Parametric Definition and 674 Threads

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 2cos(t) y = sin(t) z = t At the point (0,1,pi/2) Homework Equations The Attempt at a Solution r(t) = <2cos(t),sin(t),t> r'(t) = <-2sin(t),cos(t),1>...

Homework Statement Homework Equations r = <x,y,z> r' = <x',y',z'> The Attempt at a Solution I started by finding the derivatives of each part of the vector and got: x= 2/sqrt(t) y= 3t^2+1 z= 3t^2-1 Then I plugged the point (5,2,0) into that and got (2/sqrt(5), 13, -1). This should be...

Homework Statement Here's the equation: slove for t x=at^3+bt^2+ct+d Homework Equations Parametic Equations, removing the t value and such, to "simplify" the equation. The Attempt at a Solution This is as far as I got: (x-d)/t = t^2(a+(b/t)+(c/t^2)) I'm stumped. Is...

Hi guys, after using the forum for ages for help I decided to make an account, so hopefully I might be able to contribute something as well, who knows :) I'm a first timer with MATLAB and have been set an assignment. I'm completely stuck on question one: The following image shows my code and...

Find parametric equations for the line through Po=(3,-1,1) perpendicular to the plane 3x+5y-7z=29. Hey guys I am slightly confused on where to even start on this one the only way i can think about doing it would be finding two other coordinates on the and then taking the cross product of...

Basically, I'm supposed to write my name using splines in Matlab. Now, I'm having some trouble getting a parametric spline to work and I can't for the life of me figure out the problem. I'm making use of the spline toolbox and I have written a script as so: %segment for the S x1 = [0 2 1 2...

Homework Statement Find a set of parametric equations for the line passing through the point (1, 0, 1) that is parallel to the plane given by x + y + z = 5, and perpendicular to the line x = −2 + t, y = 1 + t, z = 2 − t. Homework Equations The section deals with distances betweens points...

hello, I've posted this question on a math forum, but they weren't much help - this really is more appropriate in physics ;) i'm working on a computer program and I'm using a library that generates a 2D graphics of a circle given a theta and phi. if i want to make the ball rotate around its...

these are fairly simple questions that only require you to plot points and then find a Cartesian equation of the curve. My question is when trying to solve for the Cartesian Equation, whether to solve for X first or Y? I will give an example. X=3t-5 , y=2t + 1 Graphing this is simple...

So, the parametric equations of a line segment from (x0,y0,z0) to (x1,x2,x3) are x = (1-t)x0 + tx1 y = (1-t)y0 + ty1 z = (1-t)z0 + tz1 right? But how are these equations derived? I don't really see where the (1-t) is coming from. I would be really thankful if anybody could explain...

Homework Statement I need to know why: \frac{d^{2}y}{dx^{2}}=\frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}} y=y(t) , x=x(t) The Attempt at a Solution I know that: \frac{dy}{dt}=\frac{dy}{dx}\frac{dx}{dt} From here: \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}...

Hey, I have a calculus 3 test coming up that involves calculating the mass of an object using a density function. I know how to use the double integral form for x-y equations, but the practice test my professor gave me has a question using parametric equations and I don't know how to...

Homework Statement I have the following: x(t) = acos(kt) + bsin(kt) y(t) = aksin(kt) + bkcos(kt) The Attempt at a Solution I'd like to show this is an ellipse, by actually explicitly finding the equation, but I honestly I have no clue about how to do this. Wiki gives the equation of an...

Homework Statement Find a parametric curve in R3 that has zero curvature at the origin and infinite curvature as the parameter t goes to infinity. 2. The attempt at a solution I was thinking it would look like a spiraled cone with the radius getting infinitely bigger, but I didn't know what...

The equation for a circle is x = r cos(u) y = r sin(u) Where u is 0 <= u <= 2 pi, because 2 pi is for calculating circle. While a sphere is x = r cos(u)cos(v) y = r sin(v)cos(v) z = r sin(v) Where u is the same, 2 pi but v is 0<= v <= 1 pi. Why only 1 pi for v? and not 2...

Homework Statement The ellipsoid 4x^2+2y^2+z^2=16 intersects the plane y=2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2) Homework Equations sin(t)^2 + cos(t)^2 = 1 The Attempt at a Solution After plugging 2 in for y, I get...

Homework Statement Find parametric equations for the portion of the plane x+y = 1 that extends between the planes z = -1 and z = 1 The attempt at a solution z = u -1\lequ\leq1 x = ? y = ?

