Parametric Definition and 650 Threads

Homework Statement Find parametric equations and symmetric equations for the line through P0 and perpendicular to both given vectors. (P0 corresponds to t = 0.) P0 = (1, 1, 0) i + j and j + k Homework Equations The Attempt at a Solution For the symmetric equations, I did...

Homework Statement Describe the solution(s) of the system Ax=b in parametric vector form where A = 0...-2...9...5 0...1...2...-6 and b = 0 0 The attempt at a solution I got this far: 1...0...13...7...0 0...1...2...-6...0 How do I continue to get it into...

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 Find parametric equations for the part of sphere x2+y2+z2=9 that lies between the planes y=1 and y=2. Homework Equations The Attempt at a Solution Okay knowing that the p=3 I wrote the parametric equations for a sphere as x=3sin\phicos\theta...

I want to graph the following parametric curve using matlab: x = 31cos(t)-7cos(31/7)t y = 31sin(t)-7sin(31/7)t 0 ≤ t ≤ 14π This is the code I used: syms t t=[0:1:19*pi] x=31*cos(t)-7*cos(31/7)*t; y=31*sin(t)-7*sin(31/7)*t; plot(t,y,t,x) But the graph which Matlab generated is...

Homework Statement A curve is defined parametrically by x=sin3t, y=cos3t, 0≤ t ≤ 2pi. Find the equation of the line tangent to the curve at the point defined by t=2pi/9. Homework Equations The Attempt at a Solution ?

Homework Statement Are these systems of linear equations coincident planes, two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line. X₁+2 X₂-X₃=2 X₁+X₂+X₃=3 Homework Equations X₁+2 X₂-X₃=2 X₁+X₂+X₃=3 The...

Hello, sorry for my Englich:D Homework Statement I must count a line integral on the length which lies on the line which is defined by equations: \begin{cases}x^2+y^2+z^2=R^2\\ \left(x-\frac{R}{2}\right)^2+y^2=\left(\frac{R}{2}\right)^2\end{cases} it is a column which is cutting a sphere...

Problem to solve: x^{2}y''+xy'+(\lambda^{2}x^{2}-\frac{1}{4})=0 subject to y(0)=finite,y(\pi)=0 Let t=\lambda x which give t^{2}\frac{d^{2}y}{dt^{2}}+t\frac{dy}{dt}+(t^{2}-\frac{1}{2})y=0 With that first linear independent solution is J_{\frac{1}{2}}[\sqrt{\frac{2}{\pi\lambda...

I have 2 parameters, p and q. rmin depends on p and q in a complex way, but for a given p and q it can be solved for numerically. I have three functions L(p,q,rmin) Theta(p,q,rmin) S(p,q,rmin) What I want to do is to plot S against L for a set of the values p,q for which Theta is...

Homework Statement Given:H0-1.6, time in air - 3.02 s, horizontal distance thrown - 10m Solve:V0 and write parametric equations for x(t) and y(t) - the horizontal and vertical positions of the ball Homework Equations h(t)=-4.9t^2+V0t+h0 The Attempt at a Solution for V0 I got 14.268...

Hi Can anybody help me with these 3 problems?: 1) Express (3x-1)/(x+3)^2 in the form A/(x+3) + B/((X+3)^2) where A and B are constants. 2) A curve C has parametric equations: x=cost and y=2-cos2t (between 0 and pi) a)prove this can be expressed as the cartesian equation y=3-2x^2 b)...

Hi I have define a 3D object with ParametricPlot3D, something similar to a sphere called "obj." I then want to use a matrix, I define as "move," to translate the object around, I have been trying: obj = ParametricPlot3D... move = AffineTransform[{{1, 1, 2}, {0,1 , 1}, {0, 0, 1}}]...

Homework Statement http://img704.imageshack.us/img704/5760/pqg.jpg Homework Equations The Attempt at a Solution So i know that graph 2 is C also i know that A and G can't be any of those because its a circular shape.. the rest i have no idea how to do in order to get those...

Homework Statement x=cos^2(t) y=cos(t) (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? Homework Equations Length of an Arc: integral of alpha to beta sqrt((dx/dt)^2+(dy/dt)^2) The...

Homework Statement Find a parametric representation for the lower half of the ellipsoid 3x^2 + 5y^2 + z^2 = 1 x=u y=v z=?? we need to find what z is The Attempt at a Solution i solved the equation for z getting z= sqrt(1-3x^2-5y^2) then i plugged the given x=u and y=v...

