Parametric Definition and 650 Threads

The question states: Two towns A and B are located directly opposite each other on a river 8km wide which flows at a speed 4km/h. A person from town A wants to travel to a town C located 6km up-stream from and on the same side as B. The person travels in a boat with maximum speed 10km/h and...

The question states: Two towns A and B are located directly opposite each other on a river 8km wide which flows at a speed 4km/h. A person from town A wants to travel to a town C located 6km up-stream from and on the same side as B. The person travels in a boat with maximum speed 10km/h and...

2. Determine vector and parametric equations for the z-axis. (Just so everyone is clear, The z-axis is actually a line in space. So you need to write the vector and parametric equation of this line)

x=t2 and y=t3-3t, find dy/dx and d2y/dx2 I understand how to get to dy/dx but an confused on how to get to d2y/dx2 can someone please explain in depth, I know the formula is (d/dt dy/dx)/(dx/dt) I don't understand where d/dt comes from and what it is. why do we not just derive it twice? I...

Homework Statement Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°. line 1: x = 4 + 2t y = 8 + 3t z = -1 - 4t line 2: x = 7 - 6t y = 2+ t z = -1 + 2t Homework Equations not sure. I am not asking for the answer...

Homework Statement Point A (1, -1, 2) Line s = 2i - j + t(3i -j +k)The Attempt at a Solution Ordinarily these are pretty obvious, but in this case the line is also a parametrized vector. So if I consider r = r0 + st And sub in s as I would do normally, I'd end up getting t^2's, and that's...

Problem statement attached. The correct way to do this seems to plug in your given x, y, z into F then integrate the dot product of F and <x',y',z'> dp from 0 to 1, however, this results in way too messy of an integral. Answer is 3/e...

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

I have been working in complex functions and this is a new animal I came across. Let γ be a piecewise smooth curve from -1 to 1, and let A=∫γa(x2-y2) + 2bxy dz B=∫γ2axy - b(x2-y2) dz Prove A + Bi = (2/3)(a-bi) In the past anything like this defined γ and I would find a parametric...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 6 cos t, y = 6 sin t, z = 6 cos 2t; (3√3, 3, 3) Homework Equations The Attempt at a Solution So I understand that r(t)= 6cost t, 6sint...

Hi all, I want to convert a curve from polar coordinates function to a parametric function. The function is: r = 2 \cdot \cos( 4\cdot\theta ) I want to convert this for ( x(t), Y(t) ). Why do I want this? Because I saw that wxMaxima make plots of parametric functions, but I don't know...

Homework Statement Find the parametric equations through point (5,-1,3) parallel to the line of intersection between 2x-y+z=1 and 6x-y-z=3, where 0≤t≤1 Homework Equations 1. Find normal vectors for both planes 2. Take cross product of both normal planes ... The Attempt at a...

The problem is from an online homework assignment. I know it's probably fairly simple, but my brain isn't grasping it right now for some reason.[The Problem] We know: r(t) = <3t2 - 8t + 3, -9t2 + 2t + 7> And we are asked to find d2y/dx2.[Background Information] My understanding of d2y/dx2...

Homework Statement x = t^3, y = (3t^2)/2 0<= t <= √3 The Attempt at a Solution dx/dt = 3t^2 dy/dt = 3t step 1. √((3t^2)^2 + (3t)^2) step 2. 3t^2 + 3t (the book says I can't do that, I don't see why) step 3. insert √3 into t Here's the books solution I...

Homework Statement Find parametric equations for the line which passes through the point (1; 2; 3) and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 -2x. I have seen the result for this problem, but it's different than mine. I'm not sure, what I'm doing wrong. Please, help...

Homework Statement Find parametric equation for (((x-2)^2)/4)+(((y+1)^2)/9)=1 Homework Equations ((x^2)/(a^2))+((y^2)/(b^2))=1 (ellipse equation)The Attempt at a Solution I tried solving for y which gave me y=(6/(x-2))-1, but that did not work.

Homework Statement This is a problem involving parametric equations. r1= <t,2-t,12+t2> r2= <6-s,s-4,s2> At what point do the curves intersect? Find the angle of intersection, to the nearest degree. The Attempt at a Solution I found the point of intersection, (2,0,16). This is when t=2 and...

I can't seem to figure out the equation of the attached graph. I have tried polar, parametric, and cartesian, and I'm almost positive its parametric. Does anyone know what the equation might be?

Homework Statement First exercise: Compute the surface area of that portion of the sphere x2+y2+z2=a2 lying within the cylinder x2+y2=ay, where a>0. Second one: Compute the area of that portion of the surface z2=2xy which lies above the first quadrant of the xy-plane and is cut off by the...

