Curves Definition and 741 Threads

Homework Statement length of curve r=(1+cos(2 theta))^(1/2) from -pi/2..pi/2 Homework Equations L= integral sqrt(r2+(dr/d(theta))2 dr/d(theta)= -sin(2theta)-sin(2theta)cos(2theta) The Attempt at a Solution this integral seems ways to complicated is there something to simplify it...

I had a first recently. Took an exam for which there was a 5 point curve. What surprised me was that not only was the five points added to everyone's score but also to the total points available. :confused: Is that normal? For me, it increased my grade by two tenth's of one percent.

Homework Statement Find the length of the curve x=y2/3, 1≤y≤8 Homework Equations i want to see if i set this up right. and if so then how did i get started on this integral. seems really hard...The Attempt at a SolutionL= ∫ (from 1to 8) √(1+2/3y-1/3)dy

I've ready about how they don't fit the expected and all that dark matter thing, so I'd like to know what kind of variability of those curves in function of some paramete3r has been found. For example - Is it known if it varies with the galaxy's age?

The problem and attempt at solution is attached in the word document. I think I have it right but I'm not sure about the upper and lower bound.

Homework Statement Find the area enclosed by the curves: r=\sqrt(3)cos(\theta) and r=sin(\theta) Homework Equations The area between two polar curves is given by: A=(1/2)\int{R^2 - r^2dr} where R is the larger function and r is the smaller function over an interval. The Attempt at a...

Hi all, I'd like to plot a family of curves corresponding to different values of an integer n (eg. sin(nx) for n=1,2,3...) on a single graph, along with some kind of indication as to what value of n each curve corresponds to. I'm using the command Plot[Evaluate@Table[Abs[P[-t, n]], {n, 3...

Homework Statement Given \mathbf{F} = \nabla f\; where \;f(x,y) = sin(x-2y) Find a curve C that is not closed and satisfy the equation \int_C \mathbf{F}\cdot dr = 0The Attempt at a Solution \nabla f = \;<cos(x - 2y),-2cos(x-2y)> So to satisfy the dot product being 0 (I am hoping I can do...

Trying to solve a bi-quadratic eq. so I can graph in in x and y , but Z means this is a 3-D graph? , is it possible to have a overlapping graph or any ideas?? X= +100 &-100 Z= a + bX + cX² + dY + eY² + fXY

Homework Statement For \mathbb{R}^{3} find the integral curves of the vector field B = xy\frac{\partial }{\partial x} - y^{2}\frac{\partial }{\partial y}. Homework Equations The Attempt at a Solution I am having a hard time understand just how to set up the differential equations in order to...

Homework Statement Find the area of the region inside the lemniscate r^2 = 2sin(2\theta) and outside the circle r = 1 It sucks because I wish I could post a graph, but the graph on my calculator looks like a circle around the origin with radius 1, with an infinity symbol going diagonally...

Homework Statement Two curves are perpendicular f(x)= x-4/x and h(x)= x+2/x^2-4x intersect at (2,-1). How would i find if they are perpendicular i first found the derivative of the equations by using the quotient rule but i do not know what to do next.

Say we had a material which contains nanoparticles with uniaxial magnetic anisotropy - single domain "Stoner-Wohlfarth" particles. If you know what I'm talking about then you might be familiar with "field-cooled" and "zero field-cooled" curves, where the material has its magnetization plotted as...

Homework Statement I was given the following level curve (image is attached). I need to find the critical points and classify them (local max, min, saddle). The Attempt at a Solution I can find the points easily enough. Saddle at (-1,0), and then locals at each of the three...

Homework Statement Consider the line and plane below. x = 5-5t, y = 3+7t, z = 10t ax + by + cz = d Find values of a, b, c, and d so that the plane is perpendicular to the line and through the point (2, 1, 2). Homework Equations Fgrad=(x',y',z') is perp to surface if...

Usually spectral lines of spiral arms are corrected for the angle of the galaxy plane with respect to our line of sight to give a velocity curve. I guess this works except in the case when the galaxy is exactly "face-on" from our view (at 90 degrees angle from our line of sight) where no Doppler...

