Parametric Definition and 674 Threads

Homework Statement An object moves in two dimensions according to the parametric equations x(t) = At^2 + Bt and y(t) = D cos(Et). The constants A, B, D, and E are A = 2 m/s^2, B = 3 m/s, D = 4 m, and E = 1 rad/s. What is the magnitude of the total velocity of the object at t = 3 s...

Homework Statement Find a vector parametric equation r(t) for the line through the points P=(3,0,4) and Q=(1,−3,9) for each of the given conditions on the parameter t. I'm stuck on this one: r(5)=P and r(8)=Q Homework Equations The Attempt at a Solution I tried finding...

Am I doing this right? Homework Statement A.) Find the parametric equation for the line \overline{L} through (2,-1,4) and perpendicular to the lines: \overline{r_{1}}(t) = <1,2,0> + t<1,-1,3> \overline{r_{2}}(s) = <0,3,4> + s<4,1,-2> B.) Determine the point of intersection of the line...

Give a parametric representation of the following surfaces in terms of the given parameter variables: a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi. b)The graph of the function z = (x^3) - sqrt(y) in terms of the...

Generally with parametric equations to determine the direction that the line or curve is traveling in, how can you be sure as to what direction it goes in? When you plot points, how do you know if its going from the left or to the right increasing, are they asking if the x values are increasing...

The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.

i have the curve a(t) = (3t, 2t2, 2t3) and that a'(t) = (3, 4t, 6t2). my textbook tells me to verify that the tangent lines make a constant angle with the line y = 0, z = x so basically the vector (1, 0, 1). using the definition of the dot product a * b = |a| |b| cos(\theta) i have...

Homework Statement Find the vector parametric equation of the line L passing through the point p=(1,2,3) and perpendicular to the plane P having equation 2x-3y-5z=7 Homework Equations N/A The Attempt at a Solution q=P+tu (where u is the vector of the normal)...

Homework Statement Find a parametric equation of the line that satisfies the condition: The line that is tangent to the parabola y=x^2 at the point (-2,4) The Attempt at a Solution My answer came out to <x,y> = <-2,4> + t<1,2>

Homework Statement Find the parametric equation for the line through (1,0,-1) and parallel to the line 1/3(x-4)=1/2y=z+2 Homework Equations Vector equation - r=ro+tv Perhaps the scaler equation? I'm not entirely sure. The Attempt at a Solution I'm not sure where to begin; I...

Homework Statement Find a Cartesian equation relating x and y corresponding to the parametric equations x = \frac{2t}{t^3+1} y = \frac{9t^2}{t^3+1} t \neq -1 Write your answer in the form P(x,y)=0, where P is a polynomial in x and y such that the coefficient of x^3 is 729. 2...

Homework Statement Find parametric equations and symmetric equations for the line through the points (0,1/2,1) and (2,1,-3) Homework Equations The Attempt at a Solution I started out graphing the points and connecting them with a straight line. I called the first point P...

Homework Statement I have three questions regarding vectors in parametric/circle form. I understand that there is a starting point and a direction vector, but I just can't seem to get my head around this :confused: Homework Equations 1. Rewrite y=3x-1 in vector form. 2. Rewrite...

Dear colleagues, I am trying to parametrize a surface that follows an helix. The basic equations for this surface are: x = R1*cos(theta) y = R1*sin(theta) z = B1*theta + h where "theta" and "h" are the parameters and R1 and B1 are constants. I am looking for the parametrization of...

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...

Hi I am currently reading through a semiclassical approach to nonlinear optics. I learned about effects of second-order nonlinear optics like second harmonic generation and three wave mixing. I understand three-wave mixing as a process in which you send two (or three) monochromatic beams...

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?

Hello. I would like to numerically determine eigenvalues of a rectangular membrane which is twisted for \frac{\pi}{2}. Example picture: I'm solving Helmholtz equation: \nabla^2u+k^2u=0 where u=u(x,y) and \nabla^2 u=\frac{\partial^2u}{\partial x^2}+\frac{\partial^2v}{\partial y^2}...

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...