Curves Definition and 778 Threads

[SOLVED] homotopic curves Homework Statement Apparently if \gamma_4 = \gamma_2 +\gamma_3 -\gamma_1-\gamma_3, then \gamma_4 is homotopic to \gamma_5 in any region containing \gamma_1,\gamma_2, and the region between them minus z. I am not convinced that this is true. I can picture how...

[SOLVED] equations of curves a circle of diameter A rolls without slipping along the outer circumference of a stationary circle of the same diameter. use polar coordinates to derive the equation of a curve described by some fixed point on the rolling circle. "can anyone help me out in...

hello, I want to plot a set of curves on the same graph, and I want to give each of the curves labels, i.e. (1),(2),... Does anyone know how to make labels appear by the curves? Or is there another labelling scheme I can use?

[SOLVED] Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu Homework Statement Sketch the graph of the function on the interval [0, 2pi]. y = cosx - 1/2(cos2x) Homework Equations The Attempt at a Solution so the problems that i have been practicing...

Well I need to find the phase graph of the next system of ode: dx2/dt=-4x1 dx1/dt=x2 now i know the curves of x2 as a function of x1 are ellipses, but in what direction. I mean obviously i need to check dx2/dx1, and from this find if x2 is decreasing or increasing, so for the first quadrant...

Homework Statement find the area bounded by one of the four loops of: (x^2 + y^2)^3 = 4x^2y^2 Homework Equations The Attempt at a Solution I converted to polar coordinates and got r^{3/2} = sin^2(2\theta) The typical formula for polar integration for area would imply that I...

Homework Statement Find envelope of the family of curves x^2cosΘ + y^2sinΘ = a^2 where Θ is the parameter Homework Equations The Attempt at a Solution I tried differentiating and putting it = to 0 but this is coming up very messy, is there something I'm not seeing here?thanks

Find the area of the region enclosed by the curves, and decide whether to integrate with respect to x or y. y=3/x, y=6/x^2, x=5 anyone able to explain how to approach a problem like this I've tried it a few times and get the wrong answers but i don't even know what kind of answer I am...

This isn't a homework question, but from my notes that I couldn't figure out (wasn't able to copy the rest of the down) I have two functions: y=x y=x^3 , 0 \leq x \leq 2 and I have to find the area between these two curves. I know how to do it with respect to x, but I have troubles...

I want to graph curves in C++. I can program them in, find the x,y,z coordinates, but I don't know how to graph them. I am using Dev C++. How would I go about graphing them? Is there some predefined graphics library that I can use or is it more complicated than that?

Homework Statement Compute the area between the two functions as an integral along the x-axis or the y-axis: x=abs(y) x=6-y^2 Homework Equations The Attempt at a Solution I sketched the graph to determine which was to the right and which was left finding out that 6-y^2 is to...

In designing transfer curves to connect sections of straight railroad tracks, it's important to realize that the acceleration of the train should be continuous so that the reactive force exerted by the train on the track is also continuous. This will be the case if the curvature varies...

Homework Statement y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5) Homework Equations The Attempt at a Solution i put it ont he calculator but i honestly don't even no where the spot that i amtrying to find the area for is

Homework Statement Find the area between x=2(y^2) and x+y=1 The Attempt at a Solution First I'm trying to find their intersection so To solve for y I set up: 2(y^2)=1-y 2(y^2)+y=1 y=0,1 But, I notice that my teacher did: 2(y^2)+y-1=0 (2y+1)(y-1)=0 y=-1, 1/2 Why are...

I'm trying to find where x+y=1 meets x=2(y^2) To solve for y I set up: 2(y^2)=1-y 2(y^2)+y=1 y(2y+1)=1 I have y=1 and 2y+1=1 for 2y+1=1, 2y=0 so y=0 y=0,1 But, I notice that my teacher did: 2(y^2)+y-1=0 (2y+1)(y-1)=0 y=-1, 1/2 Why are these 2 methods bringing about different answers...

[SOLVED] Area inside Polar Curves Homework Statement I have spent several hours beating myself up over this and I just can't seem to solve it. It's the only problem I haven't gotten correct and it is particularly frustrating. Can you math gods here save me? :) Find the area of the region...

1) http://www.geocities.com/asdfasdf23135/advcal13.JPG Let F1 = x^2 - y^2 + z^2 -1 = 0 F2 = xy + xz - 2 = 0 F3 = xyz - x^2 - 6y + 6 = 0 My thought is to compute the gradients, grad F1 and grad F2. Then by taking their cross product, I can get a tangent vector v for the curve. Now, I can feel...

