Curve Definition and 1000 Threads

Can a potential energy curve be vertical ?

Morning all, Got some feedback on some recent work I submitted, and I've only gone wrong on one calculation (Woo!) - however I have no idea where for this one question. The Question is as follows: Find the area between the curve y=x² - x - 2 and x-axis in the range y=-3 to x=5. Here is how...

Hiya again, I am trying to solve this problem, I thought I got somewhere, but kinda stuck. The graph of y^2=x^3 is called a semicubical parabola. Determine the constant b so that the line y = -(1/3)x+b meets this graph orthogonally. I found the derivative of the curve by using implicit...

This is one I haven't worked out a solution for yet. It's probably not too hard. Hopefully someone can provide a clear explanation. http://rickmckeon.com/mathfun/puzzles/The%20Durango%20Curve%20Problem.pdf rick123

Hello! I came across Jordan Curve Theorem while reading something on Complex Analysis. I don't know much about topology and I apologize if my questions is silly, but from what I understand the theorem states that a closed curve in the complex plane separate the plane into an inner region and an...

Homework Statement http://i.imgur.com/In40pGm.png Answer: C Homework Equations f'(x)=slope=(y1-y2)/(x1-x2) The Attempt at a Solution I can't even list a valid formula for that... like I tried to integrate f'(x), but f(x) is with y so I don't think I am thinking in the right direction. What...

Hello all! I'm just wanting a quick clarification on how finding the area under a polar graph works. Say we have the polar graph of ##r\left(\theta \right)=\frac{\arctan \left(2\theta \right)}{\theta }## as shown below: I know that the area under the graph between ##0## and ##\frac{\pi...

According to the Einstein field equations, matter and energy both curve spacetime. I'm wondering how magnetic fields contribute to the curvature of spacetime. I have a few questions: 1. Does a magnetic field in a current-free region of a curved spacetime still satisfy Laplace's equation? Or is...

Hi. For a state of nitrogen in which temperature is higher than the critical temperature the state is presented on a different curve. I do not remember any curve for superheated region. Source: Introduction to Engineering Thermodynamics by Sonntag/Borgnakke. Thank you.

My understanding of the distribution curves is very basic but I do have a couple of somewhat generic questions. I looked up a number of definitions but have had a hard time finding these specific answers: - Is there an agreed on minimum number of samples that one needs to take to deem a result...

Homework Statement The curve ##C## has polar equation ## r\theta =1 ## for ## 0<\theta<2\pi## Use the fact that ## \lim_{\theta \rightarrow 0}\frac{sin \theta }{\theta }=1## to show the line ## y=1## is an asymptote to ## C##.The Attempt at a Solution **Attempt** $$\ r\theta =1$$ $$\...

Hi there, I was wondering if someone could help clarify something for me. I am using excel to find the area under a curve. I am using the : (B1+B2)/2*(A2-A1) equation to do it. However, due to the nature of the graph, all the value I am getting are negative. The values on the X axis decrease...

Homework Statement Why, in: $$\frac{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}{n^{3/2}}$$ There is ##~n^{3/2}## in the denominator? Homework Equations The Attempt at a Solution it should be: $$S_n=\sqrt{c_1}\Delta x+\sqrt{c_2}\Delta x+...=\Delta x\cdot \sqrt{\Delta x}+\Delta x\cdot \sqrt{2\Delta...

Hi how can i plot a curve (red curve at this example) like this:

In integral calc, you add up very small areas to find the total area under the curve. So it would be f(x1)Δx + f(x2)Δx+ ..., summed up. But what if you wanted to find out the sum of all heights under the curve? So it would be something like f(x1) + f(x2) + ... I'm thinking the formulation would...

Homework Statement Find the line tangent to the curve f(x)=0.5x2+3x-1 which is parallel to the line g(x)=x/2+0.5 Homework Equations f'(x)=x+3 The Attempt at a Solution I know it involves taking the derivative of f(x) and using it somehow, but I don't know where to go from there.

