Curves Definition and 741 Threads

Homework Statement a.) Find the area of the region bounded by the graphs of f(x) = 1/x and 2x+2y=5 b.) Also, use the shell method to setup the integral that represents the volume of the solid formed by revolving the region bounded by the two same graphs about the y= 1/2. (Do not...

1. A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve. A circle is tangent to the y - axis at y = 3 and has one x - intercept at x = 1. a. Determine the other x-...

Homework Statement Find the area between the curves: x = r(theta-sin(theta)), y = r(1-cos(theta)) 2. The attempt at a solution Usually I would just change the parametric equations into a single equation by solving for theta and substituting back into one of the equations. But that...

This came up a while ago in a post. What is a sensible way of defining a "random" curve in R^n? Let's say n=2 in order to keep things simple.

Hey, I am wondering if anyone can help me understand a mathematical explanation as to how they work. From what I understand, the area under a closed curve is the same, independent of the path taken. So when doing an integral you only need to take the initial and final into account. There have...

Homework Statement Sketch the level curve of the surface z = \frac{x^2 - 2y + 6}{3x^2 + y} belonging to height z = 1 indicating the points at which the curves cut the y−axis. Homework Equations The Attempt at a Solution I put 1 = \frac{x^2 - 2y + 6}{3x^2 + y} but then don't...

Homework Statement a)Consider the parametric curve x = t^2 + t, y = e^t. Find all t such that the tangent line of the curve at (x(t), y(t)) intersects the x-axis at (4,0) Homework Equations The Attempt at a Solution I draw out the graph and came out with the points, I was wondering...

im trying to understand the theory of this. is a CTC supposed to actually bring an object back to the original time? or is it supposed to make it appear that way to an outside observer? I am reading up on it from wikipedia: http://en.wikipedia.org/wiki/Closed_timelike_curve but in the beginning...

What is the average number of intersections for two infinite curves confined to a plane?

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ) y = sec(θ) (1 , √2) y = ? attempt ; y - y1 = m(x-x1) y = √2 x = 1 y1 = sec(θ) x1 = tan(θ) substituting and solving it...

Question as follows f(x,y)=xy , find the level curves for c= +-1,+-2,+-3,+-4,+-5 My first attempt was to set f(x,y)=c c=xy and y=1/x C and this is an hyperbolic function. Is that right? I am also confused what values x can get. I know it is restricted and x>0. Can x get the same value as C ?

Homework Statement Given the surface: x^2 + y^2 + z^2 = 1 but x + y + z > 1 (actually greater than/equal to) I'd like to parametrize both this portion of the sphere and I'd like to find a parameterization of the boundary of the surface (that is, the intersection of the above sphere and...

Z(t)= t^2 - 1 + i(t+4) for 1<t<3 Can anyone Sketch it for me I m new on the forum ... and don't know how to skecth it

Homework Statement Find the length of the curve y=x^2-4|x|-x from x=-4 to x=4. The Attempt at a Solution I realized there is a corner at x=0 so i tried to get around this by pluggin in x for x>=0 and -x for x<0. However, my integrals don't match the answer...

Homework Statement Decide whether to integrate with respect to x or y. Then find the area bounded by these graphs x = 2y^2 and x+y = 1 Homework Equations equations for integration and anti derivatives. The Attempt at a Solution i put them in terms of x and have x = 2y^2 and x =...

they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle. there are many example of parallel of curves, for example, concentric circles...

After conducting CV measurements on Thin Film semiconductor wafers, how do we determine the behavior of the wafer based on the measurements? I have a sample of the reading obtained. I would be glad if anyone can help me.

Hi: I am trying to show that if we have a diffeomorphism f:M-->N and C is a positively-oriented Jordan curve in M ( so that., the winding number of C about any point in its interior is 1 ) , then f(C) is also positively-oriented in the same sense. It seems like something...

