Curves Definition and 741 Threads

Hi everyone..Can anyone help me to solve this problem. Consider a scaler field T(x,y) = (2x+2y) / (x2+y2) How can i find the level equations.

Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...

Homework Statement What is the area between y=x3 and its tangent at x=1The Attempt at a Solution The first derivative of y=x3, which is 3x2, tells me that the slope of the tangent at x=1 is 3. That (1,1) is a point on the tangent line tells me that the equation of the tangent line is y=3x-2...

Hi, Is it true to say on a topological manifold one can always find a unique metric such that a set of non intersecting curves become its geodesics? Is there any way to find that metric? Thanks, Owzhan

Homework Statement Find the area of the region between the two curves. y=\sqrt{x} y=\frac{1}{2}x x=9 Homework Equations The Attempt at a Solution The domain of the region is [4,9]: \int\frac{1}{2}x-\sqrt{x}dx with limits of integration [4, 9]...

When going through topics on melting and freezing, i came across 2 graphs of slightly different curvature for both the heating and cooling of naphthalene. The ending part of the graphs are the ones that confuse me, whether slope upwards or downwards. Most graphs in the internet just show...

Homework Statement Area between curves y=((e^x)-(e^-x))/2 and y=2e^-x for -1 < x < 2 Homework Equations I know the formula is the integral of ( u(x)-l(x) )dx, but I'm having a lot of trouble trying to integrate this. integral from -1 to ln(5)/2: (((2e^-x)-((e^x)-(e^-x))/2))dx + int...

i know if every simple closed curve in D can be contracted to a point it is simply connected as in the case of|R^2 Domain or R^3 it is simply connected but i am not feeling uncomfortable with |R^3 especially with the domains like when x =! 0 and y =! 0 why it is not simply connected? how...

Hi, I'm reading this piece from George Cain & James Harod's multivariable calculus material. Section 4.3, which is about Torsion, says this: I don't understand how he deduces dB/ds is perpendicular to T? Where did I get lost? Following the paragraph, it seems to me that T and N...

Homework Statement The region bounded by the given curves is rotated about x = 10 x=1-y^{4}, x=0 Find the Volume V of the resulting solid by any method. Homework Equations The Attempt at a Solution I'm using the washer method. Not sure if it is being setup properly as I'm getting the...

I looked this up but couldn't find sufficient information on it. What I know is that calibration curves are used to find the concentration of an unknown compound by graphing a series of measurements of a property like light absorbance from standard solutions of that compound. What I don't get is...

Homework Statement A concrete highway curve of radius 60.0 m is banked at a 11.0 degree angle. What is the maximum speed with which a 1500 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.) Homework Equations...

find the area of the region shared by the curves r=6cosx and r=6sinx i know that if you graph those two functions you get two circles, both with radius 3, the first one has its center on the cartesian x-axis and the other has its center on the y axis. i also know that if you draw a line...

I understand that we could think of a null curve in Minkowski space as being the curve c(s) such that the tangent vector dc(s)/ds = 0 at all s. So suppose that we have a curve c(s) = (t(s), x(s), y(s), z(s)) and we want to ask ourselves what conditions would make c a straight line. I guess...

Homework Statement sketch and find the area of the region bounded by the given curves. Choose the variable of integration so that the area is written as a single integral y = x, y = 2, y = 6 − x, y = 0 Homework Equations the usual integral fx - gx from a to b The Attempt at...

Can anyone direct me to a good source of graphs of galaxy rotation curves. I need graphs that show both the observed curve data points and the expected curve along with the names of the galaxies and labeled axis. Thanks

Homework Statement Anyone familiar with orthogonal families of curves? They're not that difficult to understand. If you have a differential equation \frac{dy}{dx} = F(x, y) you can find it's orthogonal family of curves by solving for \frac{dy}{dx} = \frac{-1}{F(x, y)} Homework...

Homework Statement Find the area of the bounded region enclosed by the curves: 6x+y^2=13, x=2y Homework Equations Integration The Attempt at a Solution Finding the area shouldn't be too much of a problem. In this particular problem, integrating with respect to y is the better...

