Parametric Definition and 650 Threads

Here is my question: When given three distict points A, B, C, find the parametric equations for the plane throught these three points. I was able to get the plane through these three points, first of all by getting the normal vector n = ABxAC, then by multiplying this vector by...

Homework Statement I've uploaded a scan of the questions. Questions 4, 5, and 6 are given in the 3 files uploaded. They all come from the given information from the first scan of the problem. Homework Equations The Attempt at a Solution I've worked everything I could on paper...

Homework Statement Find the area of the region enclosed by the parametric equation x=t^3-8t y=2t^2 The Attempt at a Solution I am not even sure how to start this problem. I read somewhere that to start with you solve for t in one of the equations. when i solve for t I end up...

Homework Statement i. x = 3cost, ii. y = 9sin2t, iii. 0\leq t < 2\pi iv.\int_0^\frac{\pi}{2} Asin2tsint \ dt 2. The attempt at a solution So this is what I am given and I am supposed to be able to show that this is the integral for the shadded area between the curve and the...

Homework Statement a curve has parametric equations: x = t - 2sin t y = 1 - 2cos t R is enclosed by the curve and the x axis. Show that the area of R is given by the integral: \int^{\frac{5\pi}{3}}_{\frac{\pi}{3}} (1-2\cos t)^{2} Homework Equations The Attempt at a...

x = 2cot t y = (sin t)^2 t is greater than 0 but less than or equal to pi/2 The cartesian can be found using trig identities to be: y = 8/ (4+ x^2) What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x =...

Homework Statement Describe motion of a particle w/ position xy Homework Equations x=cospi(t) y=sinpi(t) The Attempt at a Solution solving for t t=x/cospi so y=sinpi(x)/cospi y=tanpi(x) interval=at least one at most 2 since tan(x)=0 at pi and 2pi and this is where the...

Homework Statement A curve has parametric equaions: x = 2cot t, y = 2sin²t, 0 < t <= pi/2 Find an expression for dy/dx in terms of the parameter t The Attempt at a Solution Not sure where to go. Do i need to make a Cartesian equation first? Thanks :)

Homework Statement A particle is located at r=(2i+4j)m at t=0s. At t=3s it is at r=(8i-2j)m and has velocity v=(5i-5j)m/s a)what is the particles acceleration vector a? Homework Equations r1=r0+v0(t1-t0)+1/2a(t1-t0)^2 v1=v0+at The Attempt at a Solution v1=v0+at...

Homework Statement Find parametric equations for the line in which the planes 3x − 6y − 2z = 15 and 2x + y − 2z = 5 intersect. Homework Equations The Attempt at a Solution <2, 1, -2> - <3, -6, -2> = <-1, 7, 0> x = 2 - t, y = 1 + 7t, z = -2 Did I do this correctly??

I just have a question, when I am rotating something let's say around y=2 and the two equations are x=t^3 + 1 and y = 4t+1 how would i set it up?

A parametric equation, say r(t), is smoothly parametrized if: 1. its derivative is continuous, and 2. its derivative does not equal zero for all t in the domain of r. Now that sounds simple enough. Now let's say we have the tractrix: r(t) = (t-tanht)i + sechtj, ... then r'(t) = [...

I've just had a brain block... how do I work out the distance between a point (-5,10,13) and a parametric equation: x(t) = 57- 4t y(t) = 75 + 5t z(t) = -t

Calculate the distance between the 2 lines and use this distance to prove that the are not going to intersect. x(t) = 2 + t y(t) = -1 –t z(t) = t x(t) = 3 – s y(t) = 1 z(t) = 1 + s I have no idea where to start with this question! please help!

Homework Statement x(t)=2t-1 y(t)=t^2 algebraically eliminate the parameter to create a rectangular equation Homework Equations There was an example in our book that showed how to do this if the two equations contained sine and cosine, however nothing was said if they didn't. I...

Homework Statement Identify and sketch the curve represented by the parametric equations: x=1+cost y=1+sin^2t Homework Equations The Attempt at a Solution I have to isolate t in one of these equations and sub whatever t equals into the other equation right? So how do I get rid of the...

