Parametric form Definition and 22 Threads

Hi, The main question revolves around the Rhodonea curve AKA rose curve. The polar equation given for the curve is r=cos(k). The parametric equation is = cos(k(theta)) cos (theta), = cos(k(theta)) sin(theta) . Can anyone show me the conversion from the general parametric form to the general...

Dear all, I have a question regarding the computation of the area of an ellipse. The parametric form of the ellipse with axes a and b is $$x(t) = a\cos{(t)}, \ \ \ y(t) = b\sin{(t)} $$ Using this to evaluate the area of the ellipse, usually one takes one halve or one quarter of the ellipse...

Hello. How can I verify that (u,v) = (x square - x, x+1) is a parametric form of a parabola? Thank you!

I am reading David Poole's book: Linear Algebra: A Modern Introduction (Third Edition) ... I have a basic (and probably simple) question regarding Poole's introductory discussion of the vector or parametric form of the equation of a plane $$\mathscr{P}$$ (page 38, Section 1.3 Lines and Planes)...

Hi PF I've beent rying to model the lunar orbit around the sun (cardioide) as a parametric function, but have run into a problem. f(t) = r(t) : x = a cos(ωt) y = b sin(ωt) z = k t The angular frequency ω as well as the distance from to the center varies around the orbit. Is...

Homework Statement A point moves along the curve y = x3 + x such that the vertical component of velocity is always 3. Find the tangential and normal components of acceleration at the point P(2,10). Homework Equations Tangential Acceleration - aT(t) = v(t) ⋅ a(t)/ magnitude of velocity vector...

Homework Statement Let C be the straight line from the point r =^i to the point r = 2j - k Find a parametric form for C. And calculate the line integrals ∫cV*dr and ∫c*v x dr where v = xi-yk. and is a vector field Homework EquationsThe Attempt at a Solution For parametric form (1-t)i + (2*t)j...

1. Write down the equation for the line in 3D through the point a=(1,2,4), parallel to the line r=(1,-5,0)+λ(1,2,2). Then, find the distance between these lines. 2. 3. Lets say, b= (1,2,2). b is parallel to given line, so it must also be parallel to the new line. My guess is that the equation...

Hi there, I have the plane in an explicit form: 12x + 2y – 20z = -56 How do I make it in parametric form? Thanks in advance

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...

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?

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 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 Calculate lim{t-> + \infty} ( \frac{a^t + b^t)}{2}) ^ {1/t} Homework Equations The Attempt at a Solution lim _{t-> + \infty} ( \frac{a^t + b^t)}{2}) ^ {1/t} = lim_{t-> + \infty} ( a^t ( \frac{1 + b^t/a^t)}{2}) ^ {1/t} = lim_{t-> + \infty} ( a ( \frac{1 +...

Homework Statement L1 : x = (0, 1, 2) + s(1, 0, 2) L2 : x = (4, 2, c) + t(−2, 0, d) If c = 5 & d = 0, find the point P on L1 and Q on L2 so that the distance between P & Q is the smallest possible. Homework Equations the point of intersection? The Attempt at a Solution...

If x and y are defined in terms of a third vatiable say t , then to find d2y/dx2 , we cannot find d2y/dt2 and d2x/dt2 and divide them to get d2y/dx2 , i am unable to fingure out the reason for this !

How is the parametric form of the graph of an equation different from its standard graph and what the dots in the parametric form of a graph represent.

Homework Statement Let: a matrix be: -5 -0.5 -0 -8 Find an invertible P and a diagonal D such that PDP(inverse) Homework Equations DET( (I)Lamda-A))= 0 for Eigenvalues The Attempt at a Solution when y=0 at the end matrix for finding the...

[SOLVED] Converting from Cartesian to Parametric form Homework Statement Find a parametric vector equation of for the plane in R^3 having cartesian equation 4y + 5z = - 6 Homework Equations None The Attempt at a Solution What I did was, first I turned the equation into 4x +...

X1 T = 10T Y1 T = 100 + (.5 * -9.8T^2) X2 T = 100 - 12.3 T X2 T = 0 How do I put this into algebraic form? it seems easy but I just can't get it. Do you simply add the X and Y components? If so what do x and y each stand for?? Does it have something to do with sine and cosine? =/

X1 T = 10T Y1 T = 100 + (.5 * -9.8T^2) X2 T = 100 - 12.3 T Y2 T = 0 How do I put this into algebraic form? it seems easy but I just can't get it.

Hello everyone I did the following problem: Click http://img220.imageshack.us/img220/8486/untitled1copy4oq.jpg to view the problem and my answer. The row reduced form is: 1 5 0 0 -7 6 -7 0 0 1 0 -1 1 -1 0 0 0 1 - 2 -4 8 Any help would be great