Curves Definition and 778 Threads

I have to solve the differential equation (y')^2= 4y to verify the general solution curves and singular solution curves. Determine the points (a,b) in the plane for which the initial value problem (y')^2= 4y, y(a)= b has (a) no solution , (b) infinitely many solutions (that are defined for...

Answers Vmax = 13.1 m/s Vmin = 8.1 m/s ------------------------------------------------------------------------------------------ I've spent all morning attempting part 4 of this problem :/ Can someone help me please? FBD tanθ = v2 / rg v = sqrt(rg)tanθ = sqrt [(20)(9.8)tan30] =...

Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...

Homework Statement Hello everyone, I was wondering if someone could check my work on this problem as I'm not sure it's right. I'm in Calc II right now and we are doing finding volume bounded by curves rotated around an axis. So, here is the problem, y=cos(pix)+1, y=4x^(2)-9, x=0; about...

The definition of parallel curve is well defined, such that given two curves, they must remain equidistant to each other. For instance y = (x^2) + 4 and y = (x^2) - 8 are parallel curves in a function the maps x to y. These form parabolas whose vertical distance to one another remains...

Homework Statement Find the arc length of the following curves on the given interval by integrating with respect to x y=x^4/4+ 1/(8x^2); [1,2] Homework Equations Let f have a continuous first derivative on the interval [a,b]. The length of the curve from (a,f(a)) to (b,f(b)) is...

This is the answer key to one of my quizzes If you notice in the question, see attachment, were it says to integrate with respect to y the integral is integrating from 0 to 25 but this produces a negative area so this is technically wrong, yes? You don't just simply integrate from the lower...

defining a tangent vector v as the equivalence class of of curves: v = [\sigma] = \left. \frac{df(\sigma)}{dt} \right|_{t=0}, i want to show that this definition is independent of the member of the equivalence class that i choose. where \sigma represents a function from the reals to the...

In 3D the torsion  measures how rapidly the curve twists out of the osculating plane in which it finds itself momentarily trapped. So in 4D, would torsion measure how rapidly a curve twists out of the osculating 3-hypersurface in which it finds itself momentarily trapped? Or torsion of a...

I'm looking to purchase a dc motor but need to accurately know the torque-speed characteristics of it. I don't really have $$ for a good quality one that would come with accurate info (like I'm led to believe maxon motors do). When buying a cheap dc motor (i.e. from ocean controls. For...

Homework Statement [PLAIN]http://img688.imageshack.us/img688/5336/unledaty.jpg The Attempt at a Solution I underlined a = 3, which doesn't make sense seeing the foci is at (plus/minus3, 3) How can this be?? Wouldn't that make a straight line?

Hi, All: Let Sg be the genus-g orientable surface (connected sum of g tori), and consider a symplectic basis B= {x1,y1,x2,y2,..,x2g,y2g} for H_1(Sg,Z), i.e., a basis such that I(xi,yj)=1 if i=j, and 0 otherwise, where I( , ) is the algebraic intersection of (xi,yj), e.g...

I need to find the point of intersection of the curves x^2 + y^2 =1, z= 0 and x=cost, y=sint, z=t. I plugged in the latter equation into the former and got (1,0,0) as an answer but I'm not exactly sure why that works, I can't visualize how plugging in the parts of a parametric equation will...

Homework Statement I need assistance in learning the proper way to calculate error/uncertainty in a few things for my undergrad thesis.Homework Equations 1) how to calculate the uncertainty in the slope and intercept of calibration curves (peak area vs mol of compound) I have made via excel...

do they exist in reality or in nature?

Delete post. Delete, please.

"smooth" curves with cusps in 3d While reviewing basic calculus, I noticed that the curve (1+t^2,t^2,t^3), which clearly has a cusp at (1,0,0), has a derivative curve (2t,2t,3t^2) which is clearly smooth. This struck me as odd since differentiation usually seems to turn cusps into...

Homework Statement Two curves are said to be orthogonal if their derivatives are opposite reciprocals at the point where the two curves intersect. Are 2x^2 + y^2 =3 and x= y^2 orthogonal?Homework Equations I'm not entirely sure what to put here, but I think one relevant thing is to say that...

Homework Statement Polar plot the following sin[t] U cos[t] sin[2t] U cos[2t] sin[3t] U cos[3t] sin[4t] U cos[4t] sin[5t] U cos[5t] Notice that cos[t] and sin[t] are the same graph rotated 90 degrees only? Interesting! Just like the cartesian graph. Now here is something more...

Hello, I have a quick question about Characteristic curves. [PLAIN]http://pokit.org/get/1958a855486487230cd4e3c0a1cc0908.jpg First: Do these curves go to infinity, i mean in theory? If I had a steeper load line, I would hit saturation later. And what about that portion of load line between...

Homework Statement Set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point y = f(x) = (x)^3, at (1,1) Homework Equations Area in between two curves The Attempt at a...

Homework Statement i'm studying for an exam. and I'm pretty sure i know how do do these types of problems. this is aneven problem in the book so i wanted to know if my answer is right. Find the length of the curve for r=\sqrt{1+\cos2\theta} , \pi/2\leq\theta\leq\pi/2 Homework Equations...

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...

Hello, I have a (simple) question concerning proton binding behaviour. Maybe someone can help me to understand the topic. Let us regard one type of molecule in solution with only one binding site and let f(pH) describe the percentage of protonated molecules of all molecules. Then for...

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...