Homework Statement Consider a coordinate transformation from (t,x) to (u,v) given by t=u\sinh vx=u\cosh v Suppose (t,x) are coordinates in a 2-dimensional spacetime with metric ds^2=-dt^2+dx^2 Sketch, on the (t,x) plane, the curves u=constant and the curves v=constant.Homework Equations None...

Homework Statement Hi, my teacher gave me this homework assignment and I'm having trouble graphing this one graph. I don't understand her notes that well and am having trouble getting the equation for this graph. See attached for the graph. The graph is a inner loop that is turned...

Homework Statement Fine the area of the region inside the polar curve r=4sin(theta) and outside the polar curve r=2. Homework Equations area under polar curve = 1/2 integral (a,b) r^2 d\Theta The Attempt at a Solution I set up the integral like follows: integral (0,pi/2)...

Homework Statement Let G be a smooth Lie group with Lie algebra \mathfrak g . Consider a curve X: [t_0,t_1] \to G whose dynamics are given by \frac{dX}{dt}(t) = H X(t) for some H \in \mathfrak g . Show that this equation is well defined for all time. The Attempt at a Solution Okay, so...

So in my mechanics of materials class we were taught about stress-strain curves. I asked a couple of times for the meaning of the broken diagonal line on the graph but no one seemed to give me a logical answer so I decided to ask here.

lets say i have a parameterized curve r(t) if i do r'(t), is it the same as if i were to do a partial differentiation of d/dx d/dy d/dz ? so i get r'(x,y,z) = (dr/dx, dr/dy, dr/dz) ? that means these all discribe the tangent line to the curve right? thanks

I have a question about the Remark on the page posted. When it says "If γ and all its derivatives take the same value at a and b, there is a unique way to extend γ to a (b − a)-periodic (smooth) curve γ : R → R^n" what does this exactly mean? I suppose that the condition that the derivatives...

Homework Statement http://images3a.snapfish.com/232323232%7Ffp733%3B%3B%3Enu%3D52%3A%3A%3E379%3E256%3EWSNRCG%3D33625%3B9674347nu0mrj Find the area s between the curves: y^{2}=x 2y=x x=16 Homework Equations The Attempt at a Solution So i am rather certain that I...

Homework Statement sketch and find the area : y=X^3, Y=X, X>/ 0 Homework Equations The Attempt at a Solution I'm getting pi(1/10) but the right answer is 4pi/21 so can anyone explain to me what am doing wrong? thankx

Hello, I'm investigating duality for plane curves, and I came across an 'original' interpretation of the Biduality theorem , that uses the notion of caustic curve. Because everything is still very obscure to me, I try to share the whole with you, in the hope that we can help to fix ideas...

Homework Statement a = (y^3 + y)dx + (xy^2 + x)dy = A1dx + A2dy Characterise the set of points in R2 which can be joined to (1,1) by a null curve. Homework Equations If v = z(t) is a piecewise continuous curve, and dv/dt lies in the null space of [A1(x(t)),A2(x(t))] then it is a null curve...

Homework Statement At time t, a comet has the position R = (t2-1)i + 2tj At t = 2, find the radial and circumferential components of velocity and acceleration Homework Equations Vr = V * Ur Vθ = V * Uθ ar = a * Ur aθ = a * Uθ Ur = cosθ i + sinθ j Uθ = -sinθ i + cosθ j...

I'd like to have someone explain to me the purpose of the variable change in the proof of the following theorem: A parametrized curve has a unit-speed reparametrization if and only if it is regular. Proof: Suppose first that a parametrized curve γ: (a,b) → R^n has a unit-speed...

Homework Statement find the area bounded by : 4x+y^2=12 x=y Homework EquationsThe Attempt at a Solution f(x)= √4x-12 g(X)= x √4x-12=x √3x-12=0I'm lost how am i supposed to set them equal to each other if the second equation is y=x? can anybody help me please

Homework Statement find the area bounded by: y=X^2-2x y=X+4 Homework Equations HERE'S A LINK TO THE PROBLE: http://picasaweb.google.com/luaykhouri/UntitledAlbum# <embed type="application/x-shockwave-flash" src="http://picasaweb.google.com/s/c/bin/slideshow.swf" width="288" height="192"...