For less than BH_h, deep in gravitational potential well, with very extreme curvature, might one have a future light cone tipping over sufficiently to become spacelike and then wrap around to join up (glued) to past light cone? This is like a closed timelike curve, which can not be shrunk to a...

hey guys, I asked my( well she's not mine since i don't take physics yet)physics tacher if there is an equation to find out how much a body can curve space-time, but she gave me f=Gm1m2/r^2. But I'm pretty sure that's not it. I know that the equation is not linear. Could one of you guys who...

Homework Statement Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = x/(1+kx) 2. The attempt at a solution I have been trying this problem for hours, and I get a different answer every time...

Homework Statement What is the maximum speed with which a 1050-kg car can round a turn of radius 77m on a flat road if the coefficient of static friction between tires and the road is .80? Homework Equations F = mv^2 / r a = v2 / r Ffr = mustatic x mgThe Attempt at a Solution I found the force...

f(t)=(t^3, |t|^3) is a parametric representation of y=f(x)=|x|. Consider y=|x|, the left hand derivative f '-(0)=-1 and the right hand derivative f '+(0)=1, so f(x) is clearly not differentiable at 0. But f '(t)=(3t^2, 3t^2) for t>=0 f '(t)=(3t^2, -3t^2) for t<=0 f '(0)=(0,0) and f(t)...

I have to justify that the envelope of a uniparametric family represented by f(x,y,c)=0 is the solution to the next system f(x,y,c)=0, \frac{\partial f(x,y,c)}{\partial c}=0. How I justify it, I don't know how to justify at all!

people i an doing a research on this topic "the importance of curves sketching in real world" i need some answer but i am a bit tied up so can i have some help please:

Q: A particle is following the path C: f(t)=(2cos(t), 2sin(t), t), t>=0, and flies off on the tangent line at time t=3pi/2. Find the position of the particle at time t=5pi/2. Solution: f'(t)=(-2sint,2cost,1) f'(3pi/2)=(2,0,1) f(3pi/2)=(0,-2,3pi/2) Equation of the tangent line...

Let the function f(z) = u(x,y) + iv(x,y) be analytic in D, and consider the families of level curves u(x.y)=c1 and v(x,y)=c2 where c1 and c2 are arbitrary constants. Prove that these families are orthogonal. More precisely, show that if zo=(xo,yo) (o is a subscript) is a point in D which is...

Homework Statement what is the frequecy F for the alterating current U(T)=15cos(314t) A Homework Equations Am really new at this kind of problem but i think 314 is how many times the current rotates or fluxuates in 1 period so the F has to be the distance between waves? The...

Evaluate \int\int_{Q}\left(1 - x^{3}\right)y^{2} dA where Q is the region bounded by y=x^2 and x = y^2 So I have drew the graphs of y=x^2 and x=y^2 and found that they intersect at (0,0) and (1,1). Now I am confused what to replace Q with, but I think it should be this: please tell me if I am...

Homework Statement The fast French train known as the TGV (Train Grande Vitesse) has a scheduled average speed of 216 km/h. (a) If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, what is the smallest...

This is a topic that I simply know very little about. The question is asking me to determine the pKa value from the titration curves that I graphed in a recent experiment. Although I know the "buffer region," I have no idea how to determine the pKa. The weak base was 1M, 0.75M, 0.50M, and...

Homework Statement I need to sketch level curves of T(x, y) = 50(1 + x^2 + 3y^2)^{-1} and V(x, y) = \sqrt{1 - 9x^2 -4y^2} The Attempt at a Solution Is it correct that they are ellipses? ie [tex] 1 = \frac{9}{1 - c^2} x^2 + \frac{4}{1 - c^2}y^2[/itex] for V(x, y) = c = constant I feel so...

Spacetime -- it warps, it curves, but can't expand?? I have a problem understanding this. The general consensus of respected posters in cosmology is that space (and I assume spacetime) is nothing, therefore it cannot expand. Distances just increase. On the other hand, when it comes to gravity...

What are all these time-like and space-like things? Are these considered with light cones? Can anybody explain me in full detail the light cone because the more I read about it the more I get confused. I don't want basic information and can anybody also explain me void?

silly question. didnt know where it was meant to go so i just put it here as safest option:) suppose a curve C is defined by, r(t) = (sint, cost) with 0 \leq t \leq 2\pi if a sketch of C was required then would you simply just draw the graphs for sint and cost?

