Parametric Definition and 674 Threads

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...

The parametric vector form of the line 1  is given as r1 = u1 + rv1 (r element of real field) where u1 is the position vector of P1 = (1,1,−3) and v1=vectorP1P2  where P2 = (3,3,−2) . The parametric vector form of the line 2  is given as r2 = u2 + sv2 (s element of real field)...

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...

Hi! I am trying to segment a parametric surface into different sections. What I have is a surface G(u,v) with parametric values u=[0,1] and v=[0,1]. Also, I have some discrete points on that surface which can be connected to form curves. Is there an appropriate way to segment the surface...

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...

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...

2. Determine vector and parametric equations for the z-axis. (Just so everyone is clear, The z-axis is actually a line in space. So you need to write the vector and parametric equation of this line)

x=t2 and y=t3-3t, find dy/dx and d2y/dx2 I understand how to get to dy/dx but an confused on how to get to d2y/dx2 can someone please explain in depth, I know the formula is (d/dt dy/dx)/(dx/dt) I don't understand where d/dt comes from and what it is. why do we not just derive it twice? I...

Homework Statement Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°. line 1: x = 4 + 2t y = 8 + 3t z = -1 - 4t line 2: x = 7 - 6t y = 2+ t z = -1 + 2t Homework Equations not sure. I am not asking for the answer...

Homework Statement Point A (1, -1, 2) Line s = 2i - j + t(3i -j +k)The Attempt at a Solution Ordinarily these are pretty obvious, but in this case the line is also a parametrized vector. So if I consider r = r0 + st And sub in s as I would do normally, I'd end up getting t^2's, and that's...

Problem statement attached. The correct way to do this seems to plug in your given x, y, z into F then integrate the dot product of F and <x',y',z'> dp from 0 to 1, however, this results in way too messy of an integral. Answer is 3/e...

Hi there, I have the plane in an explicit form: 12x + 2y – 20z = -56 How do I make it in parametric form? Thanks in advance

I have been working in complex functions and this is a new animal I came across. Let γ be a piecewise smooth curve from -1 to 1, and let A=∫γa(x2-y2) + 2bxy dz B=∫γ2axy - b(x2-y2) dz Prove A + Bi = (2/3)(a-bi) In the past anything like this defined γ and I would find a parametric...

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 parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 6 cos t, y = 6 sin t, z = 6 cos 2t; (3√3, 3, 3) Homework Equations The Attempt at a Solution So I understand that r(t)= 6cost t, 6sint...

Hi all, I want to convert a curve from polar coordinates function to a parametric function. The function is: r = 2 \cdot \cos( 4\cdot\theta ) I want to convert this for ( x(t), Y(t) ). Why do I want this? Because I saw that wxMaxima make plots of parametric functions, but I don't know...

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...

The problem is from an online homework assignment. I know it's probably fairly simple, but my brain isn't grasping it right now for some reason.[The Problem] We know: r(t) = <3t2 - 8t + 3, -9t2 + 2t + 7> And we are asked to find d2y/dx2.[Background Information] My understanding of d2y/dx2...

Homework Statement x = t^3, y = (3t^2)/2 0<= t <= √3 The Attempt at a Solution dx/dt = 3t^2 dy/dt = 3t step 1. √((3t^2)^2 + (3t)^2) step 2. 3t^2 + 3t (the book says I can't do that, I don't see why) step 3. insert √3 into t Here's the books solution I...

Homework Statement Find parametric equations for the line which passes through the point (1; 2; 3) and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 -2x. I have seen the result for this problem, but it's different than mine. I'm not sure, what I'm doing wrong. Please, help...

Homework Statement Find parametric equation for (((x-2)^2)/4)+(((y+1)^2)/9)=1 Homework Equations ((x^2)/(a^2))+((y^2)/(b^2))=1 (ellipse equation)The Attempt at a Solution I tried solving for y which gave me y=(6/(x-2))-1, but that did not work.

Homework Statement This is a problem involving parametric equations. r1= <t,2-t,12+t2> r2= <6-s,s-4,s2> At what point do the curves intersect? Find the angle of intersection, to the nearest degree. The Attempt at a Solution I found the point of intersection, (2,0,16). This is when t=2 and...

I can't seem to figure out the equation of the attached graph. I have tried polar, parametric, and cartesian, and I'm almost positive its parametric. Does anyone know what the equation might be?

Homework Statement Hello. I'm currently doing some work with bezier curves and have come across a certain format, which, from what I can tell, is called the parametric form of a bezier curve. I've run several searches and can't seem to find anything that explains how to obtain this form. The...