Homework Statement Find the area between the curves y= (7-x)/5, y = +sqrt(x+7) , y = -sqrt(x+7) Homework Equations The Attempt at a Solution I found the points of intersection of the graphs are at x=-7, x=-3 and x=42. So I know I need to do two integrals: One from -7 to -3, and...

Homework Statement i have to create a mathematical forumal from data of high and low tide depths and times. from that predict the next weeks outcome. it has to have sin or cos in the equation. a*COS (bx+c)+d or sin. this is the data given Mon 09/03/2009 Tue 10/03/2009 Wed 11/03/2009...

Homework Statement A 1200 kg car rounds a curve of radius 67 m banked at an angle of 12 degrees. If the car is traveling at 95 km/hr, will a friction force be required? If so how much and in what direction? Homework Equations F=ma a=v2/r The Attempt at a Solution I don't know what...

Homework Statement A car rounds a slippery curve. The radius of curvature of the road is R, the banking angle is theta and coefficient of friction is mu. What should be the cars speed in order that there is no frictional force between the car and the road? Homework Equations F=mv^2/r...

x^{2}-y^{2}-2x+4y+5; let x^{2}-y^{2}-2x+4y+5 \ = \ c; To sketch this as a level curve, I'm not sure how to proceed. I can't seem to rearrange the function into anything familiar. For the sake of trying to find a reference point, I let x=0 and found y \ = \ 2 \ ^{+}_{-}\sqrt{9-c}...

I have a function: y=e^x the tangent line at the point (1,e) would be x*e? in order to find the area between the tangent line, the y-axis and y=e^x i equate these functions and solve for x? I got this far (e^x)/(x)=e how do i solve for x

Homework Statement z=f(x,y)= -\sqrt{9-2x^2-y^2} Sketch the level curves for f(x,y) Homework Equations The Attempt at a Solution I am really poor at this. I let z = c (a constant) . Substituting c into the equation and rearranging it, I got this 9-c^{2}=2x^{2}+y^{2} From this, I...

To the moderator: I'm not sure if this should go here or in the Computational Physics forum. Please shift it there if you think that's the appropriate place for it. Hi everyone Merry Christmas! I'm writing a computer program in C, to explicitly compute the band structures for a 1D...

I encountered a few problems for a few questions while doing my homework. 1. Angular measure problem: A Ferris wheel with a radius of 25.3m makes 2 rotations every minute. a) Find the average angular speed of the Ferris wheel in radians per second. b) How far does a rider travel if the ride...

I've attempted to solve this problem but I'm not really sure if I'm doing it right. I've looked up other threads containing the same question, but they just don't have the answers I'm looking for. Thank you in advance to anyone who helps. Homework Statement A race-car driver is driving her...

Homework Statement Alright so the problem: Find the reigon in the xy plane that is bounded by the curves: x = y^2 and 2y + x = 3 quickly solving for the y coordinates of intersection, i get y = -3 and 1 so using horizontal components i got: \int^{1}_{-3} 3-2y - y^2 and...

Are there surfaces that have a geodesic curve which completely covers the surface, or (if that's not possible) is dense in the surface? In other words, if you were standing on the surface and started walking in a straight line, eventually you would walk over (or arbitrarily close to) every...

I know its a really dumb question and if i reached this far in math i should know but..how do you draw the diagrams for this topic? Like they give you a region in a plane defined by some kind of inequalities such as (x-2y^2 greater than or equal to 0), (1-x- IyI greater than or equal to 0) and...

Hello, I am an amateur developing the math to describe the motion of a robot of sorts. At this stage I'd like to use http://en.wikipedia.org/wiki/Bézier_curve" as user input to describe the motion path/s that it will make over time... (imagine it sitting flat on the cartesian 'floor')...

I must demonstrate in two ways that if c(t) is an integral curve of a smooth vector field X on a smooth manifold M with c'(t_0)=0 for some t_0, then c is a constant curve. I found one way: If \theta denotes the flow of X, then because X is invariant under its own flow, we have c'(t)=X_{c(t)} =...

