Parametric Definition and 650 Threads

Sketch and represent parametrically the following: (a) \mid z+a+\iota b\mid =r \ \mbox { clockwise}\\ , (b) ellipse 4(x-1)^2 + 9(y+2)^2 =36 \ . Taking (a) first \mid z + a + \iota b \mid = r \mbox{- is the distance between the complex numbers }\ z=x+\iota y \ \mbox{ and } \ a + \iota b \...

I CAN'T SEEM TO GET THE ANSWER THAT IS CONSISTENT WITH MY UNDERSTANDING OF THE USE OF DOT AND CROSS PRODUCTS AND THE USE OF THE PARAMETRIC EQUATION OF THE LINE. LOOK AT THIS PLEASE: the parametric equation of the line is: x = 2 + 3t y = -4t z = 5 + t the plane is 4x + 5y - 2z = 18...

parametric and cartesian equations?? HELP! 1. x = 3t, y = 9t^2, negative infinity<t<positive infinity 2. a) What are the initial and terminal points, if any? Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the grap of the Cartesian equation...

OK, I'm a wee bit sleep deprived and cannot recollect some facts about the Dirac quantization of gauge theories. With the quantization of the parametrized nonrelativistics particle, do we still change the Poisson bracket into commutators? More specifically, for the non-relativistic particle...

Okay, I was doing 3D modelling. To save space I used vector functions to render terrain. Anyway, I came up with 3 parametric equations - each a function of an axis: e.g.: x=4t, y=5t+6, z=7t-9. How can you convert this into a Cartesian Equation?:confused:

Homework Statement The equation X(t)=A+tL is the parametric equation of a line through the point P:(2,-3,1). The parameter t represents distance from point P, directed so that the I component of L is positive. We know that the line is orthogonal to the plane with the equation 4x-6y+5z=6...

Homework Statement Consider a particle along a curve C and whose position is given by the vector: s(t) = < sqrt(t2), t3 - 3t > Last part of the question: There is an unknown force that is keeping this particle on trajectory C. At what value of t must the force cease in order for the...

Homework Statement Give parametric questions for the plane : 2x-3y+z-6=0 The Attempt at a Solution i know that the normal is (2,-3,1) how do i find the direction vector of the plane?

Suppose that you have a parametric curve given by x = f(t), y = g(t), a ≤ t ≤ b What will the Surface of revolution and Volume of revolution around the x-axis be? I have two candidates: Surface: S = 2*pi*int( |g(t)|*sqrt( (df(t)/dt)^2+(dg(t)/dt)^2 ) , t=a..b) Volume: V = pi*int(...

What are you trying to do when you find parametric equations for a geodesic lines on a surface? Take the metric ds^2 = dq^2 + (sinh(q)*dp)^2 Are you simply trying to get q as a function of s? and p as a function of s? If so, why? Thanks

Determine the vector and parametric equations of the plane that contains point C(1,-2,6) and the z-axis I take this to mean that any point on the z-axis is valid so does that mean either (0, 0, 1) or (1, -2, 5) are also on the plane?

3-dimensional parametric equations [Updated] Look lower for update... Homework Statement Well, my problem is that I need to give some examples on 3-dimensional parametric equations. So far I've found out what parametric equations are, and more specifically what 3-dimensional parametric...

Homework Statement 5. Find parametric equations for the tangent line to the curve of intersection of the surfaces z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5). The Attempt at a Solution f(x,y,z) = x^2 + y^2 - z^2 g(x,y,z) = x^2 + 2y^2 + z^2 Partial derivz...

Given: \begin{array}{l} x = 2\cos t \\ y = 2\sin t \\ \end{array} find \frac{{dy}}{{dx}} I started by finding dy/dt and dx/dt \begin{array}{l} \frac{{dy}}{{dt}} = 2\cos t \\ \frac{{dx}}{{dt}} = - 2\sin t \\ \end{array} Now, dy/dx = (dy/dt) / (dx/dt)...

I am trying to represent a helical pipe in x,y,z co-ordinants, would the x and y co-ordinants simply be multiplied by the equation of a circle if the growth of the helix is in the z direction? Any help would be appreciated. Thanks

Homework Statement Notice the curve given by: f(t) = x = 36-t^2 g(t) = y = (t^3)-25*t The curve makes a loop which lies along the x-axis. What is the total area insde the loop. Homework Equations Integral from alpha to beta of g(t)*f'(t) dt The Attempt at a Solution Ok, so I...

Homework Statement \frac{x^2}{a^2}+\frac{y^2}{a^2(1-e^2)} =1 The ellipse meets the major axis at a point whose abscissa is \lambda. Find lim \theta ->0. Homework Equations Parametric coordinates of an ellipse: (acosx,bsinx) The Attempt at a Solution The abscissa is the x...

Hi, Can someone explain to me what a parametric equation is exactly? Why it is used (instead of a normal function)? In other words, what is the significance of it? Second, to be more specific, in my book, there is an example where r(t) 2 costi + 2sintj + tk t>0. Then what they say is...

The semicircle \mbox{f(x) = }\sqrt{a^2-x^2} \mbox{ -a} <=\mbox{ x }<= \mbox{a }, ( see my last thread) has the parametric equations x= }a cos\theta\mbox{, y=} a sin\theta, 0 <= \theta <= \pi, show that the mean value with respect to \theta of the ordinates of the semicircle is 2a/\pi(.64a)...

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...

I learned that vertifcal tangents occur at a parametric curve if the derivative of the curve is undefined. That is given dy/dx = dy/dt / dx/dt, a vertical tangent occurs when dx/dt = 0. I don't understand why this is so. I know that vertical tangents occur when the slope is infinite, but...

Homework Statement 1) Consider the paramerric curve given by x = t^2 + 3t and y = 4 - t^2 a) Find an equation of the tangent lne to the curve at the point (x,y) = (0,-5) b) Determine the equation of every vertical tangent line to this parametric curve. 2)For each of the following...

I get the first derivative correct, but what's wrong with my attempt to find the second derivative? http://www.badongo.com/pic/421533

Which one would you say this is :confused: : E(|x1-x2|) x1, x2, xn - a sample of n values on the underlying random variable... I was thinking this is a statistic :frown:

Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational numbers for (aside from the trivial ones): x^3+y^3=u^3+v^3 Actually, I'm given the answer (which is really messy) and am supposed to show how to derive it. The book gives the...

Hello, My textbook says that to determine concavity we calculate the second derivative of the curve. This is a problem from my book, x = t^2 and y = t^3 - 3t the second derivative of this is (3(t^2+1))/(4t^3) I know all the steps to get to this point.. However, the book says that...

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.

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...