Parametric Definition and 674 Threads

In coordinates (u,v,\theta): x = \sqrt{uv} \cos{\theta}, y=\sqrt{uv} \sin{\theta}, z = \frac{1}{2}(u-v) What does this represent?

1 If x = t^{3} - 12t , y = t^{2} - 1 find \frac{dy}{dx} and \frac{d^{2}y}{dx^{2}} . For what values of t is the curve concave upward. So \frac{dy}{dx} = \frac{2t}{3t^{2}-12} and \frac{d^{2}y}{dx^{2}} = \frac{2}{3t^{2}-12} So 3t^{2}-12 > 0 and t > 2 for the curve to be concave...

Hi there I was just wondering how to type Optimatiozion of a Parametric equation, in LaTeX?

given x^2-y^2=1 find the parametric equation... i have no clue where to start... it looks like a cirlce equation but i know that not right so what the hell?

ok I am give a parametric equations of x= 4 cos t and y=5 sin t I know that i have to solve the x equation for t then stick it in the y equation but i getting stuck or not rembering some simple stuff i should be. I believe i get t= cos(inv) (x/4) and substiute it into t in y. if so...

Hi all, if I have a problem like: The path of a particle is described by y=4x^2, and it has a constant velocity of 5 m/s. How do I make a parametric equation out of this? I tried doing: r = xi + f(x)j r = ti + 4t^2j, but then v = \frac{dr}{dt} = i + 8tj, so |v|=\sqrt{1+64t^2}, and at, for...

X1 T = 10T Y1 T = 100 + (.5 * -9.8T^2) X2 T = 100 - 12.3 T X2 T = 0 How do I put this into algebraic form? it seems easy but I just can't get it. Do you simply add the X and Y components? If so what do x and y each stand for?? Does it have something to do with sine and cosine? =/

X1 T = 10T Y1 T = 100 + (.5 * -9.8T^2) X2 T = 100 - 12.3 T Y2 T = 0 How do I put this into algebraic form? it seems easy but I just can't get it.

Let L be the circle in the x-y plane with center the origin and radius 57. Let S be a moveable circle with radius 30 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on S before S is rolled and the path of P is studied. The initial position of P...

Convert to Parametric Equation of surface? How would I go about converting 9x^2+4y^2+z^2 = 640 I tried just to solve for each variable but this doesn't seem rightfor example \sqrt{\frac{640-z^2-4y^2}{9}}=x \sqrt{\frac{640-z^2-9x^2}{4}}=y \sqrt{\frac{640-4y^2-9x^2}{1}}=z

Hello Im working on some line integral problems at the moment. The first one is really only a check - I think I've worked it out... Compute the line integral of the vector field B(r) = x^2 e(sub 1) + y^2 e(sub 2) along a straight line from the origin to the point e(sub 1) + 2 e(sub 2) + 4...

a wheel or radius r rolls along a horizontal straight line.Find parametric equations for path traced by point P on the circumference of the wheel somebody pls help. thanx

I would like to convert these parametric equations into a single f(x,y) = 0 function. X(t) = t^2 + t + 1 Y(t) = t^2 - t +1 In fact, what stops me is the imaginary roots of the parametric polynomials. Is there a way to get around the seemingly impossible explicit solving of the...

y=t+cost x=t+sint dy/dt=1-sint dx/dt=1+cost dy/dx= (dy/dt).(dt/dx) = (1-sint).1/(1+cost) = (1-sint)/(1+cost) = 1-tant and how do i get from there to the second order differential?

I find parametric equations to be simply amazing. I was wondering if there is a website, or better yet a book that covers them in more detail? I found it incredible how we can describe circles, ellipses, lines and other analytical geometrical shapes by them...so I wanted to know how deep...

I need to take a surface integral where S is x^2 + y^2 + 2z^2 = 10. I need help with the parametrization of the curve. Letting x=u and y=v makes the problem too complicated. Can you let x=cos(u), y=sin(u) and z=3/sqrt(2)?

Hi, I'm getting confused over a few points on the derivative of a parametric equation. Say we the world line of a particle are represented by coordinates x^i . We then parametrize this world line by the parameter t. x^i = f^i(t) . Now here is where I get confused. The partial...