Homework Statement A hockey puck of radius 1 slides along the ice at a speed 10 in the direction of the vector (1,1). As it slides, it spins in a counterclockwise direction at 2 revolutions per unit time. At time t = 0, the puck’s center is at the origin (0,0). Find the parametric equations...

Homework Statement A jet takes off from (1, 1, 0) at time t = 0 and moves with constant speed v = (−5, 0, 1). In a flight simulator, the trajectory of the jet is displayed in the yz-plane as it would appear to an observer at the point (1, 0, 0). Find the formula (in the form y = y(t), z =...

Homework Statement evaluate the line integral, where C is the given curve x sin(y) and line segment from 0,3 to 3,7 i know the formulas and how to do the integrals the part I am getting stuck on is finding the parametic equation for the function (x sin(y)) i need this in...

Homework Statement Find parameterizations for the circle of radius 3 about the point (3,4) Homework Equations The Attempt at a Solution The circle of radius 3 about the origin looks like cos2t + sin2t = 3 But I can't figure out how to parameterize it around (3,4), any advice?

Homework Statement Given a + b + c = 7, find a, b and c such that the point (a,b,c) lies on the line passing through the points (3,-4,0) and (2,-2,3) a = b = c = Homework Equations None The Attempt at a Solution My instructor didn't go through this portion and I was...

Homework Statement Having trouble understanding this the example I saw was; Solve \int^{\infty}_{0} x^3 e^{-9x} dx using integration by parametric differentiation.The Attempt at a Solution well, i do know how to do this, so i set out my integral; \int^{\infty}_{0} e^{-\alpha x} dx =...

Homework Statement Find the Cartesian equation of the parametric surface: [2cos(t)cos(s), 3sin(s), sin(t)cos(s)] Find eqn. of the tangent plane when S = 0, t = pi/2Homework Equations The Attempt at a Solution I'm not quite sure what to do. All I've done is squared each term, which gave me...

Homework Statement Graph the parametric equation. t is greater than or equal to zero and t is less than or equal to 2 pi. x=sint y=cost Homework Equations None The Attempt at a Solution Assuming that I don't have a calculator, how would I graph this? I know that...

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 !

Homework Statement The parametric equation of a surface is given by: x = s + t, y = (s2/2) + s f(t) + t, u = s + f(t) where f is some given function (e.g. f(t)=t/2). I would like to eliminate s and t from these equations and describe the surface in terms of x, y and u only. Homework...

Homework Statement Find parametric equations for the tangent line at the point (\cos(\frac{4 \pi}{6}) ,\sin(\frac{4 \pi}{6}) ,\frac{4 \pi}{6}) ) on the curve x=\cos t,\ y=\sin t, \ z=t Homework Equations The Attempt at a Solution Took the derivative r'(t)=( -sint...

Homework Statement Show that the curve with parametric equation : x = sint t; y = cos t; z = sni^2 t is the curve of intersection of the surface z = x^2 and x^2 + y^2 = 1. The Attempt at a Solution From polor equation I know that x = rcos(t) and y = rsin(t); from this we...

i need a parametric equation of a circle in 3d space that is perpendicular to a vector <a,b,c>. (as t goes up the circle is traced counterclockwise, as viewed from the head of the vector.) in the form x[t],y[t],z[t] i know that x^2+y^2+z^2=constant and that ax+by+cz=0 But i cannot figure...

Homework Statement Consider the line which passes through the point P(-1, 4, 3), and which is parallel to the line x = 1 + 3t, y = 2 + 4t, z = 3 + 5t Find the point of intersection of this new line with each of the coordinate planes: xy-plane: ( , , 0 ) xz-plane: ( , 0 , )...

Homework Statement Find parametric equations for the path of a particle that moves around the given circle in the manner described. x^2 + (y-2)^2 =4 Homework Equations halfway around counterclockwise, starting at (0,4). x(t)= ? y(t)= ? The Attempt at a Solution unsure...

Homework Statement Show (by eliminating the parameter) that the equations, x=x_{0}+(x_{1}-x_{0})t, y=y_{0}+(y_{1}-y_{0})t , represent the line passing through the points (x_{0},y_{0}),(x_{1},y_{1}) . Homework Equations The Attempt at a Solution I get...

Homework Statement Find the arc length of the curve described by the parametric equations: x=2e^t & y=3e^3t/2 ln3≤t≤2ln3 Homework Equations S = ∫(a->b) √[(dy/dt)^2 + (dx/dt)^2]dt The Attempt at a Solution Differentiated the two parametrics: dy/dt = 2e^t dx/dt = (3/2)*3e^3t/2 =...

