Parametric Definition and 650 Threads

Homework Statement This is a part of a bigger problem I am working on for my calculus 3 class. There is a parametric surface: ^{\vec{}}r(u,v)=<u+v,u-v,1-2u> It represents the plane through points (1,0,0), (0,1,0) (0,0,1). As part of the problem, I need to set up a surface integral...

Evaluate the line integral by two methods: A) directly and B) using Green's Theorem. \oint xydx +x^2y^3dy where C is the triangle with vertices (0,0) , (1,0), and (1,2). I don't need the whole problem done, but I need someone to show me the work for finding the parametric equations for...

The two equations are: x=2sin(t) y=5sin(2t) i have to find the area under this graph (lemniscate) I know how to integrate it and all, but my question is how do i find the limits?

For an assignment, I am supposed to find the parametric equation for the circle: x^2+y^2=a^2, using as a parameter the arc length, s, measured counterclockwise from the point (a,0) to the point (x,y). I understand that the parametric equation for a circle is x=a*cos(t) and y=a*sin(t), but...

Determine vector and parametric equations for the z-axis. HOW DO YOU ANSWER THIS QUESTION?

1. Determine vector and parametric equations for the line through the point A(2, 5) with direction vector = (1, −3). 2.Determine parametric equations for the line through (-2, 3) and parallel to the line with vector equation = (−2, 1) + t(6, 4). 3.Find vector and parametric equations for...

Homework Statement On Mathematica. Let's say I want to plot y = 4 - x x = 6, x = 0 So a parametric equation would be y = 4 - t x = t So I tried ParametricPlot[{y = 4 -t, x = t},{t,0,6}] But the range (the t values) aer only expanding the y-values.

Given the parametric function defined by x = a cos ^3t, y = a sin^3t, plot the curve. So I converted the above to (x/a)^(2/3) + (y/a)^(2/3) = 1, and from that got y +-a(1-(x/a)^(2/3))^(3/2). However, I have no idea of how to actually plot a function of this form. Is my only choice to make a...

general equation of parabola is y^2=4*a*x. it's parametric equation is ((a*t^2),(2*a*t)) [as in my book] but i think there can be other kind of parametric equations also like( ((t^2)/4*a),t) it defines a parabola easily. is using ((a*t^2),(2*a*t)) as parametric equation of parabola is convention...

Homework Statement Find the parametric equations of the intersection line of two planes 2x - 3y - z + 1 = 0 and 3x - 2y + 3z - 4 = 0 Homework Equations N/A The Attempt at a Solution First I'll label them: 2x - 3y - z + 1 = 0 [1] 3x - 2y + 3z - 4 = 0 [2] Then I get rid of the...

Homework Statement So I'm studying for my test. doing even and odd problems from the book. I wanted to see if this answer is right. Q: find an equation for the line in the xy-plane that is tangent to the curve at the point corresponding to the given value of t.Also, find the second derivative...

Homework Statement Determine whether the points P(7,10,4) and Q(5,22,5) lie on the given line: Homework Equations r(u,v)=<2u+3v, 1+5u-v, 2+u+v> The Attempt at a Solution x=x(u,v)=2u+3v, y=1+5u-v, z=2+u+v x+y+z=8u+3v+3

Homework Statement Find the area of the part of the sphere x^2 + y^2 + z^2 = a^2(a > 0constant) that lies inside the cylinder x^2 + y^2 = ax. Homework Equations double integral of the cross product of the vector Ra and Rb with respect to dA. The Attempt at a Solution I tried to parametrize...

Homework Statement [PLAIN]http://img191.imageshack.us/img191/5128/unledymj.jpg My book says r = <3cos\theta, 3sin\theta, z> I understand what they are doing, but why don't they set z = 2 for the parametrization instead? r = <3cos\theta, 3sin\theta, 2> Like the radius, don't...

Calculate in parametric form and describe how the planes intersect Where: P1 = x-3y+5z=6 P2 = 2x-7y+9z=2 My attempt Put planes in matrix form: 1, -3, 5, 6 2, -7, 9, 2 Find Echelon Form 1, -3, 5, 6 0, -1, -1, -10 Z = free variable = a So: -y-z=-10 y = 10 -...

I am trying to turn a 3D parametric equation into a vector field for an experiment, but I am not having much luck. [x,y,z]=[r*cos(u),r*sin(u),a*u] is the equation, I'm using grapher on the Mac. I want it all going in a helix, which is what the equation is for. Thanks!

Homework Statement I have http://img543.imageshack.us/img543/1608/msp481619fbgebbd2f2fg34.gif and [PLAIN][PLAIN]http://img153.imageshack.us/img153/121/msp69719fbh6if8c7b729c0.gif as my parametric equations with ''t'' as parameter. How to find its Cartesian equation? Homework Equations...