I just want to make sure my thinking is correct with a problem I'm working on. I'm trying to write a function that will take a point on a plane above a sphere, and then project it onto that sphere. From there project the point onto the x,y plane by following the normal vector of the sphere I...

Hi. I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis. I'm using the following...

Homework Statement i was given two parametric equations of two lines in R^3 and asks me to find the isometry between one line and the other knowing that point (a,b,c) of first line is mapped in point (a',b',c') of second line. Homework Equations What i have to find is a 3x3 matrix which...

Hello. I apologize if I put this in the wrong section. I got this problem with the assignment I am currently working with. I have to set the position function for motion as a parametric equation for motion in circular motion, horizontal and vertical respectively. While I do know the...

Hello forum! I have yet another question concerning calculus and the topic we're doing right now is extremely confusing for me. Homework Statement Eliminate the parameter from the parametric equations x=3t/(1+t3), y=3t2/(1+t3), and hence find an Cartesian equation in x and y for this curve...

In optical parametric conversion process, such as second harmonic generation,the conversion efficient is determined by function sinc(ΔkL),where L is the length of the crystal,and Δk is the phase mismatch condition. When the sum of wave vectors of the two fundamental photon,equals to that of the...

I am exploring the motion of a particle who's path P(x,y) is given by two parametric equations: x = f(t) = a cos(bt) + cd (1) y = g(t) = a sin(bt) (2) To get a tangential velocity for this particle, I differentiated (1) and (2) then combined them using the form sqrt( m2 + n2...

Find the length of the curve given by the parametric representation... Homework Statement Calculate the length of the curve given by the parametric representation r(t) = t2(cos t; sin t; cos 2t; sin 2t) for 1≤ t ≤+1: Homework Equations The Attempt at a Solution I know that...

I'm attempting to convert the following parametric equation into into one f(x, y, z), and am running into difficulty. (Is it even possible?) Can I get some help? x=(2+cos(3t))*cos(2t) y=(2+cos(3t))*sin(2t) z=sin(3t)

Homework Statement Consider the function F(x,y) = 1 - x3 - y2 + x3y2. Consider the curve C given parametrically as x(t) = t1/3, y(t) = t1/2 for t ≥ 0. Determine the minimum and maximum of F(x,y) along the curve C. The Attempt at a Solution I think this is basically a max/min problem with...

Homework Statement Find the area of the part of the plane 3x + 5y + z = 15 that lies inside the cylinder x^2 + y^2 = 25. Homework Equations A=∫∫(√1+(dz/dx)^2+(dz/dy)^2) dA The Attempt at a Solution my bounds were r=0 to 5 and theta=0 to 2pi ∫∫√1 + (-3)^2 + (-5)^2 dA =∫∫√35 dA...

Homework Statement Suppose you need to know an equation of the tangent plane to a surface S at the point P(2,1,3). You don't know the equation for S but you know that the curves r1(t)=<2+3t,1-t^2,3-4t+t^2> r2(u)=<1+u^2,2u^3-1,2u+1> both lie on S. Find an equation of the tangent plane at P...

Homework Statement find parametric equations for the semicircle x^2+y^2=a^2, y>0 using as parameter the slope t=dy/dx of the tangent to the curve at (x,y) Homework Equations The Attempt at a Solution well i know that to parametrize a circle i would use x=acost and y=asint for...

hi i solve numerically two coupled equation and obtain two function x[t] and y[t]. how i plot x[t] versus y[t] so that horizontal axis to be x[t] and vertical axis to be y[t]. here is the notebook of mathematica http://www.mediafire.com/?g4sa3zi630vi8nl thanks

hi... please help me this question. i am not understand this question. Find a vector equation of the plane for the following parametric equations: X= 1 +2t1 – 3t2 y = 3 + 4t1 – 4t2 z = 2 + 3t1 – 5t2 i just want a solution, just let me know if possible.

Homework Statement See Attachment Homework Equations None I can think of The Attempt at a Solution I'm fairly certain that phi_yx is zero Also I tried factoring out the cos and splitting up the equation into it's respective components, but to no avail. Am I even going about this correctly?

Homework Statement For the curve: r(t) = ⟨\frac{1}{2}t5, \frac{1}{3}t5, \frac{1}{6}t5⟩, Find the arc length s(t) Find the unit tangent T(t) and T(1) Find the principle unit normal N(t) and N(1) Find the binormal vector B(t) and B(1) Homework Equations T(t) = \frac{r'(t)}{|r'(t)|}...

Can anyone tell me how to convert this parametric equation to cartesian (x,y)? r(t)=<2.5+2cos(4t),2.1+1.23sin(4t)> I've tried so many ways and they're incorrect.

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...