Parametric Definition and 650 Threads

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...

I want to plot on the same graph: 1 < t < 2 x(t) =1.146967180*(t-1)^3-2.178399723*(2-t)^3+38.3612214*t+106.1461765 y(t)=.3047483217*(t-1)^3-.5750322227*(2-t)^3+10.1163822*t+444.0230985 2 < t < 3 x(t)=-.4672626810*(t-2)^3+1.146967180*(3-t)^3+45.2430246*t+92.3825701...

Homework Statement If x(t) = cos2t ; y(t) = t - tant Show that: (dy/dx)^2 = 1- x / 4(1+x)^3 The Attempt at a Solution dy/dx = dy/dt * dt/dx = (dy/dt) / (dx/dt) dy/dt = 1- sect^2 ; dx/dt = -2sin2t So (dy/dx)^2 = (1 - sect^2)^2 / (4 sin2t^2) From here I'm not too...

Homework Statement A baseball is hit with an initial velocity of 103 ft/sec, with an initial height of 3 ft, and at an angle of 41 degrees. There is a wind blowing 22ft/sec in the direction opposite to the horizontal path of the ball at an angle of depression of 12 degrees. Assume that gravity...

Homework Statement Find the equation of normal to curve x=cos b , y=sin b at the point where b=pi/4 . Find the coordinates of the point on the curve where the normal meets the curve again . Homework Equations The Attempt at a Solution Gradient of normal : dx/db=-sin b...

Homework Statement so dy/dx = y dot / x dot and d^2y/dx^2 = d/dx(y dot/x dot) can someone please show me the steps to get d^2y/dx^2 = (x dot y dot dot - y dot x dot dot)/ (x dot)^ 2 I've been trying to get to it for the last half an hour and failing Thanks

1. Hi. I have done part a of a question but am not sure i have completed it correctly. would somebody be good enough to check it for me please. thank you 2. Homework Equations in workings 3. The Attempt at a Solution on image

HALP! I have already killed a forest trying to work this one out on paper. Homework Statement a. Use Implicit differentiation to find the equations of the horizontal tangent lines to the parametric equation: yx^3-2x^2y^2+xy^3=192. b. Use Implicit differentiation to find the equations...

Homework Statement A surface S is formed by rotating a quarter ellipse C about the X-axis. Write an integral that represents the volume enclosed by S. the ellipse is represented by two points, (2,1) at which t= pi/2, and (4,0) at which t=0. Homework Equations Ellipse w/radii a,b, in...

Homework Statement A circle has the parametric equations: x=1+2cos\theta y=3+2sin\theta dy/dx= -1/tan\theta Find the tangent equation at the point with parameter \theta Homework Equations y-y1=m(x-x1) The Attempt at a Solution I've tried putting dy/dx in as the gradient and...

x=tan(t)+sec(t) and y=tan(t)-sec(t) I have to take the derivative, but it specifically states that I must eliminate the Parametric to do so (I think as a way to check we can do this...oops) I was thinking that I could turn the x into: x=sint+1/cost and then I could go from there, the only...

hey, i need help in solving the equation of a mathieu oscillator (ignoring damping) and showing how the condition for max parametric resonance is doubling of the natural frequency . ( got viva 2morro. I am so going to suck) D^2x + K(t)x =0 (Ko is the constant natural frequency when no...

Homework Statement Parametric equations for the motion of an object are given, where x and y are measured in meters and t is in seconds. find the speed of the object in meters per second when t is 2 seconds. x=2cost y=2sinst

Homework Statement Find the parametric equation for a line of intersection of these two planes x+2y+3z=0 4x+5y+6z=5 Homework Equations Normal to plane 1= <1,2,3> Normal to plane 2= <4,5,6> The Attempt at a Solution I know the way to do this problem is to take cross product of...

Hello, if one wants to represent a parametric curve in a N-dimensional vector space, the straightforward way is to express it as: \mathbf{v} = f_1(t)\mathbf{e}_1 + \ldots + f_n(t)\mathbf{e}_n However there are infinite representations! I could make any substitution t = g(t) as...

Sorry I am new to the forum, I don't know how to type in the integrals and stuff. Homework Statement Let S be the portion of the surface y = x2 where 0 <= z <= X <= 2. Compute the surface area of S. Homework Equations r(u,v) = x(u,v)i + y(u,v)j + z(u,v)k A(S) = integral ru X rv dAThe Attempt...

Can someone help me get started on number one please?

Homework Statement Find the parametric equation for the line tangent to the curve: x=t^3-1, y=t^4+1, z=t at the point (26, 82, 3). Use the variable t for your parameter. Homework Equations The Attempt at a Solution dx/dt=3t^2, dy/dt=4t^3, dz/dt=1 I got then that...