Parametric Definition and 674 Threads

I want to plot on the same graph: 1 < t < 2 x(t) =1.146967180*(t-1)^3-2.178399723*(2-t)^3+38.3612214*t+106.1461765 y(t)=.3047483217*(t-1)^3-.5750322227*(2-t)^3+10.1163822*t+444.0230985 2 < t < 3 x(t)=-.4672626810*(t-2)^3+1.146967180*(3-t)^3+45.2430246*t+92.3825701...

Homework Statement If x(t) = cos2t ; y(t) = t - tant Show that: (dy/dx)^2 = 1- x / 4(1+x)^3 The Attempt at a Solution dy/dx = dy/dt * dt/dx = (dy/dt) / (dx/dt) dy/dt = 1- sect^2 ; dx/dt = -2sin2t So (dy/dx)^2 = (1 - sect^2)^2 / (4 sin2t^2) From here I'm not too...

Homework Statement A baseball is hit with an initial velocity of 103 ft/sec, with an initial height of 3 ft, and at an angle of 41 degrees. There is a wind blowing 22ft/sec in the direction opposite to the horizontal path of the ball at an angle of depression of 12 degrees. Assume that gravity...

Homework Statement Find the equation of normal to curve x=cos b , y=sin b at the point where b=pi/4 . Find the coordinates of the point on the curve where the normal meets the curve again . Homework Equations The Attempt at a Solution Gradient of normal : dx/db=-sin b...

Homework Statement so dy/dx = y dot / x dot and d^2y/dx^2 = d/dx(y dot/x dot) can someone please show me the steps to get d^2y/dx^2 = (x dot y dot dot - y dot x dot dot)/ (x dot)^ 2 I've been trying to get to it for the last half an hour and failing Thanks

1. Hi. I have done part a of a question but am not sure i have completed it correctly. would somebody be good enough to check it for me please. thank you 2. Homework Equations in workings 3. The Attempt at a Solution on image

HALP! I have already killed a forest trying to work this one out on paper. Homework Statement a. Use Implicit differentiation to find the equations of the horizontal tangent lines to the parametric equation: yx^3-2x^2y^2+xy^3=192. b. Use Implicit differentiation to find the equations...

Homework Statement A surface S is formed by rotating a quarter ellipse C about the X-axis. Write an integral that represents the volume enclosed by S. the ellipse is represented by two points, (2,1) at which t= pi/2, and (4,0) at which t=0. Homework Equations Ellipse w/radii a,b, in...

Homework Statement A circle has the parametric equations: x=1+2cos\theta y=3+2sin\theta dy/dx= -1/tan\theta Find the tangent equation at the point with parameter \theta Homework Equations y-y1=m(x-x1) The Attempt at a Solution I've tried putting dy/dx in as the gradient and...

x=tan(t)+sec(t) and y=tan(t)-sec(t) I have to take the derivative, but it specifically states that I must eliminate the Parametric to do so (I think as a way to check we can do this...oops) I was thinking that I could turn the x into: x=sint+1/cost and then I could go from there, the only...

hey, i need help in solving the equation of a mathieu oscillator (ignoring damping) and showing how the condition for max parametric resonance is doubling of the natural frequency . ( got viva 2morro. I am so going to suck) D^2x + K(t)x =0 (Ko is the constant natural frequency when no...

Homework Statement Parametric equations for the motion of an object are given, where x and y are measured in meters and t is in seconds. find the speed of the object in meters per second when t is 2 seconds. x=2cost y=2sinst

First off, I'm not sure if MATLAB questions go here or not, or if they are even dealt with on this forum. If not more or remove I guess. I am no MATLAB wiz so this is mind-boggling to me. I am given a state of stress at a critical point of a component and told to plot a 3D parametric surface...

Homework Statement Find the parametric equation for a line of intersection of these two planes x+2y+3z=0 4x+5y+6z=5 Homework Equations Normal to plane 1= <1,2,3> Normal to plane 2= <4,5,6> The Attempt at a Solution I know the way to do this problem is to take cross product of...

Hello, if one wants to represent a parametric curve in a N-dimensional vector space, the straightforward way is to express it as: \mathbf{v} = f_1(t)\mathbf{e}_1 + \ldots + f_n(t)\mathbf{e}_n However there are infinite representations! I could make any substitution t = g(t) as...

Sorry I am new to the forum, I don't know how to type in the integrals and stuff. Homework Statement Let S be the portion of the surface y = x2 where 0 <= z <= X <= 2. Compute the surface area of S. Homework Equations r(u,v) = x(u,v)i + y(u,v)j + z(u,v)k A(S) = integral ru X rv dAThe Attempt...

Can someone help me get started on number one please?

Homework Statement Find the parametric equation for the line tangent to the curve: x=t^3-1, y=t^4+1, z=t at the point (26, 82, 3). Use the variable t for your parameter. Homework Equations The Attempt at a Solution dx/dt=3t^2, dy/dt=4t^3, dz/dt=1 I got then that...

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}}]...

1. Homework Statement [/b] For the surface with parametric equations r(s,t) = <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 <= 1. 2. Homework Equations [/b] 3. The Attempt at a Solution [/b] I already...

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...