Homework Statement First exercise: Compute the surface area of that portion of the sphere x2+y2+z2=a2 lying within the cylinder x2+y2=ay, where a>0. Second one: Compute the area of that portion of the surface z2=2xy which lies above the first quadrant of the xy-plane and is cut off by the...

I just want to make sure my thinking is correct with a problem I'm working on. I'm trying to write a function that will take a point on a plane above a sphere, and then project it onto that sphere. From there project the point onto the x,y plane by following the normal vector of the sphere I...

Hi. I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis. I'm using the following...

Homework Statement i was given two parametric equations of two lines in R^3 and asks me to find the isometry between one line and the other knowing that point (a,b,c) of first line is mapped in point (a',b',c') of second line. Homework Equations What i have to find is a 3x3 matrix which...

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...

In optical parametric conversion process, such as second harmonic generation,the conversion efficient is determined by function sinc(ΔkL),where L is the length of the crystal,and Δk is the phase mismatch condition. When the sum of wave vectors of the two fundamental photon,equals to that of the...

The defining equations are: dx/dt = -(y + z) dy/dt = x + ay dz/dt = b + z(x - c) where a = b = 0.2 and 2.6 ≤ c ≤ 4.2. Is there an analytic way of showing that by changing the parameter c, we can get period-1 orbit, period-2 orbit, period-4 oribt, period-8 orbit, etc. and for c > 4.2...

I am exploring the motion of a particle who's path P(x,y) is given by two parametric equations: x = f(t) = a cos(bt) + cd (1) y = g(t) = a sin(bt) (2) To get a tangential velocity for this particle, I differentiated (1) and (2) then combined them using the form sqrt( m2 + n2...

Find the length of the curve given by the parametric representation... Homework Statement Calculate the length of the curve given by the parametric representation r(t) = t2(cos t; sin t; cos 2t; sin 2t) for 1≤ t ≤+1: Homework Equations The Attempt at a Solution I know that...

I'm attempting to convert the following parametric equation into into one f(x, y, z), and am running into difficulty. (Is it even possible?) Can I get some help? x=(2+cos(3t))*cos(2t) y=(2+cos(3t))*sin(2t) z=sin(3t)

Homework Statement Consider the function F(x,y) = 1 - x3 - y2 + x3y2. Consider the curve C given parametrically as x(t) = t1/3, y(t) = t1/2 for t ≥ 0. Determine the minimum and maximum of F(x,y) along the curve C. The Attempt at a Solution I think this is basically a max/min problem with...

Homework Statement Find the area of the part of the plane 3x + 5y + z = 15 that lies inside the cylinder x^2 + y^2 = 25. Homework Equations A=∫∫(√1+(dz/dx)^2+(dz/dy)^2) dA The Attempt at a Solution my bounds were r=0 to 5 and theta=0 to 2pi ∫∫√1 + (-3)^2 + (-5)^2 dA =∫∫√35 dA...

Homework Statement Suppose you need to know an equation of the tangent plane to a surface S at the point P(2,1,3). You don't know the equation for S but you know that the curves r1(t)=<2+3t,1-t^2,3-4t+t^2> r2(u)=<1+u^2,2u^3-1,2u+1> both lie on S. Find an equation of the tangent plane at P...

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...

hi i solve numerically two coupled equation and obtain two function x[t] and y[t]. how i plot x[t] versus y[t] so that horizontal axis to be x[t] and vertical axis to be y[t]. here is the notebook of mathematica http://www.mediafire.com/?g4sa3zi630vi8nl thanks

hi... please help me this question. i am not understand this question. Find a vector equation of the plane for the following parametric equations: X= 1 +2t1 – 3t2 y = 3 + 4t1 – 4t2 z = 2 + 3t1 – 5t2 i just want a solution, just let me know if possible.

Homework Statement See Attachment Homework Equations None I can think of The Attempt at a Solution I'm fairly certain that phi_yx is zero Also I tried factoring out the cos and splitting up the equation into it's respective components, but to no avail. Am I even going about this correctly?

Homework Statement For the curve: r(t) = ⟨\frac{1}{2}t5, \frac{1}{3}t5, \frac{1}{6}t5⟩, Find the arc length s(t) Find the unit tangent T(t) and T(1) Find the principle unit normal N(t) and N(1) Find the binormal vector B(t) and B(1) Homework Equations T(t) = \frac{r'(t)}{|r'(t)|}...

Can anyone tell me how to convert this parametric equation to cartesian (x,y)? r(t)=<2.5+2cos(4t),2.1+1.23sin(4t)> I've tried so many ways and they're incorrect.