Parametric Definition and 674 Threads

find the area of the region that lies inside the first curve and outside the second curve. $r=3cos(\theta)$, $r=1+cos(\theta)$ $3cos(\theta)=1+cos(\theta)$ $2cos(\theta)=1$ $cos(\theta)=\frac{1}{2}$ $\theta= \frac{\pi}{3}, \frac{5 \pi}{3}$$A=\frac{1}{2} \int_{\pi/3}^{5\pi/3} \ (3cos(\theta))^2...

#1 find the length of the curve $x=3t^2$, $y=2t^3$, $0\le t \le 3$ $L=\int_{\alpha}^{\beta} \ \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}dt$$\frac{dx}{dt}=6t$ $\frac{dy}{dt}=6t^2$$L=\int_{0}^{3} \ \sqrt{(6t)^2+(6t^2)^2}dt$ $=\int_{0}^{3} \ \sqrt{6t^2+6t^4}dt$ $=\int_{0}^{3} \...

sketch the parametric curve and eliminate the parameter to find the cartesian equation of the curve $x=\cos\left({\theta}\right)$, $y=\sec\left({\theta}\right)$, $0\le \theta < \pi/2$ $y=\frac{1}{\cos\left({\theta}\right)}=\frac{1}{x}$ i sketched the curve. how do i do the second part?

t^2,t^4,t^6 Trying to graph this I have the traces x=y^2 for x>=0 in xy Also x=z^3 for z>=0 in xz And z=y^(3/2) for y>=0 in yz Parametricplot3d in mathematics does nothing to get a picture for this graph and drawing is proofing difficult In general what is the best way to plot...

Homework Statement Calculate the arclength of the curve given parametrically by ## x=2t^2, y=\frac 8 5 \sqrt 3t^ \frac 5 2, z=2t^3 ## for 0≤t≤2 Homework Equations ## S=∫ \sqrt(dx^2 + dy^2 + dz^2) ## The Attempt at a Solution 1. Found derivative of each and input into equation. ##...

Homework Statement http://i.imgur.com/oogkT4K.png Homework Equations y = (x-h)^2 + k The Attempt at a Solution y = (x-95)^2 + 10 ? We were assigned this in class but my teacher never taught us anything about these kinds of problems. I've learned basic parabolas and equations...

I read the definition that a plane is a point and two vectors with the equation being plane sum = {OP + tv + sw} where v and w are vectors and t and s are real numbers. This is called the parametric description of the plane. I haven't seen the equation in this form before though. Can someone...

Homework Statement Find the parametric equations for the portion of the parabola y=x^2 from (-1,1) to (3,9) Homework Equations None that I know of. The Attempt at a Solution Using knowledge of parametric equations I am not sure how to start. My teacher never went over this...

Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral. I found the solution online but with no explanation, so can someone explain how to solve this integral: thank you!

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...

1. The problem statement,ll variables and given/known data I have the first and second derivatives of a parametric function and the book is asking for when the slope of the tangent is vertical and horizontal. I get that horizontal is when dy/dx is 0. But what about vertical, is that dy/dx is 1...

Ok, so I'm really hoping someone can help me logic my way through this. I have a function to the effect of: ##r(u,v)=f(u,v)\hat{i} + g(u,v)\hat{j} +h(u,v)\hat{k}## I need to find an equation of a tangent plane at a point ##(u_{0},v_{0})## and quite frankly I'm at a loss on how to do this. So...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hi guys, I have done what I can with the following: Given a parametric curve x = xsint, y = sin(2t) where t is in R. Find an implicit equation of this curve. MY ANSWER: y = 2costsint = costx Therefore sint = x/2, cost = y/x sin^2(t) + cos^2(t) = x^2 / 4 + y^2 / x^2 = 1 Would this be...

Homework Statement The following describes a subset S of R3, you are asked to decide if the subset is a subspace of R3. x = 1-4t y = -2-t z = -2-t The Attempt at a SolutionR3 = {(1-4t, -2-t, -2-t) | t element of all Real number}If S is a subset, at least one must be true. 1) must contain...

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...

Homework Statement Homework Equations (x,y,z)=(x0,y0,z0) + t(m1,m2,m3) The Attempt at a Solution So at first I thought that since vector P1P2 is at right angles to both lines, both lines must be parallel. Quickly dismissed this idea since their direction vectors are not multiples of...

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 Determine parametric equations of the line that Is perpendicular to the lines L1= 3t-2 2t 3t L2= s-1 2s-7 3s-12 And passes through the point of intersection of lines L1 and L2 2. Homework Equations...

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...

Level function [L(x,y,z)] = (1/r^2) (x^2 + y^2 + z^2) = 1 Vector [N([x(h,g)], [y(h,g)], [z(g)])] = parametric equation to sphere Level function [L(x,y,z)] The parametric equations have 2 parameters, h and g [x(h,g)] = (r [sin (a + gv)]) [cos (b + hw)] [y(h,g)] = (r [sin (a + gv)]) [sin (b +...