Homework Statement I am working on my calc 3 project where she has given two parametric equations, one models the motion of a Ferris wheel and the other models an object being thrown to a person on the Ferris wheel. OK so I have this parametric equation that models an object being thrown...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at a given point. \[x = t^5, y = t^4, z = t^3\] at point (1,1,1) Homework Equations The Attempt at a Solution So we need to have direction vector, and a point. To find...

Convert x+y = 1 to parametric equations. I know that z = v, but after that I'm stuck.

Propose a parametric representation of a spiral. Hint: Use the parametric representation of a circle. This is the parametric representation of a circle we are given : x = r * Cos(Theta) y = r * Sin (Theta) 0 <= Theta <= 2 Pi Nope, we are not given anything background on spirals...

Homework Statement y^2 + 4y + z^2 = 5, x = 3 Homework Equations The Attempt at a Solution I know that the calculated coordinates must satisfy the above equation, but I don't know how to go about solving for those coordinates. The best I could do was to equate z = \sqrt{(-y + 5)(y + 1)}.

Homework Statement There are two questions, 1) straight line through (2, 0, 4) and (-3, 0, 9) 2) straight line y = 2x + 3, z = 7x Homework Equations r(t) = a + tb = [a1 + tb1, a2 + tb2, a3 + tb3] The book also explains how to calculate the line if b is a unit vector, but I don't...

Homework Statement Give a Cartesian equation of the given hyperplane The plane passing through (1,2,2) and orthogonal to the line x = (5,1,-1) + t(-1,1,-1)Homework Equations The Attempt at a Solution So I've looked at this for a few hours and still can't figure out how to do it. It's supposed...

A wheel radius a rolls along a line without slipping. The curve traced by a point P that is b units from the center (b < a) is called a curtate cycloid (see figure). Use the angle θ to find a set of parametric equations for this curve. I went through the book, went to the math lab at...

Homework Statement Find the parametric form for the tangent line to the graph of y=2x2−5x+3 at x=2 is Homework Equations I have no clue! The Attempt at a Solution I found the tangent line to be y=3x-5 I know that the answer has to be in the form... <x0,y0>+t<x1-x0,y1-y0> I...

Homework Statement x = t - e^{t} y = t + e^{-t} Find dy/dx and d^{2}y/dx.Homework Equations Derivative equations.The Attempt at a Solution dy/dt = 1 - e^{-t} dx/dt = 1 - e^{t} The dy/dx I came up with is: dy/dx = (1 - e^{-t}) / (1 - e^{t}) Second derivative I came up with is: d^{2}y/dx = -...

Homework Statement Write the polar equation for the graph y = x. Homework Equations x = r cos \theta y = r sin \theta The Attempt at a Solution I came up with \theta = \pi/4 because at \pi/4, the x and y coordinates match each other. I'm not sure this is correct, though.

Find parametric equations for the line through the point that is perpendicular to the given line, and intersects this line. We are given the point (0, 2, 2) and the line x = 1 + t, y = 2 - t, z = 2t. We are also given one of the parametric equations, that being x=3s. I am looking for...

Homework Statement Find the equation of the plane that contains P=(-1,0,1) and r(t)=<3t,t,8> Homework Equations The Attempt at a Solution n * <r-r0>=0 n * <t+2, 2t, 3t> = 0 I distributed the n, adding the terms and obtained: 1/t = -2n(n+2n+3n) Clearly, I've done...

Homework Statement There is points: P=(1,2,3,4) Q=(4,3,2,1) and line L passes through P and is parallel to A A=(1,1,1,1). X(t) is anypoint on line L. 1. Find the distance between X and Q as a function of t. 2. Find the minimum distance between Q and the line.(which is 2(51/2))Homework...

I have been confused about this. When come to equation of lines and curves in even 2 space, they automatically go parametric equation x(t), y(t) etc. I just want to verify my understanding: For 3 space, equation using x, y and z will automatically produce a plane or a surface. In order to...

If: x = f(t) (continuous and differentiable) y = g(t) (continuous) x is nondecreasing on [a, b] y is nonnegative on [a, b] Then when we trace the points (x,y) from t=a to t=b, we can calculate the area bounded above by the traced curve (below by y = 0, left by x = f(a), and right by x = f(b))...

