Parametric equations Definition and 208 Threads

This is for a personal engineering project. I need the parametric equations y(t) and x(t) for a very simple pendulum. Assume no friction, no forcing, no variation in gravity, a point mass, and the tether angle is significantly less than 30 degrees. It has been a while since I did differential...

Homework Statement Find dy/dx and d^y/dx^2 x=e^t; y=te^(-t) For which values of t are concave upward? (write your answer in interval notation). Homework Equations The Attempt at a Solution I used the formula to find d^2y/dx^2. d^2y/dx^2= e^(-3t)*(2t-3) Set it to zero: e^(3t)*(2t-3)>0 I...

Hey guys, I'm new here. I got a problem from my professor that is different from any other problems we have done. I'm stuck and need a little help.Homework Statement r(t) = <cos(t), t, 2sin(t)> Find parametric equations for the circle of curvature at (0, pi/2, 2)The Attempt at a Solution I...

I am having a difficult time finding the parametric equations x = x(t) and y = y(t) for line integrals. I know how to find them when dealing with circles, but when it comes to finding them for anything else, I don't see the method...it all seems very random. I did fine with finding the...

1. The problem statement, all variables and given/known Find the equation of a line passing through the point P=(-1,2,3) that is parallel to the line of intersection of the planes 3x-2y+z=4 and x+2y+3z=5 . Express your answer in parametric equations . 2. Homework Equations Cross product of...

Can I write the parametric equations for the graphs in the following case: on the x-axis, I want to plot a real number 'b'. On the y-axis, I want to plot the roots (all real roots) for x of the equation (7+b2)x3+(6-b)x2+9x-6=0. e.g. when b=1, I plot 1 on the x-axis and x=0.46124674 (the real...

Given parametric equations:[g(t)= x = t^{5}-4t^{3}] and [h(t) = y = t^{2}]Since polynomials can only be solved up to the 4th degree as I've just learned here on PhysicsForums, I guess it's not possible to isolate t in terms of x in the g(t) function and substitute into the h function to create...

What is the general method for writing Cartesian equations as parametric equations? For something as simple as y=f(x) we can write x=t and y=f(t) with the same function, but what about something more complicated, generally f(x,y)=0 - how can we make 2 parametric equations to represent a case...

This question is from the parametric equations chapter of my calc book. I am given x =\frac{1}{\sqrt{t+1}} and y = \frac{t}{t+1}, for (x> -1) Solving the x(t) for t, we get \frac{1- x^{2}}{x^{2}} Eliminating the parameters by substitution, we get y = 1 - x^{2} for (x > 0) My question is...

Even problem in 2nd semester calc book. Homework Statement Come up with three sets of PE for y=√x The Attempt at a Solution This is the first time in my math education that I've come across parametric equations where I am required to give 2 or more sets. The first one: x=t...

I'm quite rusty in Linear Algebra. If you have a plane in 3D with the equation ##z=2##, what does ##x## and ##y## equal? Does ##x=t## and ##y=t##? Because if I graph that in Wolfram Alpha, I don't get a horizontal plane in 3D at ##z=2##...

Homework Statement Compare the curves represented by the the parametric equations. How do they differ? a.) x =t , y = t^-2 b.) x = cost , y = (sect)^2 c.) x = e^t , y = e^(-2t) Homework Equations So I drew them on the calculator they all look like umm... how do I describe this...

Homework Statement Which of the following integrals represents the area of the surface obtained by rotating the parametric curve x=t-t^2 y=(4/3)t^(3/2) 1<t<2 Homework Equations A = integral ( 2pi(y) * sqrt( 1+ (dy/dx)^2))dx The Attempt at a Solution I solved for dy/dx and got...

Homework Statement find dy/dx as a function of t for the parametric equations x=cos^7(t) y=6sin^2(t) Homework Equations The Attempt at a Solution well I'm looking for dy/dx.. so first i found dy dy = 12sin(t)cos(t) and dx dx = -7cos^6(t)sin(t) dy/dx = 12sin(t)cos(t) /...