Homework Statement The path of a particle is given for time t > 0 by the parametric equations: x = t +2/t, y = 3t^2 a. Find the coordinates of each point on the path where the velocity of the particle in the x direction is zero. b. Find dy/dx when t = 1 c. Find d^2y/dx^2...

Homework Statement I'm trying to find when that parametric curve intersects with the line x=20 Homework Equations x(t)=(2t^3)/(t^2-1) ; y(t)=(2t^3)/((t^2+1)^2) The Attempt at a Solution I tried representing the line as y=t ; x=20 35=2t^3/(t^2-1) ; t=2t^3/((t^2+1)^2) I also ended up with...

Homework Statement Evaluate the line integral directly \oint_C xy^2 dx + x^3 dy C is the rectangle with vertices (0,0), (2,0), (2,3), (0,3) The Attempt at a Solution I am having problems with parametrizing the line y = 3 I did x = 2t, y = 3, t\in [0,2] Solutions...

I was able to get an answer to this homework problem, but I have no way of verifying that it is correct. I was hoping someone more experienced than me could look over my work and let me know if I did the problem correctly. Homework Statement Find the surface area of the part of the...

Homework Statement Let r(t) = <\cos(e^{-t}),\sin(e^{-t}),3e^{-t}>, find the equation of the line tangent to r(t) at the point \left ( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{3\pi}{4} \right)Homework Equations Okay, in just normal Cartesian Coord, we have y - y_0 = f'(x)(x - x_0) So I...

Homework Statement Find the parametric equation of y = cos x with max at (3, 5)Homework Equations The Attempt at a Solution There aren't any examples of going from y's and x's and turning them into functions of time. They only go from time functions to y and x functions. So I'm pretty lost on...

So I'm having a tough time figuring out this problem. John and Cory are golfing in the DV golf ball team. They are teeing off a hill 4 feet above the horizon. The hole is located 250 yards from the tee. The hole is 20 feet above the horizon. Cory is stronger than John and hits a velocity of...

Homework Statement Prove that the curve \vec{r}(t) = <cost,sint/sqrt(2), sint/sqrt(2)> is at the intersection of a sphere and two elliptic cylinders. Reparametrize the curve with respect to arc length measured from (0, 1/sqrt(2), 1/sqrt(2)) in the direction of increasing t. Homework Equations...

Homework Statement Here is the problem: x=y-1=2z and the equation of the plane is 4x-y+3z=8 Homework Equations The Attempt at a Solution Ya so i got the normal line to be <1,1,-1/2> but i do not know where to go from here? help please?

1. Find parametric equations for the line joining the points P = (1,2,-1) and Q = (5,7,5).[/b] 2. x = x0+ta y = y0+tb z = z0+tc 3. v = <(5-1), (7-2), (5+1)> so v = <4,5,6> and since v is a vector in the direction of the line and should be able to be placed in the above...

Homework Statement Convert the two equations x=x(t) and y=y(t) to a polar equation of the form r=r(\theta) Homework Equations x=r*cos(\theta) y=r*sin(\theta) r^{2}=x^{2}+y^2 The Attempt at a Solution Perhaps I'm over-thinking this, but in order to eliminate the parameter t, I...

I just want to see if my logic is sound here. If we have the paraboloid z=x2+y2 from z=0 to z=1, and I wanted a parametric form of that I think this should work for polar coordinates: \vec{r}(u,v)=(vcosu,vsinu,v^{2}) u:[0..2\pi],v:[0..1] Does this make sense?

Just a quick question... if we have f(x,y,z) and x(t), y(t), z(t), without substituting in what x y and z are in f, how do we calculate df/dt?

Homework Statement Consider the line and plane below. x = 5-5t, y = 3+7t, z = 10t ax + by + cz = d Find values of a, b, c, and d so that the plane is perpendicular to the line and through the point (2, 1, 2). Homework Equations Fgrad=(x',y',z') is perp to surface if...

Homework Statement find parametric representation for the part of the plane z=x+3 inside the cylinder x2+y2=1 The Attempt at a Solution intuitively... the cylinder is vertical with the z axis at its centre. and the plane is the whole surface inside the cylinder where y=0... visually...

Is there an analog or a more general form of the rule \frac{d}{dx} \int_{a}^{t} F(t) dt = F(x) that covers the case of F(t) being a composite function?

Hi, I'm having some trouble understanding what's going on when integrating the region M on page 10 of http://www.math.boun.edu.tr/instructors/ozturk/eskiders/fall04math488/bachman.pdf" , It may just be the language. ƒ : ℝ² → ℝ defined by (x,y) ↦ z = ƒ(x,y) = y² is the function we're...

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...

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 = ?