Homework Statement The curves with equations x" + y" = 1, n = 4, 6, 8, , are called fat circles. Graph the curves with n = 2, 4, 6, 8, and 10 to see why. Set up an integral for the length S(2k), the arc of the fat circle with n=2k. Without attempting to evaluate the integral, state the...

Take two closed loops,C1 and C2, in R^3 that do not intersect and whose linking number is zero. Chose two manifolds D1 and D2 whose boundaries are C1 and C2 and which intersect in their interiors transversally and do not intersect anywhere along their boundaries. The intersection is a...

Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...

hi... I am new to this topic and frustrated. I have a curve f(x,y)= -3y/(x2 +y2 + 1) I was asked to draw a level curve of this and I'm not getting anywhere with it. If anyone has any pointers, or can help me with solving this question I would be gretfull. The only other thing this...

Homework Statement After plotting log(I/A) vs E/mV, you get a tafel curve. calculate the exchange current density, Io, the cathodic transfer coefficient ac and the rate constant of the reaction k. Homework Equations The Attempt at a Solution Is it simply, the exchange current...

Homework Statement Find the area of the region R enclosed by the line y=2x−3 and the parabola y2=4x+93. Homework Equations The Attempt at a Solution \int_{-9}^{11} 2x-3 dx~-~\int_{-9}^{11} (4x+93)^0^.^5 /6 dx [x2-3x]11-9 - [(4x+93)1.5 / 6 ]11-9 i get: The area of the...

I want to graph the following parametric curve using matlab: x = 31cos(t)-7cos(31/7)t y = 31sin(t)-7sin(31/7)t 0 ≤ t ≤ 14π This is the code I used: syms t t=[0:1:19*pi] x=31*cos(t)-7*cos(31/7)*t; y=31*sin(t)-7*sin(31/7)*t; plot(t,y,t,x) But the graph which Matlab generated is...

Homework Statement a) r=a(2+ cos(\theta)) Find the area of the region enclosed by the curve giving answers in terms of \pi and a b) Show that the area enclosed by the loop r=2(1-sin(\theta))\sqrt{cos(\theta)} is \frac{16}{3} and show that the initial line divides the area...

Homework Statement Find the area between the two curves: r=2sin(\theta), r=2(1-sin(\theta)) Homework Equations A=\frac{1}{2} \int_{\beta}^{\alpha} r^2 d\theta The Attempt at a Solution I've got the points of intersection at (1,\frac{1}{6}\pi) and...

Homework Statement [/b] Graph the locus represented by the following. \left|z+2i\right| + \left|z-2i\right| = 6 Homework Equations The Attempt at a Solution z = x + iy so z-2i = x + (y-2)i and z+2i = x + (y-2)i So I have: sqrt(x^2 + (y-2)^2) + sqrt(x^2 + (y+2)^2) = 6...

Homework Statement a) Find the area enclosed by the curve r=2+3cos(\theta). b) Find the area enclosed by the curve (x^2+y^2)^3=y^4 (after converting to polar form) Homework Equations The general equation for the area of a sector of curve: A=\frac{1}{2} \int_{\beta}^{\alpha} r^2...

f I consider the area of the family of curves as y = (1 - x^1/p)^n where x is greater than or equal to zero but less than or equal to one, I can write that in as integral as the integral from 0 to 1 of (1 - x^1/p)^n dx but I'm not sure how to write that as a summation, which I have been...

Does anybody know why you hear the train wheel SCREECH when the train makes a curve?

Homework Statement Parabolas with vertex on the x-axis,with axis parallel to the y-axis,and with distance from focus to vertex fixed as "a". the question is pick your own value of "a". Then for "a" value pick value of "h". What does it mean? I'm confuse.. T__T Homework Equations (x-h)²...

What are they? And what does it mean to say that all elliptic curves are modular? Trying to understand Fermat's Last Theorem.

Simple question: can a chi-squared be represented as a gaussian distribution? I'm wondering if I can take some chi-squared numbers that I have and represent them as increasing/decreasing widths of FWHM of a gaussian. Can I?

