Parametric equations Definition and 199 Threads

So I'm having a tough time figuring out this problem. John and Cory are golfing in the DV golf ball team. They are teeing off a hill 4 feet above the horizon. The hole is located 250 yards from the tee. The hole is 20 feet above the horizon. Cory is stronger than John and hits a velocity of...

1. Find parametric equations for the line joining the points P = (1,2,-1) and Q = (5,7,5).[/b] 2. x = x0+ta y = y0+tb z = z0+tc 3. v = <(5-1), (7-2), (5+1)> so v = <4,5,6> and since v is a vector in the direction of the line and should be able to be placed in the above...

Just a quick question... if we have f(x,y,z) and x(t), y(t), z(t), without substituting in what x y and z are in f, how do we calculate df/dt?

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 2cos(t) y = sin(t) z = t At the point (0,1,pi/2) Homework Equations The Attempt at a Solution r(t) = <2cos(t),sin(t),t> r'(t) = <-2sin(t),cos(t),1>...

Homework Statement Homework Equations r = <x,y,z> r' = <x',y',z'> The Attempt at a Solution I started by finding the derivatives of each part of the vector and got: x= 2/sqrt(t) y= 3t^2+1 z= 3t^2-1 Then I plugged the point (5,2,0) into that and got (2/sqrt(5), 13, -1). This should be...

these are fairly simple questions that only require you to plot points and then find a Cartesian equation of the curve. My question is when trying to solve for the Cartesian Equation, whether to solve for X first or Y? I will give an example. X=3t-5 , y=2t + 1 Graphing this is simple...

So, the parametric equations of a line segment from (x0,y0,z0) to (x1,x2,x3) are x = (1-t)x0 + tx1 y = (1-t)y0 + ty1 z = (1-t)z0 + tz1 right? But how are these equations derived? I don't really see where the (1-t) is coming from. I would be really thankful if anybody could explain...

Hey, I have a calculus 3 test coming up that involves calculating the mass of an object using a density function. I know how to use the double integral form for x-y equations, but the practice test my professor gave me has a question using parametric equations and I don't know how to...

Homework Statement The ellipsoid 4x^2+2y^2+z^2=16 intersects the plane y=2 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1,2,2) Homework Equations sin(t)^2 + cos(t)^2 = 1 The Attempt at a Solution After plugging 2 in for y, I get...

A wheel radius a rolls along a line without slipping. The curve traced by a point P that is b units from the center (b < a) is called a curtate cycloid (see figure). Use the angle θ to find a set of parametric equations for this curve. I went through the book, went to the math lab at...

Find parametric equations for the line through the point that is perpendicular to the given line, and intersects this line. We are given the point (0, 2, 2) and the line x = 1 + t, y = 2 - t, z = 2t. We are also given one of the parametric equations, that being x=3s. I am looking for...

Homework Statement Consider the ellipse given by the parametric equation x=3cos(t) y=sin(t) 0\leqt\leq2\Pi. Set up an integral that gives the circumference of the ellipse. Also find the area enclosed by the ellipse. Homework Equations \int\sqrt{1+(dy/dx)^2}dt The Attempt at a...

Homework Statement Consider a projectile launched at a height of h feet above the ground at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modled by the parametric equations x=(v[SUB]0cos θ)t and y=h + (v[SUB]0 sin θ)t-16t2. The...

Homework Statement Given the parametric equations, x=t^3-3t , y=t^2/(1+t^2) i am asked to sketch this curve. Homework Equations The Attempt at a Solution I am unsure how to get the cartesian equation here..

Find the asymptotes of the parametric equations The graph looks like this: My attempt: Is my presentation correct? Do I also need to consider as x approaches 0 ? The reasons I ask is because I couldn't find the asymptotes of if I use the above presentation... Please...

x=rT-dsinT y=r-dcosT trochoid for d<r integrating this on 0,2pi = 4x[0,pi/2] I am getting 2r^2pi-8rd+d^2pi text is just showing 2r^2pi+d^2pi

Homework Statement Solve the following parametric equations for y = f(x) x(t) = e^{-t} + t y(t) = e^{t} - t The Attempt at a Solution I'm completely stuck on this one. I've noticed x + y = e^{-t} + e^{t} and also y = \frac{1}{x-t} - t but that's about as far as I've gotten.

