Curves Definition and 778 Threads

i am new at relativity, it said mass can curve spacetime, does this mean spacetime will curve to a new 5th dimension (1-3 for space dimension, 4 for time dimension)?

A) Find all values on [0,2pie) such that (thita0) produces the tip of a petal (maximum magnitude of r) all values for which r=0, and sketch a graph? a) r = 5 sin 2 (thita0) a) r = 5 sin 3 (thita0) a) r = 5 sin 4 (thita0) B) considering what you can observe in the previous graphs, what are...

Hello to everyone, I'm trying to find some data about the relation between galaxy age and rotational curve... until now without success. Are there any teams working on this? Are there any studies in this direction? Thanks!

just something I need quickly to illustrate a homework help, don't want to spend much time on. What is the code in WolframAlpha just to plot an ornery family of curves? Searched WA and find all sorts of fancy things, not this ornery one. Should. be something like e,g. For n= 1 to 20 c= n*0.05...

Homework Statement I have to find length of the curve: y2 = (x-1)3 from (1,0) to (2,1) Homework Equations s = ∫ √(1 + (f '(x) )2 ) dx where we have integral from a to b The Attempt at a Solution I'm bit confused: I'm thinking of writing function regarding x, f(x)...

Homework Statement This is a conceptual issue which I am trying to understand: When you are describing a vehicle traveling on a banked curve, force parallel (the force which is found to be parallel to the surface of the road pointing down the bank) is omitted from the FBD and the equations...

Member warned to type the problem statement, not just post an image with type that is too small to read Homework Statement See attached. Homework EquationsThe Attempt at a Solution Ok so the first thing you want to do is find the equation of the tangent line which is done in the usual way to...

Homework Statement For a vector field $$\begin{equation} X:=y\frac{\partial{}}{\partial{x}} + x\frac{\partial{}}{\partial{y}} \end{equation}$$ Find it's integral curves and the curve that intersects point $$p = \left(1, 0 \right).$$ Show that $$X(x,y)$$ is tangent to the family of curves: $$x^2...

I have been reading this article https://tritonstation.wordpress.com/2018/10/05/it-must-be-so-but-which-must/ so why does Mond fit so well over dark matter models?

Could anyone please explain how can I know mathematically whether the logarithmic spiral curve spirals inward or outward? In which sense does the outward spiral spirals? Thank you very much for your help

These are apparently Closed Timelike Curves that don't violate causality, do they exist?

What's the difference between Closed Timelike Curves seen in physics and the time loops in movies where a character relives a period of time over and over, but retains memories? I'm just curious about this stuff.

Homework Statement If I have the two curves ##\phi (t) = ( \cos t , \sin t ) ## with ## t \in [0, 2\pi]## ##\psi(s) = ( \sin 2s , \cos 2s ) ## with ## s \in [\frac{\pi}{4} , \frac{5 \pi}{4} ] ## My textbook says that they are equivalent because ##\psi(s) = \phi \circ g^{-1}(s) ## where ##...

I have seen the equations relating energy, momentum, pressure/stress to the metric tensor and the curvature of spacetime, as I’m sure most people have. But what is the mechanism? I’ve read an interpretation in Quora (horrid source, I know) where energy and stress are basically “pushing” space...

When you put a mass on a trampoline it causes the trampoline to V. If you put another similar or same sized mass on the same trampoline at a great enough distance, will the curve on the trampoline/space-time look like a W or a U ? If you can get the curves on a trampoline/space-time to look...

I am looking for a way to get, by a simple numerical computation, the 3 curves on the following figure: For this, I don't know what considering as abcissa (comoving distance ?, i.e ##D_{comoving} = R(t)r## with ##R(t)## scale factor and ##r## the coordinate which appears into FLRW...

Some exact solutions to Einstein's General Relativity show that Closed Time like Curves may theoretically exist. Could they actually exist in our universe? And if so, how would it change the understanding of physics and our universe?