Homework Statement Consider the ellipse given by the parametric equation x=3cos(t) y=sin(t) 0\leqt\leq2\Pi. Set up an integral that gives the circumference of the ellipse. Also find the area enclosed by the ellipse. Homework Equations \int\sqrt{1+(dy/dx)^2}dt The Attempt at a...

Homework Statement See figure. Homework Equations N/A The Attempt at a Solution I've dealt with parametric equations for lines before in my linear algebra class but I'm not sure how I'm suppose to model two curves with one. Anyone have any suggestions?

Homework Statement Consider a projectile launched at a height of h feet above the ground at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modled by the parametric equations x=(v[SUB]0cos θ)t and y=h + (v[SUB]0 sin θ)t-16t2. The...

Hi I'm reading Lang's Intro to Linear Algebra Page's 30 -36 and I'd just like some input on whether I understand this or not. Basically my problem is with Planes but the parametric eq. thing is just clarification. Parametric Representation of a Line Basically, if you have two n-tuples (n=2 for...

Homework Statement Given the parametric equations, x=t^3-3t , y=t^2/(1+t^2) i am asked to sketch this curve. Homework Equations The Attempt at a Solution I am unsure how to get the cartesian equation here..

Find the asymptotes of the parametric equations The graph looks like this: My attempt: Is my presentation correct? Do I also need to consider as x approaches 0 ? The reasons I ask is because I couldn't find the asymptotes of if I use the above presentation... Please...

Homework Statement Let c(t) = ( cos(At), sin(At), 1) be a curve. (A is a constant) Show that the normal to c(t) is always directed toward the z-axis. The Attempt at a Solution I am not sure how to show this. (For example, is the question "asking" us to show the cross product of...

Homework Statement Find the length of the path over (2 cos t - cos 2t, 2 sin t - sin 2t) 0<=t<=(pi/2) Homework Equations sin^(2) x = (1-cos 2x)/2 The Attempt at a Solution I have worked my way thru the problem and I have arrived at 2 (sq root 2) antiderivative (sq root (1-cos t))...

The unit normal vector N of a given curve is equal to the first derivative with respect to t of the unit tangent vector T'(t)divided by the norm of T'(t) (For a parametric vector equation of parameter t.) I realize this works because T(t) is orthogonal to T'(t), but I don't understand why the...

x=e^(2t) y=t+1 t= ( lnx ) / 2 y= ( lnx ) / 2 + 1 or blah

x=rT-dsinT y=r-dcosT trochoid for d<r integrating this on 0,2pi = 4x[0,pi/2] I am getting 2r^2pi-8rd+d^2pi text is just showing 2r^2pi+d^2pi

Elipse [0,2pi] x=acosT y=bsinT\ by symmetry 4I(y,x) chossing the limits of integration my text is showing 4I(y,x,0,a) T=0=>x=a T=pi/2=>x=0 so wouldn't this be 4I(y,x,a,0) proceeding inthe books case gives pi(ab) while in the later case gives -pi(ab) Also x= (t-1)/t y=(t+1)/t...

Homework Statement Find an equation y=f(x) for the parametric curve x = cos (theta) y = cos (theta) + sin^(2) (theta) Homework Equations The Attempt at a Solution I know I need to solve for theta but I'm not sure how to go about this. Can I plug x into the theta's in y or do I...

Homework Statement Solve the following parametric equations for y = f(x) x(t) = e^{-t} + t y(t) = e^{t} - t The Attempt at a Solution I'm completely stuck on this one. I've noticed x + y = e^{-t} + e^{t} and also y = \frac{1}{x-t} - t but that's about as far as I've gotten.

Now first, as I'm sure you all know, for any two parametric equations x(t) and y(t), the slope of the curve thus generated is equal to the quotient (dy/dt)/(dx/dt). Also, we know that the concavity of the function (or change of slope, as I'm not sure if concavity is actually a correct term) is...

Homework Statement write the vector equation and parametric equation of the line through A(-1,2,1) and B(1,2,1) Basically I was wondering If i found AB or BA would it be equivalent? Homework Equations AB= OB-OA= (1,2,1)-(-1,2,1) = (2,0,0) BA= OA-OB= (-1,2,1)- (1,2,1) = (-2,0,0) thus ...

Homework Statement How can one model the vertical and horizontal motion of a swing? The maximum height was 258 cm, the lowest 38cm and the horizontal movements went from 2.39m on the left to 2.44m on the right. The period was approx 2.5793 seconds. (The data was hand collected, so it is not...