I need to find the vertical sections and level curves of the function z=max(x,y^{2}) associated with the constants 1,2,3 and 4. I know that the function defined in this way basically means that f(x,y)=x if x\geqy^{2} or f(x,y)=y^{2} if x\precy^{2} But I don't know where to go from here...

I need to find the vertical sections and level curves of the function z=max(x,y^2) associated with the constant 1,2,3,4 so that I can sketch them. I know given z=f(x,y) then the vertical sections of the function are z=f(c,y) where c is a constant and the level curves are c=f(x,y). I've been...

Hello everybody I am new here, so not sure if this is really the right category. Have recorded numerous hysteresis (x-y) curves experimentally and want to average them all out to get one clean master curve. Does anybody know if algorithms exist for that in Matlab or in Excel ? Then a...

fx=3x^3-3x, gx=3x, and hx=9-x. Find the area I kown top - bottom and right - left. but in here i am not sure what to do and what the boundaries are. can some one show me the work how to do this problem? i am kinda confuse how to do this kind of problem with 3 curves. THANK YOU!

Okay so i have a test and so I'm reviewing for it, and one of the questions i came across was: 1. A curve of radius 180 m is being designed in a new highway to allow cars traveling at 70 km/h to round the curve with zero frictional forces. a) At what angle must the road be banked? b) What is...

https://www.physicsforums.com/attachment.php?attachmentid=21003&stc=1&d=1255013927 I need help for number 1(b) State the distance between the two athletes as the winner passes the 100 m mark. Tried to find the are under graph, but does not work. Thanks.

Homework Statement A tank is traveling in a straight line we look at the side on view of the tank and consider its continuous track in contact with the x-axis. Its wheels have radius R and the distance between he centers of the wheels is L (The continuous track is wrapped around the wheels)...

Homework Statement 6. Show that the parametrized curve r=<t+(1/t),t-(1/t),8> lies on the curve f(x, y) = x^2 - y^2 + 4? Show your calculations. 2. The attempt at a solution I don't know where to start. I've just been plugging in random x and y and t values and haven't had any luck...

I think I understand why a vector field must have a unique set of integral curves, but I don't see why they must define a one-parameter group of diffeomorphisms. Let X be a vector field on a manifold M, and p a point in M. A smooth curve C through p is said to be an integral curve of X if...

Homework Statement Why does the lift curve, Coefficient of lift plotted against angle of attack, go through the origin of the graph for some airfoils but not for other airfoils Homework Equations The Attempt at a Solution

"Consider a first order linear PDE. (e.g. y ux + x uy = 0) If u(x,y) is constant along the curves y2 - x2 = c, then this implies that the general solution to the PDE is u(x,y) = f(y2 - x2) where f is an arbitrary differentiable funciton of one variable. We call the curves along which u(x,y) is...

Homework Statement Find the minimum distance between the curves (Parabola) y^2 = x-1 and x^2 = y-1 Homework Equations y^2 = x-1 x^2 = y-1 The Attempt at a Solution Tried to find the distance between their vertex, but the answer was wrong and no where near.

what can be interpret from dispersion curve of phonon?how to find whether a phonon can loose all its energy to a neutron from dispersion curves?are there dispersion curves for other atom apart from phonon?

1.Where did I go wrong in finding the area enclosed inside r = 3 cos θ? Homework Equations I used the formula 1/2 ∫ ((f(θ)) squared dθ from alpha to beta The Attempt at a Solution I looked for the area of the semicircle from 0 to pi and then multiplied the whole thing by 2, since the...

This is a follow up to my previous question, as they appear that in both the Godel Metric and the Van Stockum dust Perhaps a better way to put this is, could there be a model where you had rotation (maybe around a non-symmetrical axis?) and not get these CTCs?

Homework Statement 1. Set up the definite integral that gives the area of the region. (See attachment) f(x) = 3(x^3-3) g(x) = 0 2. Use integration to find the area of the triangle having the given vertices: (0,0), (a, 0), (b,c) Homework Equations The Attempt at a Solution...