I am trying to model a real heat exchanger in simulink. I don't have the geometry data. But I have UA curve with me. If I have developed the model with UA curve, will it be dynamic in nature?

Hi, Given a smooth distribution of lines in R2, could we assert that there is a unique distribution of curves such that: - the family of curves "fill in" R2 completely - every curve is tangent at every point to one of the smooth distribution of lines

Homework Statement I said it is 0 less than or equal to x less than or equal to 2 and 0 is less than or equal to y which is less than or equal to 2. Is that correct? Homework EquationsThe Attempt at a Solution

Homework Statement Find a piecewise smooth parametric curve to the astroid. The astroid, given by $\phi(\theta) = (cos^3(\theta),sin^3(\theta))$, is not smooth, as we see singular points at 0, pi/2, 3pi/2, and 2pi. However is there a piecewise smooth curve? Homework Equations $\phi(\theta) =...

I have been trying to find an answer to this problem for some time. So I was hoping the community might be able to point me in the right direct. https://drive.google.com/open?id=1Y2hYkRG94whLroK20Zmce07jslyRL3zZ I couldn't get the image to load. So above is a link to an image of the problem...

Hello everyone, I am trying to solve this wee problem regarding partial derivatives, and not sure how to do so. The following image shows level curves of some function \[z=f(x,y)\] : I need to determine whether the following partial derivatives are positive or negative at the point P...

Hello all, I have a question relating the drawing of levels curves. The function is: \[f(x,y)=(y-2x)^{2}\] Fairly simple if I may add. In order to draw the levels curves, I did: \[(y-2x)^{2}=k\] which resulted in: \[y=2x\pm \sqrt{k}\] So far so good. So for k=1, I get two straight...

Evaluate $\displaystyle \int_C(x+y)ds$ where C is the straight-line segment $x=t, y=(1-t), z=0, $ from (0,1,0) to (1,0,0) ok this is due tuesday but i missed the lecture on it so kinda clueless. i am sure it is a easy one.

Hey. I really like the topic of Closed Timelike Curve's, they're an interesting subject matter, since they're allowed by certain field equations of GR. I was curious if there is any way (in the future?) we could warp spacetime to create a CTC, and maybe harness it? Could be useful.. ish. Thanks.

[Moderator's note: split off from another thread since this is a separate topic.] I am confused about closed timelike curves. To say that they are possible using an exact solution to the EFEs, like the Godel metric, and that they actually correspond to something in reality is where my confusion...

Homework Statement Calculate the area between ##y = -x^2+3x+10## and ##y = -x+14##. Note that ##y = -x+14## is the tangent to the curve ##y = -x^2+3x+10## at the point ##(2,12)##. Homework EquationsThe Attempt at a Solution Is it as simple as calculating ##\int_{5}^{14} -x+14+x^2-3x-10 =...

I am filling my circular hottub, and charting the water level height. Its sides have a small, constant slope from vertical - i.e. it is a truncated, inverted cone. Imagining an ideal hottub of unlimited height*, the water level will always be increasing - but at a decreasing rate - it will...

Hello All, I need some basic understanding between theory and practical with respect to blowers. Blowers usually come with blower curves which give a relationship between Static Pressure and Flow. Usually, SP is inversely proportional to Flow, as in SP increases as flow decreases. Example of a...

I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to ##\mu(x)## (from https://arxiv.org/pdf/astro-ph/0403610.pdf). The mass discrepancy, defined as the ratio of the gradients of the total to baryonic...

I am reading "Complex Analysis for Mathematics and Engineering" by John H. Mathews and Russel W. Howell (M&H) [Fifth Edition] ... ... I am focused on Section 1.6 The Topology of Complex Numbers ... I need help in fully understanding a remark by M&H ... made just after Example 1.22 ... Example...

I apologize for the simple question, but I have not been able to find the answer. For the inner portion of a galaxy rotation curve (where the outer portion is the part invariant to distance and the inner part is where rotational velocity increases with radius), how much is simply due to...

