Curves Definition and 778 Threads

  1. karush

    MHB Find the area beween the curves y=x^2 and x+y=2 and the x axis

    Find the area beween the curves $y=x^2$ and $x+y=2$ and the x axis First on graphing these the $x-axis$ seem irrelevant in that it is outside the area to find. y=x^2;y=-x+2
  2. G

    Generalisations of area between two curves

    Homework Statement The problem consists of investigating the area between two functions of the forms (Parabolic segment): : y = mx + c and y = ax^2 + bx + c The investigation involves finding a combination that has one of each of the above functions and finding an area of one. The area...
  3. L

    How do I integrate 2/(1+x^4) to find the area between two curves?

    Find the Area between the two functions. http://www4a.wolframalpha.com/Calculate/MSP/MSP16151chba72gif4040fg0000686h2hea7f943994?MSPStoreType=image/gif&s=54&w=381.&h=306.&cdf=Coordinates&cdf=Tooltips I know the bounds are from x=[-1,1] which gives me the equation... ∫ 2/(1+x4) - x2 dx I...
  4. B

    MHB Plane that is tangent to two curves at an intersection

    Can someone please help me with how to approach/solve this question? construct a plane that is tangent to both curves at the point of intersection. 1st curve: x(v)=3 y(v)=4 z(v)=v 0<v<2 2nd curve: x(u)=3+sin(u) y(u)=4−u z(u)=1−u −1<u<1 My first approach was to find a point of intersection...
  5. M

    Finding the Area Under One Arch of a Cycloid: Where to Start?

    Homework Statement Find the area under one arch of the cycloid x=a(t-sint), y=a(1-cost) Where do I start? I could divide both sides by a and get x/a= t-sint cost=1-y/a If this is the case, how should I deal with x/a=t-sint? I need to get them into the form of sint=... or cost=... right?
  6. M

    Flat galaxy rotation curves without dark matter

    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...
  7. E

    Understanding Gibbs Free Energy Curves: Homework Statement & Equations

    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.
  8. Chemer

    Drawing distribution curves for orbitals

    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.
  9. F

    Why Is My Integration of the Region Between y=2x and y=x^2+3x-6 Incorrect?

    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...
  10. M

    MHB Characteristic Curves: Solving PDEs

    Hey! :o We have the equation $$2u_{xx}-u_{tt}+u_{xt}=f(x, t)$$ This is equal to $$\left (\frac{2\partial^2}{\partial{x^2}}-\frac{\partial ^2}{\partial{t^2}}+\frac{\partial ^2}{\partial{x}\partial{t}}\right )u=f$$ To find the characteristics do we solve the homogeneous equation...
  11. M

    MHB How do we prove the rule for differentiable curves in 3D?

    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...
  12. C

    Curves and tangent vectors in a manifold setting

    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...
  13. M

    MHB Explore Level Curves of $f(x,y)=x^3-x$

    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...
  14. D

    Why are vectors defined in terms of curves on manifolds

    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...
  15. G

    Closed Timelike Curves: Exploring the Boundaries

    [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...
  16. Calpalned

    Level curves, level surfaces, level sets

    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...
  17. Calpalned

    Partial derivatives of level curves

    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...
  18. P

    Plotting of relay current curves

    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...
  19. C

    How does regularity of curves prevent "cusps"?

    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...
  20. Buckethead

    Need data for galactic rotation curves

    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...
  21. S

    Troubleshooting DSC Curves for Metal Alloys to Accurate Interpretation

    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?
  22. A

    What can be found in the MT curves of superconductors?

    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...
  23. theofficialack

    Frictional force for bank curves

    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...
  24. N

    Time Travel to the Past: CTC or Wormhole?

    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.
  25. K

    Curve Matching Techniques for Rotated Curves in Geometric Analysis

    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...
  26. L

    Naive Question regarding Galaxy Rotation Curves

    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...
  27. RJLiberator

    Parametric Equations describing curves

    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...
  28. L

    Understanding Stress-Strain Curves and Force-Extension

    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...
  29. Hyo X

    Find capacitance from nonlinear I-V curves

    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.
  30. J

    Potential Energy/ dipole moment curves

    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...
  31. S

    Understanding Lissajous Curves for Fourier Synthesis

    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...
  32. M

    Minimum Distance between two curves

    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...
  33. T

    What is the area between two polar curves?

    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...
  34. W

    Complements of Curves in Closed Surfaces: Homeomorphic?

    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...
  35. CFDFEAGURU

    ANSYS Mechanical APDL - High Temperature Creep Modeling via Isochronous Curves

    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...
  36. admbmb

    Finding Shortest Distance between two 3d Parametrized Curves

    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...
  37. RJLiberator

    Computer the Volume of a region bounded by 3 curves

    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...
  38. R

    Calculating div(theta) and tangent curves

    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...
  39. E

    Area between two curves; choosing when to integrate with x or y?

    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!
  40. A

    MHB What are the integral curves of vector field V?

    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 +...
  41. julcab12

    Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology

    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...
  42. J

    MHB How do I solve parametric and polar curve problems in Calculus 2.1?

    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)...
  43. P

    Gradient vector perpendicular to level curves?

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

    What Are Closed Timelike Curves in Black Holes?

    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 toroidal region...
  45. J

    A path that curves more sharply (e-)?

    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...
  46. I

    MHB Curves defined by parametric curves

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

    Book suggestions for learning coexistence curves

    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...
  48. I

    MHB Did I Calculate the Length of the Parametric Curve Correctly?

    #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} \...
  49. I

    MHB Length of Curve $y^2=4(x+4)^3$: 13.5429

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

    Plotting Contour Family of Curves

    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...
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