A curve in space is specied by the one parameter set of vectors x(t). Also given is a surface in space parameterised by x(u, v): x(t)= <2+t, -t, 1+3t2> x(u,v)=(u2 - v + u, u+5, v-2> A) Show that the curve intersects the surface in exactly two points. Show that xi = <4 - \frac{\sqrt{46}}{2}...

Homework Statement Find the area of the indicated region. Enclosed by y = e^x, y = 2, and the y-axis The Attempt at a Solution So I the area should be integral of e^x - 2 which = e^x - 2x . I'm not sure what to do with the y-axis it mentions?

Hi All, I have been battling with this question for a while. Given a conservative vector field, we know that there are infinitely many closed paths where the line integral evaluated is zero. In fact this is the requirement for a conservative vector field: Every line integral of any closed...

I looked in my james stewart book and didn't find any thing helpful about that and google didn't give me any useful results so is it possible and how to?

Homework Statement Hi all, I am trying to plot multiple curves in matlab. If i have the function: y=x^i where i goes from 1 to 10. I want to plot the function y for each i. Homework Equations The Attempt at a Solution x=[1 2 3 4 5 6 7 8 9 10] for i =1:10 y = x.^i end...

Find the area bound between y2 = x + 5, and y2= 3 - x.I can't figure out how to put limits of integration, the integrand, or really anything besides just the integral sign to work with Latex, so bear with me (or better yet, direct me to a tutorial! I will search for one after this post, if there...

these are fairly simple questions that only require you to plot points and then find a Cartesian equation of the curve. My question is when trying to solve for the Cartesian Equation, whether to solve for X first or Y? I will give an example. X=3t-5 , y=2t + 1 Graphing this is simple...

my question might be simple but my professor didn't really explain this.. how do you know what function to subtract from what to find the area between the two graphs.. i know you use integrals of f(b)-g(a) and f(b) is the function that is above g(a) but how do you find it out for complex...

Hi everyone. I came across this site yesterday during some targeted Googling and thought I'd give it a shot. I have a basic question about speed/torque curves for brushless DC motors. I would like to compute a speed/torque curve for a small three-phase brushless DC motor that I have. It...

Homework Statement A wire lies along the piecewise linear curve extending from the point (4,3) to the point (6,15) to the point (12,15). If the density of the wire is given by (xy)=3xy+2y, use a line integral to find the mass of the wire. Homework Equations The Attempt at a Solution...

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

1. Let R be the region bounded by the curves y = x2 and y = x + 2. (a) Sketch the region R and label the points of intersection between the two curves. (b) Suppose we rotate R about the x-axis. Compute the volume of the resulting solid. (c) What is the volume of the solid obtained by rotating...

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

Homework Statement f(x,y)=y-x i) compute the gradient ii) at the given point (2,1) compute the gradient vector gradf(2,1) iii) compute the level curve that passes through the point (2,1) iiii) on the xy-plane, sketch the level curve from iii and the gradient vector gradf(2,1) you found in...

we represent electromagnetic waves by sinosoidal curves. magnitude of what changes sinosoidally? or what does that represent?

Please guys i have only one shot and I tried but i couldn't her is the prblem http://img87.imageshack.us/img87/5229/27745883.jpg My Try: [PLAIN][PLAIN]http://img806.imageshack.us/img806/9801/scan0002y.jpg

Homework Statement two particles travel along the space curves r1(t)=<t, t2, t3> r2=<1+2t, 1+6t, 1+14t> Do the particles collide? Do their paths intersect? [b]2. Homework Equations if vector r(t)=<f(t), g(t), h(t)>, then lim r(t) t-->a = <lim f(t)t-->a, lim g(t)t-->a, lim h(t)t-->a>...

Homework Statement Using the domain 0 < x < pi sketch the two functions y=2sin(x/3) and y = 2x/pi on the same axes. Find the area Homework Equations The Attempt at a Solution I have sketch the graphs. And attached my working so far - can someone confirm my workings so far...

Homework Statement Find the area of the lemniscate r2=6cos(2w) located to the right of the line r=3/2sec(w). Homework Equations Area of a polar region is the integral from a to b (in this case a and b are where the curve intersects the line, I believe) of 1/2*r2d(w). The Attempt at...