Homework Statement For the surface with parametric equations r(st)=<st, s+t, s-t>, find the equation of the tangent plane at (2,3,1). Find the surface area under the restriction s^2 + t^2 <=(lessthanorequalto) 1 Homework Equations The Attempt at a Solution I already figured out...

Homework Statement Express the surface x = 2cos(theta)sin(phi) y=3sin(theta)sin(phi) z=2cos(phi) as a level surface f(x,y,z) = 144, f(x,y,z) = ? Homework Equations The Attempt at a Solution I figured they wanted the equation f(x,y,z) in x^2+y^2+z^2=144 so I though that by...

So I'm looking at this example in my textbook where they're trying to find the vert. & horizontal tangent lines of r = sin Θ, 0 < Θ < pi. they say to first change it to parametric equations where x = r cos Θ = sin Θ cos Θ and y = r sin Θ = sin Θ sin Θ = sin^2 Θ But now I'm just really...

Homework Statement Find the area between the curves: x = r(theta-sin(theta)), y = r(1-cos(theta)) 2. The attempt at a solution Usually I would just change the parametric equations into a single equation by solving for theta and substituting back into one of the equations. But that...

parametric and symmetric equations in R^3?? Homework Statement Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R3. Support your answer using...

question: how do i find the area under f[x,y] bounded by a closed parametric curve x[t],y[t]? it doesn't look like i can use a change of variables. it seems as though double integrals only with functions where the curve is given explicitly such as y[x] or x[y].

Hi all; I want to run a parametric Sweep analysis and I want to store the temperature value at just one point in the geometry. Is there anyone to know how to do that ?

I have found a lot of information about how to solve and graph parametric equations, but what I want to know is, what is the point, or why do they exist at all? The way I have seen it explained is that both x and y are stated in terms of another "term", usually t. But if I can state x and y in...

I'm interested in generating entangled photons from barium borate but have a few questions: 1) Taking one of the virgin entangled photons- before any measurements - does it have a random polarization? Ie, if I put any polarizer in its path will 50% of photons make it through? 2) I know...

I interesting about Parametric quintic spline(Parametric -> chord length). This equation Reference Data is ... http://books.google.com/books?id=kYG17apHcrYC&pg=PA1&dq=%22Computer+Aided+Geometric+Design%22&ei=woL-RoujEJ3qpwLyw_jsBQ&sig=z19_EIHAvEi9bLZ6lC7s1mdtg3I#PPA92,M2 But this...

converting cartesian to parametric equation R3 hi, I can't convert cartesian to parametric equation this equation 3x-y+4z-6=0 In example is given only 3x-y+4z-6=0 and says to convert it to parametric form ? how this can be done ?

Homework Statement Find the coordinates of the point where the line (x+1)/7 = (y-1)/-4 = (z-5)/-5 intersects the plane 3x + 3y + 2z = 5 Homework Equations none The Attempt at a Solution parameterized the equation of the line to x = -1 + 7t y = 1 - 4t z = 5 - 5t

Write a pair of parametric equations for the figure whose rectangular equation is ((y-2)^2)/49)-((x-1)^2)/9)=1 please help me

Find the area under the parametric curve (clearly a circle): x=5sin(t) y=2cos(t) domain of t: [0,2pi] h(t)=x g(t)=y integral from alpha to beta (lower to upper) of g(t)h'(t)dt integral from 0 to pi/2 of 10cos(t)^2 10(x/2+sin2x/4) evaluated from 0 to pi/2 solution: 2.5pi...

Homework Statement a)Consider the parametric curve x = t^2 + t, y = e^t. Find all t such that the tangent line of the curve at (x(t), y(t)) intersects the x-axis at (4,0) Homework Equations The Attempt at a Solution I draw out the graph and came out with the points, I was wondering...

Homework Statement Determine a parametric representation for the part of the sphere x2 + y2 + z2 = 4 that lies between the planes z = 1 & z = -1. Homework Equations The Attempt at a Solution We never learned spherical coordinates in class so I am not sure if I am using this...

Homework Statement Check Stokes Theorem for the Vector Field F(x,y,z)=(z,x,y), on the region defined by z=x^2-y^2 and x^2+y^2<=1. Attempt at Solution: Should be pretty easy problem; I tried two parameterizations, one worked and the other didn't... but I feel like they are equivalent...