Homework Statement
I'm a year 12(final/senior year) student in Australia and in my specialist maths course we have an assignment worth 20% of our grade. Anyway it has to show good a lot of good maths in a self explanatory investigation(approx 10+ pages). For my assignment i wanted to do...
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
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...
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter.
x = tan(θ)
y = sec(θ)
(1 , √2)
y = ?
attempt ;
y - y1 = m(x-x1)
y = √2
x = 1
y1 = sec(θ)
x1 = tan(θ)
substituting and solving it...
Homework Statement
Estimate the length of the curve with parametric equations x = t^3, y = t^3, z = t^4, 0<=t<=3. Round to the 3 decimals place.
Homework Equations
The Attempt at a Solution
virst i found the magnitide.. ||v|| = (4t^2 + 9t^4 + 16t^6)^1/2
i tool the integral...
Homework Statement
Hi all.
I am given the following parametric function in the complex plane C:
\gamma = \left\{ {\begin{array}{*{20}c}
{t^2 + it\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in [0,1]} \\
{t + i\,\,\,\,\,\,\,\,\,\,\,\,{\rm{for }}\,\,t \in ]1,2]} \\
\end{array}} \right.
In...
Homework Statement
Find the length of the curve y=x^2-4|x|-x from x=-4 to x=4.
The Attempt at a Solution
I realized there is a corner at x=0 so i tried to get around this by pluggin in x for x>=0 and -x for x<0. However, my integrals don't match the answer...
I've been looking everywhere for a tutorial or lesson on Parametric equations and can't find one that shows how to derive the actual equations. Either they show how to eliminate the parameter or sketch the graph. Let's say you had a function like y = x^2 + x - 3
What would you do to find the...
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...
What parametric equation would one use to describe a sphere in General Relativity in order to calculate curvature? My main problem is what to do with the time dimension... And no, this is not a homework question.
Homework Statement
http://mathbin.net/equations/8457_0.png
My result does not seem like a "valid" equation. Is there any other approach I can take or anything that I can do to make it look prettier?
Thanks.
In both exercise, eliminate the parameter.
Problem 1 :
http://mathbin.net/equations/8157_0.png
When I graph this, it is a circle. THAT does not appear like a circular equation.Problem 2 :
http://mathbin.net/equations/8159_0.png
I am afraid of the absolute value signs. How do I deal with this...
I'm currently making a two dimensional game on my computer and I'm having a problem that pertains to parametric curves.
Currently I'm trying to figure out an equation for a graph on any angle (say a sin curve). The reason for this is to make the "flight paths" of the ships in the game more...
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 -...
Homework Statement
http://img21.imageshack.us/img21/7910/68588225.th.jpg
Homework Equations
The Attempt at a Solution
I know that the velocity is the derivative of the position vector.. but I am kind of confused how to do this
Homework Statement
(a) The parametric curve x = (3t + 4)2, y = (3t + 4)2 - 9 for 0 t 3 is a line segment.
(b) A parameterization of the graph of y = lnx for x > 0 is given by x = et, y = t for - < t < .
(c) The line parameterized by x = 8, y = 5t, z = 6 + t is parallel to the x-axis...
Hello!
I'm having a pretty big problem intersecting parametric lines. I'm using the equations:
x = x1 + t(x2 - x1)
y = y1 + t(y2 - y1)
Given the 2 lines:
x = x1 + t(x2 - x1)
y = y1 + t(y2 - y1)
x = x3 + t(x4 - x3)
y = y3 + t(y4 - y3)
I calculate the intersection, using this:
t...
Homework Statement
Two equations for two planes in 3-D
2x+y-2z=1
x-2y+z=-3
Find the parametric equation for the line of intersection of the two planes by solving these two equations togeather.
The Attempt at a Solution
Gauss Jordan gives:
1 0 -3/5 -1/5
0 1 -4/5 7/5...
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
For the field \bold{F} = (y+z) \bold{i} - (x+z) \bold{j} + (x+y) \bold{k} find the work done in moving a particle around the following closed curve:
from the origin to (0,0,2π) on the curve x=1-cos t, y=sin t, z=t; and back to the origin along the z-axis. The answer is 2π...
Homework Statement
Can someone please tell me how to get the average speed of a particle moving along a path represented by parametric equations? Is it \frac{1}{b-a}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2}
Isn't this the arc length formula?
Homework Statement
Given a continuous parametric function f : R2 -> R3 specifying a 2D
surface in 3D space, define a continuous implicit function g : R3 -> R
corresponding to the same surface.
Homework Equations
You’ll likely want to use the infimum function.
You can ignore the...
Homework Statement
Find the equation of the following planes in cartesian and (vector) parametric form:
a) the plane through the point (1,4,5) and perpendicular to the vector (7,1,4)
b) the plane through the origin and the points (1,1,1) and (1,2,3)
The Attempt at a Solution
For part...
Homework Statement
I have a problem with a nonlinear ODE, but this is my first time at using the forum. Can anyone tell me how I can introduce equations into the thread. I have MS Word which allows me to generate equations in a document. Is there a way I can stream an MS Word document into a...
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
a particle is on a trajectory defined by the parametric equations x(t)= 2t^2,y(t)= t^2-4t,
z(t)= 3t-5, where t is the time.Find the components of its velocity and acceleration at time =1, in the direcion i-3j+2k.
Homework Equations
what i thought is r(t)=x(t) i...
I haven't taken calculus yet, but I'd like to determine the closest parameter value for when a parametric curve crosses a line (for a program I'm writing). The curve is such that I need to use calculus in some way or another - it is unsolvable algebraically.
Newton iteration will find a point...
How is the parametric form of the graph of an equation different from its standard graph and what the dots in the parametric form of a graph represent.
Homework Statement
find the slope and concavity of the funtion at the given point.
x=t^2
Y=t^2+t+1
(0,0)
Homework Equations
t=x^(1/2)
The Attempt at a Solution
t=0 when x=0
x'=2t
y'=2t+1
M=2t/(2t+1)=0
for the second deritive would you take the deritive of 2t/(2t+1) devided by...
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...
I know this is very simple, but the end integral just kills me
Homework Statement
Given equation in Parametric form
x=\sqrt{2t+1}), y=6t
Find arc length
Homework Equations
The Attempt at a Solution
take x' & y'
then Take integral of \int\sqrt{1/(2t+1) + 36}
This is where I got stuck ...is...
Greetings,
I'm trying to find the surface area of the part of the sphere x^{2}+y^{2} + z^{2}=1 above the cone z=\sqrt{x^{2}+y^{2}}.
I know, that a surface area of a surface r(u,v) = x(u,v) + y(u,v) + z(u,v) can be given by,
A(S) = \int\int | r_{u} \times r_{v} | dA
A function, z=f(x,y) can...