Homework Statement Draw a contour map of the function showing several level curves. f(x,y) = x^3 - y Homework Equations f(x, y) = x^3 - y The Attempt at a Solution I think I should be finding the domain and range, but other than that I am not sure what else I need to do.

Homework Statement Find the area of the region enclosed by the asteroid: x=a*cos^{3}\theta y=a*sin^{3}\theta Homework Equations A = \int\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}The Attempt at a Solution \frac{dy}{d\theta} = 3asin^{2}\theta(cos\theta) \frac{dx}{d\theta} =...

Homework Statement At what point do the curves r1(t) = <t, 1 - t, 3 + t^2> and r2(s) = <3 - s, s - 2, s^2> intersect? Find their angle of intersection correct to the nearest degree. Homework Equations The Attempt at a Solution I set t = 3 -s 1 - t = s - 2 3 + t^2 = s^2 I got...

for a graph that has the velocity as the x-axis and the number of molecules as the y axis, i know that as the number of molecules increases, the average velocity will become lower and lower, but what if the molecules being tested are in relative amounts? for example you have air which is...

for a graph that has the velocity as the x-axis and the number of molecules as the y axis, i know that as the number of molecules increases, the average velocity will become lower and lower, but what if the molecules being tested are in relative amounts? you have the equation speed = sqrt...

I've been reading a bit on these, not in a rigorous way yet, and it's an enjoyable read. But now I've a few questions. As I understand it, they allow for a continuous index set in \Re to completely cover a higher dimensional \Re^{n}. Everywhere continuous, but nowhere differentiable, so it...

Homework Statement An automobile club plans to race a 740 kg car at the local racetrack. The car needs to be able to travel around several 175 m radius curves at 85 km/h. What should the banking angle of the curves be so that the force of the pavement on the tires of the car is in the normal...

1. Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle theta. A car can safely travel along the unbanked curve at a maximum speed Vo under conditions when the coefficient of static friction between the ties and the road is ms=0.81. The banked...

Homework Statement Solve for the vector function that represents the curve of intersection in the following two surface: z = sqrt(x^2 + y^2) and z = 1 + y Homework Equations The Attempt at a Solution Through blind trial and error, I managed to get the book-specified answer of x =...

Homework Statement Compute the area between the graphs of f(x) = 8sin(2x) and g(x) = 5sin(x)+3sin(2x) on the interval [0,pi/2] Homework Equations Area = Integral of [f(x)-g(x)]dx The Attempt at a Solution I first did f(x) - g(x) = 5sin(2x)-5sin(x)...after integrating, I got...

Sketch the following function, showing all work needed to sketch each curve. y = \frac{1}{3 + x^2} The question is asking for all the work done to find x and y intercepts, vertical, horizontal and slant asymptotes; critical points and points of inflection, i have completed the question...

I have three questions that I'm going to roll into one. I'm going insane trying to figure these out. 1. Find the unit tangent vector T to the cycloid. Also find the speed at theta=0 and theta=Pi, if the wheel turns at dtheta/dt=1. that dtheta/dt is the speed, right? I'm a little...

I've been involved for a long time going over astronomical influences on climate. My job is to be an astronomer and I don't know about climate. Maybe you think this is impossible, but I think it would be too complex to say whether a record of some sort within the ice was the driving force of all...

Need help checking if my reasoning is sound for this. Homework Statement Isobars are lines of constant temperature. Show that isobars are perpendicular to any part of the boundary that is insulated. Homework Equations u(t,\underline{X}) is the temperature at time t and spatial...

I'm really having trouble with these three problems. I'd post my attempts but most of it is in graph from. 3. David subjects a cylindrical can to a certain transformation. During this transformation the radius and height vary continuously with time. The radius is increasing at 4 in/min...

i was going over some relativity search online and came across what is called a closed timelike curve and that i actually allows time travel, am i right?

On galaxy rotation curves, the velocities of stars (or gas) rotating about their galactic centre remain fairly constant as the distance from the galactic centre increases. But these rotation curves show a drop in rotation velocity towards the centre of the galaxy...