Curves Definition and 741 Threads

I need someone with more experience in the field who has knowledge of excel to check over my work. Given the gravitational attraction between two bodies is F = (GMm)/r^2, and the centripetal force required to keep a body in orbit is F = (mv^2)/r, therefore (mv^2)/r = (GMm)/r^2 therefore...

Homework Statement Can anyone explain to me the gibbs free energy curve? Homework EquationsThe Attempt at a Solution [/B] What is the domain of the curve and how should I interpret it?Thanks.

Hi, can anyone please guide me how to draw the distribution curves for radial wave function of an orbital? Please explain stepwise and in easy way. Thanks.

Homework Statement Find the region bounded by y= 2x and y = x^2 + 3x - 6. I found the points of intersection to be x= -3, 2 by setting the equations equal to each other and solving for x. I concluded that y = x^2+3x-6 is bigger since I tried a point in between the points of intersection and it...

Hey! :o How could we prove the following rule for differentiable curves in $\mathbb{R}^3$ ?? (Wondering) $$\frac{d}{dt}[\overrightarrow{\sigma}(t)\times \overrightarrow{\rho}(t)]=\frac{d\overrightarrow{\sigma}}{dt}\times \overrightarrow{\rho}(t)+\overrightarrow{\sigma}(t)\times...

Consider the following definition: (##M## denotes a manifold structure, ##U## are subsets of the manifold and ##\phi## the transition functions) Def: A smooth curve in ##M## is a map ##\gamma: I \rightarrow M,## where ##I \subset \mathbb{R}## is an open interval, such that for any chart...

Hey! :o I have to describe the behaviour, while c is changing, of the level curve $f(x,y)=c$ for the function $f(x,y)=x^3-x$. I have done the following: The level curves are defined by $$\{(x,y)\mid x^3-x=c\}$$ For $c=0$ we have that the set consists of the lines $x=0,x=1,x=-1$. Is it...

What is the motivation for defining vectors in terms of equivalence classes of curves? Is it just that the definition is coordinate independent and that the differential operators arising from such a definition satisfy the axioms of a vector space and thus are suitable candidates for forming...

[Mentor's note: split from https://www.physicsforums.com/threads/gravity-instantaneous.801033/ ] If masses can not just appear and disappear, how do solutions with closed timelike curves work? If you have some mass happily looping around such curve, from some other point of view you have some...

Homework Statement I know that the equation ##z = f(x,y)## gives a surface while ##w = f(x, y, z) ## gives an object that has the same surface shape on top as ##z = f(x,y)## but also includes everything below it. If these statements are correct, what is the level surface of a function of three...

Homework Statement Let ##C## be a level curve of ##f## parametrized by t, so that C is given by ## x=u(t) ## and ##y = v(t)## Let ##w(t) = g(f(u(t), v(t))) ## Find the value of ##\frac{dw}{dt}## Homework Equations Level curves Level sets Topographic maps The Attempt at a Solution Is it true...

When Plotting relay current curves using log paper, I understand that all curves should be plotted on a common base voltage (converting currents accordingly) and the curves can be cut at the maximum fault current level that the device is likely to see (corrected to the base current). What I...

A regular curve on a manifold ##M## is a curve ##\gamma:I \to M## such that ##\dot \gamma(t) \neq 0## for any ##t \in I##. In John Lee's "Introduction to Curvature" he says that this intuitively means that we prevent the curve from having "cusps" and "kinks". How can I see that this is the...

I'm looking for sources of data for galactic rotation curves but need not only the observed rotation curves but also the expected (Keplerian) curve data to load into a spreadsheet to experiment with. After extensive searching I found a few pockets of data for observed velocities but not for...

I have now idea how can I interpret these DSC curves (they are curves of metal alloys with different composition). But the first question is: are they made properly?

I am confused about the magnetic susceptibility vs. temperature curves (or MT) of superconductors (SCs). In the normal conduction state (I measured from 4.5K to 300K), the susceptibility curve can obey the Curie-Weiss law. But when I fitted the data via the Curie-Weiss law in a different...

Homework Statement A 1453kg car rounds a curve of 122-m radius at a speed of 48 km/h. How large must the force of friction between tires and pavement to prevent the car from skidding? Homework Equations F=(coeficient)mg Net force=Ff+Fcen*cos (-) +mgsin(-) tan(-)=(v)^2 / grThe Attempt at a...