I'm looking at different ways to express the derivative a curve, like circular and tangent/normal components. Is there no such way that let's you express a vector integral in terms of information from the vector you want to integrate?

Is the derivative of a function everywhere the same on a given curve? Or is it just for a infinitesimally small part of the curve? Thank you for the answer.

Hello I am doing research on kinematic and dynamic scattering of xrays on a crystals. I am attempting to simulate the diffraction patterns of a silicon substrate and I have already simulated two other layers of a Silicon Quantum Well and SiGe from which the hetero structure was composed of. In...

Homework Statement For what values of c is there a straight line that intersects the curve ##y = x^4+c x^3+12x^2-5x+2## in four distinct points ? Homework Equations Concept of concavity, Vieta's formulas (link) The Attempt at a Solution Suppose a straight line ##y = mx+b## intersects this...

Given that an unstable particle has a constant probability of decaying per unit time, why is it said that its chance of surviving falls exponentially?

Homework Statement Find the equation of the tangent line to the curve ##\ xy^2 + \frac 2 y = 4## at the point (2,1). Answer says ##\ y-1 = -\frac 1 2(x-2)## And with implicit differentiation I should have gotten ##\frac {dy} {dx}= -\frac {y^2} {2xy-\frac {2} {y^2}}## Homework Equations ##\...

Hello, I am doing a physics exam, where I have chosen to create a Brachistochrone curve, and perform various tests on it. Furthermore, I also have to write a physics report, containing the theory behind the curve, but I am not 100% sure what some of the theories behind the curve are. I suppose...

Quick question. I know that if we have a curve defined by ##x=f(t)## and ##y=g(t)##, then the slope of the tangent line is ##\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}##. I am trying to find the second derivative, which would be ##\displaystyle \frac{d}{dx}\frac{dy}{dx} =...

The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...

Homework Statement Let γ be a regular closed curve in Rn. Show that there is a regular homotopy Γ through closed curves with Γ(−, 0) = γ and Γ(−, 1) an arclength parametrization of γ Homework EquationsThe Attempt at a Solution Hey guys, I just posted another question about homotopy but often...

Homework Statement Show that regular homotopy of regular curves γ : I → Rn is an equivalence relation, that is: i) γ ∼ γ (where the symbol ∼ stands for “regularly homotopic”); ii) γ ∼ γ˜ implies ˜γ ∼ γ; iii) γ ∼ γ˜ and ˜γ ∼ γˆ implies γ ∼ γˆ (here you have to use a smoothing function)...

Homework Statement Find the unit vector perpendicular to the level curve of f(x,y) = x2y-10xy-9y2 at (2,-1) Homework Equations Gradient The Attempt at a Solution I'm not sure what it's asking. Wouldn't this just be the gradient of f(x,y) evaluated at (2,-1) then normalized? or am I missing...

Homework Statement Provide a complete proof that a regular plane curve γ : I → R2 can near each point γ(t0) be written as a graph over the tangent line: more precisely, there exists a smooth real valued map x → f(x) for small x with f(0) = 0 so that x → xT(t0) + f(x)JT(t0) parametrizes γ near...

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...

The definitions of the winding number, that I have found, do not consider the case in which the point lies over the curve. Is there the winding number undefined ? I'm interested in this issue because I'm writing an algorihm for polygon offsetting that as first step creates a row offset polygon (...

Homework Statement [/B] This is a problem from my Differential Geometry course A velociraptor is spotting you and goes after you. There is a shelter in the direction perpendicular to the line between you and the raptor when he spots you. So you run in the direction of the shelter at a...

Homework Statement Let γ : I → Rn be a regular smooth curve. Show that the map γ is locally injective, that is for all t0 ∈ I there is some ε > 0 so that γ is injective when restricted to (t0 − ε , t0 + ε ) ∩ I. Homework Equations The Attempt at a Solution [/B] So I know a function (or a...