Homework Statement write the vector equation and parametric equation of the line through A(-1,2,1) and B(1,2,1) Basically I was wondering If i found AB or BA would it be equivalent? Homework Equations AB= OB-OA= (1,2,1)-(-1,2,1) = (2,0,0) BA= OA-OB= (-1,2,1)- (1,2,1) = (-2,0,0) thus ...

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 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

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...

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

Can someone help me get started on number one please?

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...

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...

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)...

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 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 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 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 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 =...

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...

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...

Hey guys so I had trouble with this problem, I hope it's not too long and you can help me out. Homework Statement A point moves following (starting at λ = 0 and increasing): x = 4·cn(λ) y = 3·sn(λ) z= am(λ) Find the distance the point has traveled when the speed vector is parallel to (-4, 3...

The center field fence in a ballpark is 10 feet high and 400 feet from home plate. A baseball is hit at a point 3 feet above the ground. It leaves the bat at an angle of (theta) degrees with a horizantal at a speed of 100 miles per hour. x = (v0 cos(theta))t and y = h + (v0 sin(theta))t -...

Hi everyone, I'm an 18-year-old from Germany and I'm making use of MIT's OpenCourseWare programme. Currently, I'm watching the Calculus II course, and am having some trouble understanding how to find the equation: z=z0 + a(x-x0) + b(y-y0) by using parametric equations/vectors. a and b being...

Homework Statement L1 L2 x= 1+t x= 1+2s y= 1+6t y= 5+15s z= 2t z= -2+6s My professor said to find a normal vector and project the lines, but I'm new to this calculus and all these words are just a fuzzy cloud over my head. Homework Equations Projection of c...

Homework Statement In the xy-plane, the curve with parametric equations x=cost and y=sint, 0<=t=<pi, has what length? The Attempt at a Solution I drew the graphs x=cost and y=sint and shaded the area where the graphs intersect between 0 and pi. I don't know where to go from here.

Homework Statement Find parametric equations of the tangent line at the point (-2,2,4) to the curve of intersection of the surface z=2x2-y2 and the plane z=4 Homework Equations Not sure The Attempt at a Solution Not sure quite how to approach this. take the gradient of...

Homework Statement Question is "The Cartesian equation of the plane containing the line x=3t , y =1+t , z=2-t and passing through the point (-1,2,1) is?" Homework Equations \begin{array}{l} n \bullet (r - r_0 ) = 0 \\ < n_1 ,n_2 ,n_3 > \bullet < x - x_0 ,y - y_0 ,z - z_0 >...

Homework Statement Consider the parameterization of the unit circle given by x=cos(3t^{2}-t), y=sin(3t^{2}-t) for t in (-\infty,\infty). In which intervals of t is the parameterization tracing the circle out in a clockwise direction? In which intervals of t is the parameterization tracing...

Homework Statement If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. In the accompanying figure, the circle in question is the circle (x^2)+(y^2)=1 and the tracing point starts at (1,0). The unwound...

Homework Statement Determine if any of the lines are parallel or identical L1 (x-8)/4 = (y+5)/-2 = (z+9)/3 L2 (x+7)/2 = (y-4)/1 = (z+6)/5 L3 (x+4)/-8 = (y-1)/4 = (z+18)/-6 L4 (x-2)/-2 = (y+3)/1 = (z-4)/1.5 Homework Equations L1 pt(8,-5,-9) V<4,-2,3> L2 pt(-7,4,-6) V<2,1,5> L3 pt(-4,1,-18)...

Homework Statement Let R be the region in the 1st quadrant in the region enclosed by x=2cos(\theta) and y=sin(2\theta) Suppose R is rotated around the x-axis. Find the volume of the resulting solid. Homework Equations The formula for the solid of revolution is: V= \pi\int...

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...