Let be a open curve on R^2 so x^{n}-c-ky=0 where k,n and c are integers, are there any methods to calculate or at least know if the curve above will have integer roots (a,b) so a^{n}-c-kb=0 ?? or perhaps to calculate the number of solutions as a sum (involving floor function) over integers of...

Homework Statement Sketch on the same axis the graphs of y = |x| and y = 2 - x^2. For which values f x is the inequality |x| < 2 - x^2 Homework Equations The Attempt at a Solution I don't really understand what it is asking me to do, I've sketched the two curves, y = |x| 45...

Hi all. I have say 5 curves in a 2-D plot and they are of different colors. I would like to label them according to their colors or pattern. Say, --- Sin[[x] ___ Cos[x] What command shall I refer to?

Are there notes on the net or books that give a gentle introduction on Riemann surfaces ( say undergraduate math or math for physicists type level)? Always read of the importance and beauty of Riemann surfaces but can't find surveys or intros for outsiders. Same for elliptic curves...

Doing some extra credit and got stuck on this one. Find the differential equation of the family of curves and of the orthogonal trajectories. y = c - 2x Needing a little help on this one... Thanks

Homework Statement The picture is found here (top picture): http://www.iastate.edu/~statics/examples/centroid/centroida.html#ysubc Homework Equations The Attempt at a Solution I get the wrong sign (ie: negative area) when I integrate to find the area between 2 curves when I...

Homework Statement This is so basic and yet I'm not getting it. Find the volume of the solid when the region enclosed is revolved arond the y axis. x = \sqrt{1 + y} x=0, y=3 Homework Equations The Attempt at a Solution So I first graphed the thing, finding that the...

Ok, I've been trying to work this out for a couple of hours now and I'm completely stumped. Not even Google was helping much. The question is: Find and Sketch the level curves of the scalar field T(x,y) = (x +y)/(x2 + y2) for T = -1, -0.5, 0, 0.5, 1 I know that I should equate the...

Homework Statement I want to show that if the chhord length ||f(s)-f(t)|| depends only on |s-t| then the f is part of a line or circlle. f may not be regular or unit speed. Homework Equations The Attempt at a Solution I'm trying to differentiete it and taking ||f'(t)||, but I...

I'm looking for a program which can draw 3D graphs which can identify the generating curves and ruling. i'm trying to draw up these 2 graphs z = 2x^2 + y^2 x^2/9 + y^2/9 + z^2/16 = 1 any ideas?

hi, hope you can help with this. For your reference I am 16 doing the nationwide 16 year olds exam (GCSE) so please if you can avoid using stuff I havn't done that'd be great :D Homework Statement The x coordinates of the points of intersection of the curve y = x^3 - 2x^2 - 5x and a...

Currently in chemistry, we are doing titrations and buffers for acid base equilibrium. I've noticed that titration curves have the distinct characteristics of sigmoid curves. So, can titration curves be modeled with a sigmoid function?

y = x^2 ,\,\,y = \frac{2}{{x^2 + 1}} It looks obvious from the graph that the intersections are -1 and 1, but just to verify: \frac{2}{{x^2 + 1}} = x^2 \,\, \Leftrightarrow \,\,x^2 \left( {x^2 + 1} \right) = 2\,\, \Leftrightarrow x^4 + x^2 = 2,\,\,x = - 1,\,\,1 So my...

Homework Statement Find the area of the region bounded by: y=cosx, y=sin2x, 0, x=pi/2 Homework Equations The Attempt at a Solution I made a graph. I believe I'm trying to find the area I shaded. red=cos(x), blue=sin(2x) I need to find the intersection point so I will know...

Hi, I have two parametric curves defined in three dimensions, which are functions of a variable t, like so: x1 = f1(t) y1 = f2(t) z1 = f3(t) x2 = f4(t) y2 = f5(t) z2 = f6(t) I am trying to find the intersection of these two curves, but I am having some difficulty with the...

Homework Statement Find equations of the tangents to the curve x=3t^2+1, y=2t^3+1 that pass through the point (4,3). The Attempt at a Solution I was able to find the equation y=x-1 as a tangent line through the point (4,3) for the part of the curve above the x-axis since (4,3) is on...