Homework Statement At which point is the tanget line to the following curve horizontal? y= a sin^{3}\theta x = acos^{3}\theta Homework Equations The Attempt at a Solution \frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} When \frac{dy}{dx} = 0 , this means that that the tanget...

Homework Statement Find the place where the parametric curve intersect itself x = 1-2cos^{2}t y = tant(1-2cos^{2}t) Homework Equations The Attempt at a Solution So I started with the x values.. 1-2cos^{2}t_{1} = 1-2cos^{2}t_{2} By canceling the same stuff on...

Homework Statement Find and verify parametric equations for an ellipse. Homework Equations x=acost y=bsint The Attempt at a Solution lets say the equation is x=3cost, y=3sint, domain: 0 to 2pi x2 y2 -- + -- = 1 a2 b2 point does verify when t=0 x=3, y=0 which =1...

So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times.. Find the length of the parametrized curve given by x(t) =t^{2}-8t + 24 y(t) =t^{2}-8t -7 How many units of distance are covered by the point P(t)...

Question: If f is a vector-valued function defined by f(t)=(e^(-t), cos(t)), find f''(t). I'm not even quite sure how to start. Any help would be loved! Thank you!

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...

I was wondering if someone could give me an overview of what they are and how to get them. Thanks

Homework Statement i want to make t the subject of any of the following equations inorder to find the cartesion equation. any ideas?: x=t^2+t y=t^2-t Homework Equations The Attempt at a Solution

Homework Statement Reduce these parametric functions to a single cartesian equation: $\displaylines{ x = at^2 \cr y = 2at \cr} $ $\displaylines{ x = 3{\mathop{\rm Sec}\nolimits} \left( \alpha \right) \cr y = 5{\mathop{\rm Tan}\nolimits} \left( \alpha \right) \cr} $...

[SOLVED] Parametric equation of the intersection between surfaces Homework Statement Given the following surfaces: S: z = x^2 + y^2 T: z = 1 - y^2 Find a parametric equation of the curve representing the intersection of S and T. Homework Equations N/A The Attempt at a Solution The...

Homework Statement Consider the curve of intersection of the cylinders [x^2+y^2=4] and [z+x^2=4]. Find parametric equations for this curve and use them to write a position vector. Homework Equations Thats what I am looking for. What to set t equal to. The Attempt at a Solution I set...

Find the parametric and symmetric equations of the line of intersection of the planes x+y+z=1 and x+z=0. I got the normal vectors, <1,1,1> and <1,0,1> and their cross product <1,0,-1> or i-k. I set z to 0 and got x=0, y=1, z=0. How do I form parametric equation out of this?? I know...

Hi, I am having trouble reversing the formula x=R(\theta - \sin(\theta)) to get \theta in terms of x. Am I missing something obvious or is it just impossible? To put it into context this is part of the parametric equation for a cycloid. The other part of the parametric equation is y = R (1-...

Homework Statement Show that every point on the line v = (1,-1,2) + t(2,3,1) satisfies the equation 5x - 3y - z - 6 = 0 Homework Equations The Attempt at a Solution So what I did was solve the equation v by adding the x,z,and z components to get x = 1 + 2t y = -1 + 3t z =...

Homework Statement how can we eliminate the parameter of these functions: x= t-2 y= t^2 +1 and sketch its curve Homework Equations The Attempt at a Solution I can't find the relations between these 2 functions

Homework Statement sketch the curve of parametric equations: x= e^-t + t y= e^t - t Homework Equations The Attempt at a Solution I don;t know how to eliminate the parameter Can anyone help me?

Homework Statement At time t, a projectile launched with angle of elevation a and initial velocity Vo has position x(t)=(Vocosa)t and y(t)=(Vosina)t-0.5gt^2, where g is the accerleatio due to gravity. The Attempt at a Solution (a) A football player kicks a bal at an angle of...

Homework Statement Each of the three circles A, B and C of the figure below can be parameterized by equations of the form x = a + k cos t, y = b + k sin t, 0 ≤ t ≤ 2. What can you say about the values of a, b and k for each of these circles? (figure attached below) The Attempt at a...

