Parametric Definition and 650 Threads

The third line is the type of problem I have: Derive the parametric equation for a circle with a distance 'b' from the circle with a radius 'r'. So from the edge of the circle to the red dot is a distance 'b' but from the center to the edge of the circle is 'r' I know the parametric...

Is this graphic wrong, see, http://en.wikipedia.org/wiki/File:Spontaneous_Parametric_Downconversion.png Shouldn't k_s + k_i be less than k_pump in the top graphic because |k_s| + |k_i| = |k_pump|, as energy is proportional to momentum? If so is momentum transferred to the crystal after the...

Homework Statement Consider the parametric curve given by the equation x(t) = ti + t^(1/3)j1. Calculate x'(t). Does the vector exist at t=0? 2. Find a new parametrisation of the curve for which the tangent vector is well defined at all points. What is the value of the vector at the origin?The...

Homework Statement I'm told to find the 2 points the two curves P and Q will intersect on and the parametric equations are: P (x=t, y=2t-1) Q (x=3t-t^2, y=t+1) The Attempt at a Solution I know I'm supposed to set x-equations and y-equations equal to each and solve so 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...

Hello MHB, I start read about area of parametric equation and got some problem understanding. I got two question. here is a link 1. Does it mather if we say $$x=f(t)$$ and $$y=g(t)$$ on $$a \leq x \leq b$$ Does this both formula works? $$\int_\alpha^\beta g(t)f'(t)dt$$ and $$\int_\alpha^\beta...

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...

This is about change of parameter from (u,v) plane to (x,y) plane. If you read the begining, it said σ is a smooth parametric surface on a region R. It went on and talk about continuous and all in region R shown in Fig 15.4.10 (a). But that is not correct. If you read on, this is about mapping...

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 A curve is defined by the parametric equations: $$x=tan(t-1)\ \ \ \ \ \ \ y=cot^2(t+1)$$ Homework Equations The Attempt at a Solution I think rearranging the first equation for t gives: $$t=tan^{-1}(x)+1$$ However that doesn't help me as I don't know how to...

Homework Statement Plane: 4x−2y+10z =16. Homework Equations The Attempt at a Solution So I've used two parameters, "u" and "v" with x = u and y = v Re-arranging z in terms of "u" and "v": z = 1.6 - 0.4x + 0.2y Hence r(t) = (u , v , 1.6 - 0.4 x + 0.2y) Is this correct?

Homework Statement Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°. L1: x = 4 + 2t y = 8 + 3t z = -1 − 4t L2: x = 7 - 6t y = 2+ t z = -1 + 2t Homework Equations vector, parametric, symmetric equations of line...

Homework Statement Write parametric and symmetric equations for the z-axis. Homework Equations vector, parametric and symmetric equations, in general form. The Attempt at a Solution I believe I have obtained the correct answer, would just like confirmation. Let our direction...

I need the answer of the following question in 500 words. It was set in a university exam. But no where I found the straight forward answer. Please help Question: Differentiate between Parametric and non-parametric data. How these data are analysed? (Word limit 500)

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

Homework Statement x(t) = (t^2 -1) / (t^2 +1) y(t) = (2t) / (t^2 +1) at the point t=1 Homework Equations Line equation = y-y1 = m(x-x1) chan rule = (dy/dt) / (dx/dt) = dy/dx The Attempt at a Solution I find the y1 and x1 values by subing in t=1 to the x(t) and y(t)...

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 stuck on the following task; Create a 2D Parametric Plot showing a spiral path. The parametric equations for a logarithmic spiral are x=k^u Cosine(u), y=k^u Sine(u), where k is a constant, and u is the plot parameter. What does the value of k determine? I have been typing in the...

"C4 question, please help.? the curve C has parametric equations x = sint , y = sin2t, 0<t<pi/2 a) find the area of the region bounded by C and the x-axis and, if this region is revolved through 2pi radians about the x-axis, b) find the volume of the solid formed How do you do this...

[b]1. if y(t)= (a/t, b/t, c/t) [b]2. Prove that this curve is a straight line. Find the equation of the line [b]3. i found the first part without a problem, i just am not sure how to find the equation f the line.

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...

Hi there, I'm working on a simulation of the travel patterns of cars. There are many variables and conditional probabilities in the model. My question is, is there anything wrong with fitting all non parametric distributions to variables (both continuous and discrete)? The software I'm...

