The textbook seems to imply that it is zero but cos and sine are undefined at infinity. Also,all the exponentials seem to vanish from the final result of Eqtn 5.8...

Don’t know exactly where to ask this, so I’ll try here first. Okay, so a few weeks ago my internet went out. I ended up receiving a new modem in the mail the next day after I called. It didn’t work. I was finally able to be home for a technician to check it out this week. He told me that...

Hi! I think I solved the problem but I would like you to take a look at it please, is it right? is there a better way to solve it?

Let the point P(2,8) be a point in xy-plane and line m: y = -0.75*x+3.25 be a line in the xy-plan. The distance from a point P to a point B is 7 unites. Where the x coordinate of B is negative. Find the acute angle between PB and m. To find B I then construct a circle of radius 7 with center...

How to find image of $f(x)= x + sinx$ about the given line $y = - x$ . Similarly can we take image of a function about a function? OR is it necessary about which we take image should be a point, line only?

A particle moves on a straight line. It starts at a point O on the line and returns to O 100 s later. The velocity of P is v m/s at time t s after leaving O where v= 0.000t^3- 0.015t^2 +0.5t. 1) Find the values of v at the times for which the acceleration of P is zero I got when t= 21.1s, V=...

Hi, I found this question online and made an attempt and would be keen to see whether I am thinking about it in the right manner? Question: Find the probability of two line segment intersecting with each other. The end points of lines are informally sampled from an uniform distribution...