All variables and given/known data and Relevant equations: So I got the functions for a bottle design (one side with the bottle lying horizontally): 1. y=-1/343x^3+3/98x^2 + 2.5 ; 0<x<7 2. y=3; 7<x<15 3. y=-1/98x^2+15/49x+69/98; 15<x<22 Combined they give the volume of 570.2mL using the volume...

hi please refer to the inline image: What do the stars mean? I can't find a reference or definition elsewhere in my textbook...

How to know if a surface is closed ? Surfaces such as x^(2/3) + y^(2/3) + z^2 = 1 or x^6 + y^6 + z^6 = 1. Is there a way to know if these surfaces are closed ( without the help of a computer program) ? Is there a general way to know if a surface is closed ? What about curves ? How to know if a...

Hello Maths Help Board Users, I was hoping for some guidance on the following problem. Thanks in advance for your contributions and time. "A fish population grew according to the following quadratic model - the number of fish on day t is given by P (t) = 800t - t2" Q) Find the average growth...

g(x)= √(19x) = upper curve f(x)= 0.2x^2 = lower curve Firstly, I found the point of intersection, which would later give the upper values for x and y. x=7.802 y=12.174 Then I found the area under g(x) and took away the area under f(x) to get the area between the curves. 31.67 units^2 This is...

Hello everyone Im new on the forum and I just discovered what are sync machines... I have really basic question what I still cannot figure out.. I did some experiments with motor for different field currents and torques. In the result I measured armature currents and did V curves. But next...

For the following random curves for example. Can you really get one derivative equation that can reproduce all of them? How? Or is it multiple individual derivative equation for each unique curve such that the equations that reproduce the following?

General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.

Homework Statement Let γs : I → Rn, s ∈ (−δ, δ), > 0, be a variation with compact support K ⊂ I' of a regular curve γ = γ0. Show that there exists some 0 < δ ≤ ε such that γs is a regular curve for all s ∈ (−δ, δ). Thus, we may assume w.l.o.g. that any variation of a regular curve consists of...

I know that the generalization of parallel lines to curves in 2D is just "parallel curves", but is there any term which generalizes the idea of skew lines to curves? "Skew curves" doesn't work, this term already being co-opted by statistics. Example: if you had two curves coiling around each...

I'm have trouble understanding a fundamental question of a derivative. So a derivate gives me a tangent line at any given point on a function. this makes sense for me for a function y=x^2 because the derivative is y'=2x which is a straight line function. But what about y=x^3 where the...

Homework Statement Find the area between the parametric curve, x(t)=cos(t), y(t)=sin^2(t) and the x-axis Homework Equations - A = ∫ₐᵇ y(t) x'(t) dt The Attempt at a Solution =http://imgur.com/a/UA48d - My work shown in the link provided without the bounds, sorry for not rotating the image and...

Hello I am interested in the Frenet-Serret Formulas (theory of curves?) relationship to theory of surfaces. 1) Can one arrive to the Frenet-Serret Formulas starting from the theory of surfaces? Any advice on where to begin? 2) For a surface that contain a space curve: if the unit tangent...

Ok, so I'll start off by saying this is NOT a homework problem, but it is a problem I'm having with a project I'm working on, and my supervisor has no clue as to why I'm getting the wrong results from a calculation I'm doing. So as you all reading this likely know, we can model the rotation...

Homework Statement find the slope of tangent line to curves cut from surface z = (3x^2) +(4y^2) - 6 by planes thru the point (1,1,1) and parallel to xz planes and yz planes ... Homework EquationsThe Attempt at a Solution slope of tnagent that parallel to xz planes is dz/dy , while the slope of...

Is it correct to say that the Lorenz curve is the normalized integral of the quantile function with respect to the x-axis?

Homework Statement Match the parametric equations with the graphs. In this case, I am stuck on this equation: x = cos t y = sin t z = 1/(1+t^2) Homework EquationsThe Attempt at a Solution So far I have: x^2 + y^2 = cos ^2 t + sin ^2 t = 1 I know this is a circle in the xy-plane, and thus...