I have a few trivial questions regarding finding equations of the tangent line: 1) Find an equation of the tangent line to the parametric curve: x = 2 sin 2t y= 2 sin t at the point (\sqrt{3}, 1) The textbook says that point "corresponds to the parameter value t= \frac{pi}{6}" How do they...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Homework Statement Find the parametric equations for the line of intersection of two planes Homework Equations Equations for the two planes... z=x+y,-------(1) 2x-5y-z=1 -----(2) The Attempt at a Solution My answers are not correct so I guess I'm going about it the wrong way. Someone...

Homework Statement Suppose that r = f (θ) defines a polar graph. Find an expression for dx/dθ. It should not involve the letter r. Explain a procedure to determine the farthest that the graph r = f (θ) extends to the left and to the right (Hint: If x = x0 is the x - value of the point that...

Homework Statement "Eliminate the parameter and graph the plane curve represented by the parametric equations." x=t^2, y=t-1; -1 ≦ t ≦ 3 Homework Equations The Attempt at a Solution No need for you guys to graph; I can do that on my own. It would be a lot of work to have you guys...

Here is the question: Here is a link to the question: Distance formula problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement The figure illustrates a Keplerian orbit, with Cartesian coordinates (x,y) and plane polar coordinates (r,φ). F = -(G*M*m)/r^2 The parametric equations for the orbit: r(ψ) = a ( 1 − e cos ψ) tan(φ/2) = [(1+e)/(1-e)]^(1/2)* tan(ψ/2) t(ψ) = (T/2π) ( ψ − e sin ψ) where ψ is the...

I'm trying to find information on the origin of parametric equations. Such as who developed them, and around what time. Unfortunately I can't seem to find any information, beyond the basics of what parametric equations are. I was hoping someone here might be able to point me in the right...

Here is the question: Here is a link to the question: MATH 141 For which values of t is the curve concave upward? (Enter your answer using interval notation.)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Parametrize the curve by a pair of differentiable functions x = x(t), y = y(t) with [x '(t)]2 + [y '(t)]2≠0, then determine the tangent line at the origin. y=2x^3 The Attempt at a Solution Honestly I don't really understand what it's asking for. I assume it wants...

I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d2y/dx2=(-3cosec3θ)/49

Homework Statement The Attempt at a Solution So I am trying to find the gradient because in class we were taught that the surface area is the magnitude of the gradient divided by the magnitude of the dot product between the gradient and normal to the projected surface. I noticed...

If x = t, y = 2t, and y ≠ f(x), how to graph these equations?

parametric equations --> acceleration Homework Statement An object is moving at constant acceleration in the x-y plane. Its position and velocity at two different times are given by the following equations: What is the magnitude of the object’s acceleration (in m/s2) as it moves from the...

I am sure that this can be done, but I haven't been able to figure it out, Is there a way to integrate a differential form on a manifold without using the parametric equations of the manifold? So that you can just use the manifold's charts instead of parametric equations? If you a function...

A curve has parametric equations x = 2 cot t, y = 2sin² t , 0 < t ≤ pi/2 (a) find an expression for dy/dx in terms of the parameter t (b) Find an equation of the tangent to the curve at the point where t = pi/4 (c) Find a cartesian equation of the curve in the form y = f(x). State the...

Finding parametric equations for the line through the point that is perpendicular to plane and parallel? What is the difference when finding parametric equations for a line through a point that is perpendicular vs. parallel? Surely there must be some difference but I cannot seem to figure it...

y=x^5 x=y(y-1)^2 find points of intersect correct to 1 decimal point

Homework Statement The surface z=f(x,y)=√(9-2x2-y2) and the plane y=1 intersect in a curve. Find parametric equations for the tangent line at (√(2),1,2).Homework Equations Partial derivativesThe Attempt at a Solution Okay, so I'm just trying to work through an example in my textbook, so...

Homework Statement Find parametric equations for the three level curves of the function W(x,y) = sin(x) e^y which pass through the points P = (0,1), Q = (pi/2, 0) and R = (pi/6, 3) Also compute the vectors of the gradient vector field (gradient of W) at the points P, Q an R Homework...