I'm having trouble with the following: The problem is to find the arc length of the following parametric function: x=(e^-t)(cos t), y=(e^-t)(sin t) from 0 to \pi I found that \frac{\partial y}{\partial t} = e^{-t}(\cos{t}-\sin{t}) , \frac{\partial x}{\partial t} =...

hi apologise if this is in the wrong forum :) my lecturer has told me that i need to be able to express parametric equations as a cartesian equation in my exam later this month. my mind boggles ! here is an example i have found. Express the parametric equations x = 2 t - 2 and y = 3 t -...

considering the surface 25x^2+25y^2+4z^2=54 The parametric equation for a line going thought point P=(1,1,1) is x=1+50t y=1+50t z=1+8t A plane an equation for the tangent plane through P. Here's what I know: the equation for a plane needs a perpendicular vector to the plane and a...

Circle A is fixed at center (1,0) with a radius 1. Circle B, also with radius 1, rotates at one revolution per (2*PI) seconds. Circle B is always connected to circle A at a single point. If at t=0, circle B is centered at (3,0) and point P (point p is on the edge of circle B) is at (4,0), what...

The lemniscate of Bernoulli is the curve that is the locus of points the product of whose distances from two fixed centres (called the foci) a distance of 2c apart is the cosntant [c^2. If the foci have Cartesian coordinates (\pmc, 0) the Cartesian equation of the lemniscate is ([x-c]^2 +...

1. I am given a curve defined parametrically by x= 2/t , y=1-2t i have found the equation of tangent at t=-2 to be y=4x+9, they have asked whether it cuts the curve again. how do i find that, since i don't know the original equation of the curve and can't solve them simultaneously. 2. Also...

Could someone please give me a clue how to solve these parametric equations or a starting position. torus specified by these equations x=(R+rcosΦ)cosθ y=(R+rcosΦ)sinθ z=rsinΦ calculate the normal to the torus N(θ,Φ) and entire surface area p.s anyone recommend a book or a...

Find the parametric representation for the surface: The part of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z = -2 and z = 2. okay, i know that i have to use spherical coordinates which is x = 4sin(phi)cos(theta) y = 4sin(phi)sin(phi) z = 4cos(phi) i know how to find...

How does one conclude that \frac{d^{2} y}{dx^{2}} = \frac{dy\'/dt}{dx/dt} ? Thanks

If someone could check my work and make sure I'm doing these problems right, I would really appreciate it. 1.Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x= h + r cos \theta , y= k + r sin \theta (x-h/r)^2 + (y-k/r)^2 = 1 2.Find the arc length...

Find an equation of the tangent line to the curve with parametric equations x=tsint, y=tcost at the point (0,-π). went dy/dt / dx/dt --> cost - tsint/sint + tcost t not given so figured it could be: x=t(sin(1)) --> t= x/sin(1) or y=t(cos(1)) --> t= y/cos(1) wondering if...

F(x,y,z)=(-\frac{y^2+2z^2}{x^2},\frac{2y}{x},\frac{4z}{x}) "Find parametric representations of the field lines." How do I parametrize all possible field lines?

Hello everyone, I'm having troubles seeing how this works. The directions are: Find parametric equations for the tagent line to the curve with the given parametric equations at the specified point. Here is my work and problem...

Can someone please help me with this question? x = 1-sint, y = 2+cost, rotate about y = 2 Find the surface area of the parametric curve. I don't know how to do it with y=2, I only know how if the question askes for rotating about the x-axis. The answer to the question is 2(pi)^2.

need parametric equations to the tangent line at the point (cos 0pi/6, sin 0pi/6, 0pi/6) on the curve x = cost, y = sint, z = t x(t) = ? y(t)=? z(t)=? now from my understanding, i have to find the derivatives of x, y, and z right? and i did this... now alll i should do is plug in the...

Hello everyone I did the following problem: Click http://img220.imageshack.us/img220/8486/untitled1copy4oq.jpg to view the problem and my answer. The row reduced form is: 1 5 0 0 -7 6 -7 0 0 1 0 -1 1 -1 0 0 0 1 - 2 -4 8 Any help would be great

I was wondering what the surface area would be when the curve: x=e^tsint, and y=e^tcost where (t) is greater than or equal to (0) and (t) is less or equal to pi divided by (2). when it is revolved about a) the x-axis b) the y-axis (approximation...