In theory, is time travel to the past possible by traveling completely around the loop of the CTC (where it would seem future links with its own past) or is a wormhole the only way to time travel by way of short cutting the CTC.

I need to perform geometry matching of curves (see http://www.tiikoni.com/tis/view/?id=c54d9b8 ). As it can be seen, the big problem is that curves might be rotated, though they have similar shape. Do I need to make curve fitting and look at the parameters of analytical models? But, I guess...

Many apologies in advance if this question is ridiculous or if it has already been answered on another thread. I've searched and searched through the forums and haven't found the answer - please do direct me accordingly if that's possible. If not - please help! Preamble: We know from...

Homework Statement Homework EquationsThe Attempt at a Solution For part A) my answer was:[/B] \int_a^b \sqrt{(dx/dt)^2+(dy/dt)^2}dt The work I used for part A was based off this sites explanation: http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength.aspx For part B) I simple took...

So a stress-strain curve: σ on the x-axis and ε on the y axis. σ = F / A and ε = ΔL / L of course, L is a constant, and A is a constant if the material can be assumed to not-deform. Can a stress-strain curve therefore be thought of as a force-extension curve? i.e. essentially F on the x-axis and...

I have some experimental circuit element that exhibits both resistance and capacitance, and results in nonlinear I-V curves. can i extract capacitance and resistance of this element just from the I-V curve? or do I need time-axis data? a suggestion on what equation to use to fit this data? thanks.

Hi, I wasn't sure if this is more Physics/Astro or chemistry because its actually all 3. i've got some conceptual issues with some tasks at hands, and was wondering if anyone could clear that up for me. (These questions are all regarding molecules) 1) How do you create a potential energy...

i have a question about Fourier synthesis and how this relates to lissajous curves. I have two sets of test data; spatial data in the x and y directions. When I plot the x data against the y I get an ellipse. ( it represents a wing moving in a circular motion) I am trying to recreate this...

Minimum Distance between y^2=4x and x^2+y^2-12x+31=0. Attempt:I got that the parabola has vertex at(0,0) and focus at(1,0).The Circle is centred at (6,0)and its radius is sqrt 5.I figured that the double ordinate that passed through (6,0) would be bisected at the point.So I found out the chord...

Homework Statement Find the area inside one loop of r = 2cos(3 theta) and outside the circle r = 1 Homework EquationsThe Attempt at a Solution I need to clarify something about the limits of integration. I found the intersection of the two curves to be at an angle of pi/9. This is how I...

Hi, let ## \alpha, \gamma ## be non-isotopic curves in a compact, oriented surface S. There is a result to the effect that ## S-\alpha## is homeo. to ## S- \gamma ## . This is not true as stated; we can , e.g., remove a disk (trivial class) in a copy of S and then remove a meridian ( a...

ANSYS can be used to model creep in a number of different ways. If you are designing to ASME Section VIII, Div., 2 you might have to verify that your design meets the "shake down to elastic action" criteria. Basically, that means that the strains do not continue to increase over the number of...

So I have two parametrized equations for two different 3d curves: Rm(t) = (1.2*sin(2πt) + 0:3)i + t4j + 1.1cos2(2π(t + 0:2))k and R(t) = Sin(2πt)i + t3j + Cos2(2πt)k I need to figure out if these two curves come within a certain distance of each other (0.5). I cannot understand how to find...

Homework Statement Let R be the region in the first quadrant bounded by all three of the curves x = 2, y = 1, and y = (x−4)^2. Compute the volumes V1, V2, and V3 of the solids of revolution obtained by revolving R about the x-axis, the y-axis, and the x = 5 line, respectively. FIRST, I...

Homework Statement Calculate ∇Θ where Θ(x)=\frac{\vec{p} \cdot \vec{x}}{r^3}. Here \vec{p} is a constant vector and r=|\vec{x}|. In addition, sketch the tangent curves of the vector function ∇Θ for \vec{p}=p\hat{z} (b) Calculate ∇ (cross) A → \vec{A}=\frac{\vec{m}x\vec{X}}{r^3} m is...

Hello! I'm having some trouble determining, when trying to find the area between two curves, when to integrate with respect to y or respect to x, given two equations only? Thanks!

My problem is this: Find the integral curves of $\textbf{V} = (log(y+z),1,-1)$. I first set up the system: \frac{dx}{log(y+z)} = \frac{dy}{1} = \frac{dz}{-1} I have two find two curves, $u_1$ and $u_2$ that work as integral curves. The first, and most obvious, function is $u_1(x,y,z) = y +...

http://arxiv.org/abs/1402.2158 Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology Yuri I. Manin, Matilde Marcolli (Submitted on 10 Feb 2014 (v1), last revised 9 Jul 2014 (this version, v3)) We introduce some algebraic geometric models in cosmology related to the...