I have been working through the book: "Almost All About Waves" John R. Pierce Dover 2006 This is a fascinating read & offers some deep insights into the inner workings of waves, from a practitioner's perspective. Chapter 13 - Parametric Amplifiers - is extremely interesting & is...

My book really doesn't go into a lot of depth but I was wondering if this is correct If we are asked to find the tangent line of a specific value of t for a given parametric equation then we can find the equation of the tangent line in either rectangular or parametric functions. Rectangular...

Homework Statement A particle moves in the xy-plane so that its position at any time t, 0 =< t =< pi, is given by: x(t) = \frac{t^2}{2}-ln(1+t) y(t) = 3sint -- At that time is the particle on the y-axis on the interval? Find the speed and acceleration vector of the particle at this time...

f(t)=(t^3, |t|^3) is a parametric representation of y=f(x)=|x|. Consider y=|x|, the left hand derivative f '-(0)=-1 and the right hand derivative f '+(0)=1, so f(x) is clearly not differentiable at 0. But f '(t)=(3t^2, 3t^2) for t>=0 f '(t)=(3t^2, -3t^2) for t<=0 f '(0)=(0,0) and f(t)...

Just wanted to check and see if this is right. The k-component of the vector is what I'm unsure of...I've always sucked at converting to parametric form. :) Homework Statement Convert to parametric form: x^{2} + y^{2} = 9, z = 4arctan(y/x) The Attempt at a Solution The i- and...

Hey I have a problem with question 4 of this problem set http://www.physics.ubc.ca/~mattison/Courses/Phys170/p170-ps5.pdf Number 4. I have found Vmin to be 0.84m/s which i know it is correct, but i cannot solve Vmax? i thoguht you could maybe approach this question with 2 parametric...

Homework Statement At what point does the curve x = (1-2cos^2(t), y=(tan(t))(1-2cos^2(t)) cross itself? Find equations of both tangents at that point. Homework Equations The Attempt at a Solution To begin, I figured that x=y when it crosses itself, so I set x=y and got 1 = tan(t), so t=\pi/4...

Homework Statement Find the area of the region enclosed by the parametric equation x=t^3-5t y=7t^2 Homework Equations The Attempt at a Solution I know how you set it up \int (7t^2)(3t^2-5)dt, but how do you find the bounds. I tried finding t and got t= (+/-)\sqrt{y/7} and you...

Q: A particle is following the path C: f(t)=(2cos(t), 2sin(t), t), t>=0, and flies off on the tangent line at time t=3pi/2. Find the position of the particle at time t=5pi/2. Solution: f'(t)=(-2sint,2cost,1) f'(3pi/2)=(2,0,1) f(3pi/2)=(0,-2,3pi/2) Equation of the tangent line...

Homework Statement Give a parametric representation of the plane x + y + z = 5. Homework Equations I am really not sure, I've been over the chapters we've covered for a little over an hour now, and the only mention i can find of a parametric representation of a plane is in passing...

[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 +...

so the question is: eliminate the parameter in the pair of parametric equations x = h + a secθ y = k + b tanθ to find the corresponding rectangular equation. im taking an online course of calculus and i can't find an explanation of how to do this anywhere...ive been trying but it...

i have a couple questions that confuse me that would help me on doing my homework on parametric equations... do the parametric equations x=t^2 and y=t^2 describe the line y=x? and if y is a function of t and x is a function of t, then is y a funcion of x? and last, does x=cos t, y=cos^2(t)...

I have an upcoming exam, and I'm having trouble grasping some concepts. The things that are currently perplexing me are parametric equations and rectangular equations and converting between the two. I have a problem like this Given the parametric equations x = e^(-t) + 1 and y = e^(-2t) -...

I am confused myself, so I post the Q. when we talk about "definite integral of area" in rectangular or polar coordinates, the "area" is quite clear, at least people do it in this way in general: rectangular coordinate: area between locus y=f(x) and x axis. polar coordinate: sector area...

I need samples of parametric equations: x=Fx(t); y=Fy(t); the samples must be useful or famous in math, physics or engineer, not be created randomly meaningless. one that I know is to describle ellipse: x=A*cos(t); y=B*sin(t); I need 2 or more good samples for my report. thanks...