Homework Statement An object moves so it's coordinates at the time t is given by the relationships x = 25t y = 20t-5t^2 What is the object's speed and direction at 3 sec? t = 3 sec Homework Equations v = √(dy/dt)^2 / (dx/dt)^2 Pythagoras theorem The Attempt at a...

Hi all, How do you find out if this Parametric equation x = -2t + 3 ; y = -t - 1 ; z = -3t + 2 Is perpendicular to this parametric equation x = -2 + 6t ; y = 3 - 6t ; z = -3 - 2t Thanks Stephen

I am having difficulty finding the length of the curve represented by parametric equations. The difficulty comes from not knowing how to determine if the curve transverses once, twice,... in a given interval. The only solution I can think of is (say x = g(t) and y = f(t) and y = F(x) on...

Homework Statement Find the area enclosed by the inner loop of the curve r=1-3sinθ Homework Equations A=o.5\int r^2 dθ The Attempt at a Solution I found the integral but i don't know how to find the interval at which i will be integrating from. I tried finding when r=0 and it turns...

Homework Statement ∏1: 2x + y - z = 4 ∏2: 3x - 2y +z = 6 Find the parametric equation of the line L... The Attempt at a Solution So I make them simultaneous equations... 2x + y = 4 - t (1) 3x - 2y = 6 - t (2) multiple equation 1 by 2. 4x + 2y = 8 - 2t (1) 3x - 2y = 6 - t...

The question states: Two towns A and B are located directly opposite each other on a river 8km wide which flows at a speed 4km/h. A person from town A wants to travel to a town C located 6km up-stream from and on the same side as B. The person travels in a boat with maximum speed 10km/h and...

The question states: Two towns A and B are located directly opposite each other on a river 8km wide which flows at a speed 4km/h. A person from town A wants to travel to a town C located 6km up-stream from and on the same side as B. The person travels in a boat with maximum speed 10km/h and...

Homework Statement The goal of this exercise is to plot parametric equations so that the image looks like the Agnolotti Pasta shell given in the link below. http://www.nytimes.com/interactive/2012/01/10/science/20120110_pasta.html?ref=science. Homework Equations The relevant...

Homework Statement Find the parametric equations through point (5,-1,3) parallel to the line of intersection between 2x-y+z=1 and 6x-y-z=3, where 0≤t≤1 Homework Equations 1. Find normal vectors for both planes 2. Take cross product of both normal planes ... The Attempt at a...

Hello. I apologize if I put this in the wrong section. I got this problem with the assignment I am currently working with. I have to set the position function for motion as a parametric equation for motion in circular motion, horizontal and vertical respectively. While I do know the...

Hello forum! I have yet another question concerning calculus and the topic we're doing right now is extremely confusing for me. Homework Statement Eliminate the parameter from the parametric equations x=3t/(1+t3), y=3t2/(1+t3), and hence find an Cartesian equation in x and y for this curve...

Homework Statement find parametric equations for the semicircle x^2+y^2=a^2, y>0 using as parameter the slope t=dy/dx of the tangent to the curve at (x,y) Homework Equations The Attempt at a Solution well i know that to parametrize a circle i would use x=acost and y=asint for...

Homework Statement An object moves in two dimensions according to the parametric equations x(t) = At^2 + Bt and y(t) = D cos(Et). The constants A, B, D, and E are A = 2 m/s^2, B = 3 m/s, D = 4 m, and E = 1 rad/s. What is the magnitude of the total velocity of the object at t = 3 s...

two questions. I know I'm doing the work right, but I can't get my answers to match and they are pretty close. I think it's just some arithmetic errors. Help? I've been trying to solve my mistakes forever. I can't find them! Homework Statement Use the parametric equation of an ellipse x =...

Homework Statement Find parametric equations and symmetric equations for the line through the points (0,1/2,1) and (2,1,-3) Homework Equations The Attempt at a Solution I started out graphing the points and connecting them with a straight line. I called the first point P...

The two equations are: x=2sin(t) y=5sin(2t) i have to find the area under this graph (lemniscate) I know how to integrate it and all, but my question is how do i find the limits?