Homework Statement The parametric equations of a curve are ##x=\frac{1}{2}(sint cost+ t), y=\frac{1}{2} t-\frac{1}{4} sin2t##, ##-\pi/2<t\leq0##. P is a point on the curve such that the gradient at P is 1. Find the equation of the normal at P. Hence, determine if the normal at P meets the...

Homework Statement Given a pair of parametric equations, ##x=f(t)## and ##y=g(t)## , The first derivative is given by ##\frac{dy}{dx}=\frac{g'(t)}{f'(t)}## and the second derivative is actually ##\frac{d}{dt}(\frac{dy}{dx})## But why we cannot find the second derivative of a parametric...

I've been working on Multivariable Calculus with a few books. In Vector Analysis, I've had some parts which made some questions come up in my mind. I have two questions about them. 1)Can we think of surface normal vector (\vec{n}) as a vector field (\vec{F}) or just a position vector...

Homework Statement find the length of a circular helix expressed in parametric form x= cos(t), y=sin(t) and z = t from t = 0 to t =2pi Homework Equations L = integrate ds (ds)^2 = (dx)^2+(dy)^2+(dz)^2 The Attempt at a Solution I got to ds = (1 + (dt)^2)^0.5 but I can't...

When doing surface integrals of surfaces described parametrically, we use the area element dA = ndS = (rv x rw)dvdw Where dS is the surface area element and v and w are the parameters. I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS...

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...

Homework Statement We are given a sample of size 100. After some tests (histogram, Kolmogorov) we deduce the sample X is distributed uniformly. The next task is to presume the parameters are equal to values of your choice, and test if such hypothesis is true. Homework Equations The Attempt at...

Homework Statement Given the parametric equations for a satellite in orbit around a spherical mass find angular momentum L in terms of ε, a, k, m, where k=GMm. Also, find the energy E in the same terms. Lastly, I can only use the equations provided and "fundamental definitions." Homework...

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 Problem: A curve given parametrically by (x, y, z) = (2 + 3t, 2 – 2t^2, -3t – 2t^3). There is a unique point P on the curve with the property that the tangent line at P passes through the point (-10, -22, 76). Answer: P = (-4, -6, 22) What are the coordinates of...

Homework Statement Find the total length of the curve t --> (cos^3(t), sin^3(t)), and t is between 0 and ∏/2 where t is in radians. Find also the partial arc length s(t) along the curve between 0 and ∏/2 Homework Equations The length is given by: S = ∫\sqrt{xdot^2 + ydot^2} dt...

Homework Statement . Let ##C_a## a cardioid given in polar coordinates by ##r_a= a+cos(\theta)## with a being a parameter, and ##\theta## ##\in [0,2\Pi]## a)Prove that, for a>1, ##C_a## is a smooth curve. b)Calculate the tangent line to the curve ##C_a## in the cartesian coordinates point...

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 arc length of a curve given parametrically from t = 0 to t = 1. Curve given by x = 4t^2, y = 2t Homework Equations [I think] parametric arclength = integral from t = b to t = a of sqrt( (dx/dt)^2 + (dy/dt)^2)dt The Attempt at a Solution dx/dt =...

Hi, first time asking questions in this forum. I am self-learning classic mechanics this summer using Laudau's book and so far I feel everything is pretty interesting and makes sense for me. But still, I have some questions that needed to be answered. One of them is about the parametric...

y = 2.5*(fresnelC(t*2) - arcsinh(t/2)) x = 2.5*(fresnelS(t) + arcsinh(t/2)) In case you don't have anything that can graph this, this is what it looks like from t = -2*pi to 2*pi, from y = -7 to 7, and from x= -7 to 7: There are a lot of interesting ones that can be made with the fresnel...

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...

Hi everyone, I've been racking my brain about this problem, but can't seem to figure it out. It seems like it should be easy, but I keep getting confused. Let's say I have an arbitrary parametric curve r(t)=<x(t), y(t)>. I want the velocity in the tangential direction to be constant. That...

Let's say i have a parametric equation: x = t^2 y = t^3 + 4t Even though this is a 2nd and 3rd degree parametric equation, i can isolate and express in terms of y = f(x) because the parametric equation for x involves only one term for t. Thus: t = sqrt(x) and y = sqrt(x)^3 + 4(sqrt(x))...

Hi, I'm working on an independent research project - and am trying to integrate this (with respect to x between some arbitrary m and infinite). http://www.wolframalpha.com/input/?i=+x+%3D%28t%2B2%29%2F%281%2Be%5E%28t-r%29%29%2C+y%3D%28e%5E%28-t%5E2%2F2%29%29%2Fsqrt%282*pi%29 If you graph this...