Homework Statement Let γ : I → ℝ2 be a smooth regular planar curve and assume 0 ∈ I. Take t ≠ 0 in I such that also −t ∈ I and consider the unique circle C(t) (which could also be a line) containing the 3 points γ(0), γ(−t), γ(t). Show that the curvature of C(t) converges to the curvature κ(0)...

Homework Statement Show that the length of a curve γ in ℝn is invariant under euclidean motions. I.e., show that L[Aγ] = L[γ] for Ax = Rx + a Homework Equations The length of a curve is given by the arc-length formula: s(t) = ∫γ'(t)dt from t0 to tThe Attempt at a Solution I would imagine I...

Homework Statement The problem is described in the picture I've attached. It is problem number 6. Homework Equations Tangent line of a curve Length of a curve The Attempt at a Solution I don't know why I'm so confused on what seems like it should be a relatively straightforward problem, but I...

Homework Statement The problem statement is in the attached picture file and this thread will focus on question 7 Homework Equations The length of a curve formula given in the problem statement Take a polygon in R^n as an n-tuple of vectors (a0,...,ak) where we imagine the vectors, ai, as the...

Homework Statement I have the following data which I would like to model using an exponential function of the form y = A + Becx. Using wolfram mathematica, solving for these coefficients was computed easily using the findfit function. I was tasked however to implement this using java and have...

In an AC circuit with only a capacitor this diagram represents the relation between the current and the voltage in it (the current leads the voltage by 90 degrees). and because: (I= dQ/dt) and ( Q=C*V) where: Q is the amount of charge, C is the capacitance and V is the potential difference...

Consider an algebraic variety, X which is a smooth algebraic manifold specified as the zero set of a known polynomial. I would appreciate resource recommendations preferably or an outline of approaches as to how one can compute the period matrix of X, or more precisely, of the Jacobian variety...

Homework Statement Homework Equations Reluctance = small "L"/mu*A The Attempt at a Solution I went the route of using B/H=Mu ...since we know that B=1.2Tesla's and Mu=4pi*10^-7 we arrive at our "magnetic field intensity "H" as 954,929.7 H" BUT if I am trying to find Reluctance...

What does the distribution curve of IQ in the world population look like? If the average IQ for all countries is 90 (Richard Lynn and Tatu Vanhanen “IQ and the Wealth of Nations”), with an average IQ for sub-Saharan Africans of 70, I suppose that the distribution curve is higher on the downside...

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.

Homework Statement Homework EquationsThe Attempt at a Solution The answer is F. I don't how to get this. I know that it is perpendicular and must have a horizontal tangent. How do I come to this answer?[/B]

Hi, so I am learning how to parametrise curves. For the curve y^2=16x, I have said let x=t^2. Then, we can say y^2=16t^2, so that we can take the root of this and get y=4t. What I wanted to ask was do we have to say "plus or minus" in front of the 4t, or do we just leave it as positive to get...

What is the equation for a curve where x approaches infinity as y approaches infinity?

Hi I have some data from a gamma spectroscopy lab and using a series of known radioactive sources I obtain a calibration curve. The equipment is a scintillation crystal coupled to a photo-multiplier tube connected to a multi-channel analyser to obtain an energy spectrum. Using Excel I add a...

Homework Statement A compound bow in archery allows the user to hold the bowstring at full draw with considerably less force than the maximum force exerted by the string. The draw force as a function of the string position x for a particular compound bow is shown in (Figure 1) . Part A How...

They want the curve in inequality form which i am not sure if i got it right

Homework Statement http://prntscr.com/czocek Homework EquationsThe Attempt at a Solution Okay, so the things I know before hand is that f'(x) = 4x^3 however, my question is since the problem states that the line that passes through (-1.25, -8) is tangent to the curve, wouldn't it have to...