Hey Everyone! I have three questions that I do not know how to approach/solve. I've been checking online, the textbook, etc, and nothing. This is Calculus 2.1. Find the points with the given slope. x=9cos(theta), y=9sin(theta), slope = 1/2. Answer: (-9rt5/5, 18rt5/5), (9rt5/5, -18rt5/5)...

Homework Statement can anyone explain/prove why the gradient vector is perpendicular to level curves? Homework Equations The Attempt at a Solution

[SIZE="4"]Definition/Summary In mathematical physics, a closed timelike curve (CTC) is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point. 'Inside the inner horizon (of a charged/rotating black hole) there is a...

Homework Statement Electron A is fired horizontally with speed 1.00 Mm/s into a region where a vertical magnetic field exists. Electron B is fired along the same path with speed 2.00 Mm/s. Which electron has a path that curves more sharply? A does. B does. The particles follow the same...

eliminate the parameter to find a cartesian equation of the curve. $x=sin\frac{1}{2} \theta$ $y=cos\frac{1}{2} \theta$ $-\pi \le \theta \le \pi$ $x=e^t-1$ $y=e^{2t}$

I haven't studied material science anymore after high school and I do not know what is coexistence curves to answer this question. Can anyone suggest any book giving a good background of the concept coexistence curves? I searched the web and cannot find a good book suggestion and a good...

#1 find the length of the curve $x=3t^2$, $y=2t^3$, $0\le t \le 3$ $L=\int_{\alpha}^{\beta} \ \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}dt$$\frac{dx}{dt}=6t$ $\frac{dy}{dt}=6t^2$$L=\int_{0}^{3} \ \sqrt{(6t)^2+(6t^2)^2}dt$ $=\int_{0}^{3} \ \sqrt{6t^2+6t^4}dt$ $=\int_{0}^{3} \...

$y^2=4(x+4)^3$ $0 \le x \le 2$ $y=2(x+4)^{3/2}$ $y'=3(x+4)^{1/2}$ $\int_{0}^{2} \ \sqrt{1+9(x+4)},dx = 13.5429$ is that right?

Homework Statement So basically here's what the code is supposed to do: L(T_e) = 10^{-9} (T_e - 0.1) Z_{lcr}(T_e) = \left ( \frac{1}{R} + \frac{1}{10^9 iL} + 0.1i \right )^{-1} Z_{load} (T_e) = Z_{lcr} - 0.01i \Gamma (T_e) = \frac{Z_{load}(T_e) - Z_0}{Z_{load}(T_e) + Z_0} The...

y = tan 3x, y = 2 sin 3x, −π/9 ≤ x ≤ π/9 It's looking for the area in blue there. Now obviously the -pi/9 to 0 is one region, then 0 to pi/9 is the other, but presumably you could find the area of one then double it (which is what I tried to do) but it wasn't right. The incorrect answer I...

I am reading the book, "Introduction to Plane Algebraic Curves" by Ernst Kunz - which the author claims gives a basic introduction to the elements of algebraic geometry. The opening few paragraph of Kunz' text reads as follows:I am puzzled by Kunz statement: "$$ \mathbb{A} (K) := K^2 $$...

The IPCC uses a figure 1.2°C for the direct response to a doubling of CO2, from 280 ppm to 560 ppm. http://www.grida.no/climate/ipcc_tar/wg1/pdf/tar-01.pdf I came up with an equation of 4(log 560)-4(log 280)= 1.2041199. Is this the best way to fit this curve?

This paper experimentally simulates Closed Timelike Curves (CTC) through quantum optics experiment. Since I have no experience/background in this, I found it hard to understand how exactly the CTC is implemented in the circuit. [Note: I do understand QM, so no need to explain this].

Determine the area between: 1.) y=((secx)^2)/4 and y=4(cosx)^2 2.) y=e^x , y=e^-4x , and x=ln4 3.) y=5cosx and y=5cos(2x) for 0≤x≤pi

Homework Statement Obtain the differential equation of the family of plane curves described: Circles tangent to the x-axis. Homework Equations (x-h)^2 + (y-k)^2 = r^2 The Attempt at a Solution I tried to answer this question using the same way I did on a problem very similar to this...