(1)If you are given the parametric equations x = sin(2\pi\t) y = cos(2\pi\t) and 0\leq t\leq 1 how would you find the cartesian equation for a curve that contains the parametrized curve? Using the identity \sin^{2}\theta + cos^{2}\theta = 1 would it be x^{2} + y^{2} = 1 ? Thanks

Find parametric equations for the tangent line at the point (cos(-4pi/6),sin(-4pi/6),-4pi/6) on the curve x=cost, y=sint,z=t x(t) = _________ y(t) = _________ z(t) = _________ r'(t) = <-sin(t), cos(t), 1> r'(0) = <0,1,1> my answer: x = cos(-4pi/6) + 0t y = sin(-4pi/6) +1t z =...

I need to find a set of parametric equations for a hyperbolic paraboloid. The hint is that I should review some trigonometric identities that involve differences of squares that equal 1. The equation is: \frac{y^2}{2}- \frac{x^2}{4} - \frac{z^2}{9} = 1 And what I have is...

The problem says; Suppose that a bicycle wheel of radius a rolls along a flat surface without slipping. If a reflector is attached to a spoke of the wheel at a distance b from the center of the resulting curve traced out by the reflector is called a curtate cycloid. I need to find...

Stewart uses the chain rule to show how to find the tangent to parametric curves. Given: x=f(t) and y=g(t), and that y can be written in terms of t, in other words, y=h(x) then the chain rule gives us, dy/dx = (dy/dt)/(dx/dt). Thats fine. The same argument holds for polar coordinates...

calc 2 problem (area bound by parametric eq.) I'm having a problem with this question: Find the area bounded by the curve x=cos{t}\ y= e^t, 0\geq t\leq\pi/2\ , and the lines y=1\ x=0 ... I came up with \int e^t(-sin{t})dt from 0\to\pi/2 But apparently I'm missing steps...

x(t)= \left( u\cos A \right) t and y(t)= \left( u\sin A \right) t - \frac{gt^2}{2} + h represent the horizontal and vertical coordinates of a batted or thrown baseball. A is the initial angle of elevation and u is the initial speed of the ball. I need to plot x(t) and y(t)...

I have x(t)=t(1-t) and y(t)=t(1-t^2). As t goes from 0 to 1 in forms a loop and I need to know the point where the tangent line is vertical. I know this must be easy but I'm clueless right now. Any help?

Hi, I've been trying to do this one question: Let R be the region enclosed by the graph x=t^2-2 y=t^3-2t. Set up the integral for the area of R. I know that if y is continuous function of x on an interval a ≤ x ≤ b where x=f(t) and y=g(t) then \int_{a}^{b} y dx =\int_{t1}^{t2} g(t)f'(t)dt...

Hi, I'm doing a project which involves parametric curves that I have to present to a class. Basically, I'm completely exercises and I know that most computer-aided design works with parametric curves, specifically Bezier curves. For the project, I'd like to draw something in CAD or whatever and...

I've recently attempted the following problem, http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/June2001.html with the following solution http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/solutions/June2001.html I've managed to form the meaningful derivatives (as...

If f(\theta) is given by:f(\theta) = 6cos^3(\theta) and g(\theta) is given by:g(\theta) = 6sin^3(\theta) Find the total length of the astroid described by f(\theta) and g(\theta). (The astroid is the curve swept out by (f(\theta),g(\theta)) as \theta ranges from 0 to 2pi ) f/d(\theta) =...

Consider the parametric curve given by the equations x(t) = t^2+30t-11 y(t)=t^2+30t+38 How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ? well since the bounds are already given (0->9), i just need help on setting up the integral. here's what i...

Find the area of the region enclosed by the parametric equation x=t^3-2t y=9t^2 dx/dt = 3t^2-2 9t^2 - 1 = 0 t=\pm \sqrt {1/9} \int_{-1/3}^{1/3} (9t^2)*(3t^2-2) dt = -2/5 anyone know where i went wrong?

The following parametric equations trace out a loop x = 8 - 3/2t^2 y = -3/6t^3+3t+1 1.) Find the t values at which the curve intersects itself. wouldn't i just have to solve for t for one of the equaltion to find t? also, can you find the intersects using a TI-83 plus to check your...

Okay, is it possible to transform an "x-y" equation into a parametric "equation"? If so, how would I go about it? For example, if I am given the equation (x^2)/1-(y^2)/25=1, what process would I have to use to find the Parametric equations? Thank You.