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

Homework Statement The base of a 20-meter tower is at the origin; the base of a 20-meter tree is at (0,20,0). The ground is flat & the z-axis points upward. The following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i refers to x-axis...

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...

I'm having some trouble internalizing the concept of span. The question: If u = [1,2,1]; v = [-2,2,4]; and w = [-1,4,5], describe Span{u,v,w}. The attempt at a solution: I formed a matrix using column vectors u, v, and w and row-reduced to RREF: \begin{bmatrix} 1 & -2 & -1 \\ 2 & 2 & 4 \\...

I wish to write this equation: 1=√(x2+y2) as a parametric equation but WITHOUT the use of sine and cosine. Is this possible?

How dones one "flip" the graph of a parametric curve? Define the parametric curve C by x = f(t) and y = g(t) . This curve can be plotted on the Cartesian plane. Let's say we "flipped" this curve over the x-axis, that is, we reflected every point on this curve about the x-axis so that the...

[a]Give a parametric equation for the line tangent to this curve at t = \frac{pi}{4}. \vec{r(t)} <e^tcost, e^tsint> Give the equation for this same tangent line in the form ax + by = c [b]My attempt \vec{r(\frac{pi}{4})} = <e^\frac{pi}{4}cos\frac{pi}{4}, e^\frac{pi}{4}sin\frac{pi}{4} =...

This is confusing me more than it should. A curve in space is given by x^i(t) and is parameterized by t. What is the tangent vector along the curve at a point t= t_0 on the curve?

I'm given that x=cos3θ and that y=sin3θ if (d2y/dx2)=[(dy/dθ)/(dx/dθ)]/[dx/dθ] is right, wouldn´t the second derivative of the parametric be: 1/3c3θ ?? I got this by using dy/dθ=3sin2θ, and dx/dθ=-3cos2θsinθ any idea what's wrong? or is it right?

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...

Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...

Homework Statement Given a parametric eqn for the x,y coordinates , x(t),y(t) , how can i find the control points? Homework Equations de Casteljau's algorithm is used to compute the value for a given t given the control points. The Attempt at a Solution Control Points 0,3 are given...

Hey Guys! Homework Statement Find the area of the "loop" (I'm guessing it's called) formed by the set of parametrics: --> x(t)=t3-3t and y(t)=t2+t+1Homework Equations I've already drawn the graph and as said before the curve creates a "loop", I have to find the area insed that "loop" and I...

Homework Statement Given the curves r=2sin(θ) and r=2sin(2θ), 0 ≤ θ ≤ pi/2, find the area of the region outside the first curve and inside the second curve Homework Equations obviously set up an intersection to see where the two meet, then subtract the circle equation from the rose...

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

Homework Statement Evaluate the line integral over the curve C \int_{C}^{}e^xdx where C is the arc of the curve x=y^3 from (-1,-1) to (1,1) Homework Equations \int_{C}^{}f(x,y)ds=\int_{a}^{b}f(x(t),y(t))\sqrt((\frac{dx}{dt})^2+(\frac{dy}{dt})^2)dt The Attempt at a Solution I tried...

Homework Statement A curve C is defined by the parametric equation x=t^2, y=t^3-3t. a) show that C has two tangents at the point (3,0) and find their equations. b) find the points on C where the tangent is horizontal Homework Equations y-y1=m(x1-x), (dy/dt)/(dx/dt)=m, when dy/dt=0...

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...

Hi, for a presentation I am requested to give some examples of the Real world applications of Parametric Differentiation. Now i know its to do with a differentiation of 3 variables that are connected, but for the love of god i cannot think of any examples of its practical uses. any help...

Homework Statement A curve is defined by the parametric equations: x = 2t^3 y = 2t^2 t =/ 0 1)Prove that the equation of the tangent at the point with parameter t is 2x - 3ty + 2t^3 = 0. Proven, and I've no problem with this part. 2.)The tangent at the point t = 2 meets the curve...

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...

Quick question. This is kind of embarrassing actually. Suppose I have functions x(t,s) and y(t,s) (say they're parametric equations of a surface of something) and I want to know what dy/dx is. Specifically, I have x and y in terms of the parameters, which are kind of complicated functions, and I...