Curve Definition and 1000 Threads

The Troposkien (skipping rope curve) - Variational principle approach Homework Statement Consider a chain of length l and homogeneous mass density ρ rotating with constant angular velocity ω with respect to an axis which bounds the two ends. There is no gravity acting on the system, and and d...

Here is the question: Here is a link to the question: Calculus Word Problem? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

find the curve at the point (-8,1) that gives the integrals length in the picture posted i literally have no clue what to do. am i supposed to take the derivative of 16/y^3 and square it?

Is there available any online interactive curve (e.g. Bezier, B-spline, NURBS) software? Thanks guys

On Page 106 in baby rudin (diff. chapter) when he tries to calculate the derivative of the fuction $$f(x) = \begin{cases} x^2 sin(\frac{1}{x}) & \textrm{ if }x ≠ 0 \\ 0 & \textrm{ if }x = 0 \\ \end{cases}$$ rudin used the absolute value in trying to compute the limit as ##t → 0##...

Homework Statement Obtain deflection curve in terms of q, L, and EI Homework Equations Use the second order differential equation of the deflection curve to solve. Meaning that the M(x) is the second derivative and you integrate twice to get V1 and V2 The Attempt at a Solution From the...

Find the area bound by the curve y = x^3 - 2x^2 - 5x + 6, the x-axis and the lines x = -1 and x = 2. The answer is 157/12. The curve cuts the x-axis at x = -2, 1 and 3. I've shown my general idea on the attachment. I didn't end up with the correct answer so could somebody explain to me where...

Homework Statement Find the area inside the larger loop and outside the smaller loop of the limacon r=.5+cosθ Picture here http://www.wolframalpha.com/input/?i=r%3D.5%2Bcostheta Homework Equations Area = .5∫r^2The Attempt at a Solution To get the area of the outer loop, you just get the value...

Homework Statement From Goldstein Classical Mechanics, 6.16: A mass particle moves in a constant vertical gravitational field along the curve defined by y=ax4 , where y is the vertical direction. Find the equation of motion for small oscillations about the position of equilibrium. The...

Homework Statement Given this data: hours / value ----------- 2 | 1.6 4 | 1.5 6 | 1.45 8 | 1.42 10 | 1.38 12 | 1.36 fit a curve of the form Y ≈ ae^{-bx} What value can you predict after 15 hours? The Attempt at a Solution So i can rewrite the equation as Y ≈ log(a)-bx...

Homework Statement Find the area enclosed by the graph r=2+sin(4θ) Homework Equations Area = .5∫r^2 The Attempt at a Solution Area = .5∫(2+sin(4θ))^2 =.5(4.5θ-1/16sin(8θ)-cos(4θ)) I can do the integration and all, but I am having trouble finding the limits of integration I...

For my 3rd year project, I have a set of data which is the variation within an interference pattern. The outcome has clear sine curve properties (Alternating peaks and troughs of intensity) but the positions aren't regular (i.e. the peak-to-peak distance between peak1 and peak2 is larger than...

Homework Statement Find the area of the region that lies inside the curve r^2=8cos(2θ) and outside r=2Homework Equations area of polar curves = .5∫R^2(outside)-r^2(inside) dθThe Attempt at a Solution r^2=8cos(2θ) and r=2, so... 4=8cos(2θ) .5=cos(2θ) since .5 is positive, we need the angles in...

Homework Statement Prove that any curve \Gamma can be parameterized by arc length. Homework Equations Hint: If η is any parameterization (of \Gamma I am guessing), let h(s) = \int^{s}_{a} \left| \eta ' (t) \right| dt and consider \gamma = \eta \circ h^{-1}. The Attempt at a Solution...

Homework Statement A curve of radius 60 m is banked for a design speed of 100km/h. If the coefficient of static friction is 0.30, at what range of speeds can a car safely make the turn. Homework Equations Fun=ma Ff=μsFn Fc=mV2/r The Attempt at a Solution So, when it is...

Homework Statement Show that the area enclosed by a closed curve {x(t); y (t)} is given by A=\frac{1}{2} \int_{t_1}^{t_2} (x\dot{y}-y\dot{x})dt Show that the expression for the shortest curve which encloses a given area, A, may be found by minimising the expression s=\int_{t_1}^{t_2}...

Hi All! I would really appreciate your help on something that has been bothering me for the past week. I am uncertain on how to derive the deflection curve equation for a certain shaft. Loads are acting on both ends of the shaft, with the reaction forces being provided by two separate bearings...

Homework Statement Compute the flux of \overrightarrow{F}(x,y) = (-y,x) from left to right across the curve that is the image of the path \overrightarrow{\gamma} : [0, \pi /2] \rightarrow \mathbb{R}^2, t \mapsto (t\cos(t), t\sin(t)). A (2-space) graph was actually given, and the problem...

Hello, Suppose, 1. I have a function f=C1 + C2/((C3-X)^C4); where Cn is a constant; I'm looking at the Havriliak-Negami equation which has some 5 constants. 2. I have a data set whose least-squares fit looks like a curve, How can I compute the values of the function's parameters C1 to...

Greetings~ We were told to linearize this equation below: y= x^2/(a+bx)^2 after we multiply both the sides with the denominator (a+bx)^2, and then divide both the sides by y, can we apply ln to both the sides? Because I can see no other way of linearizing this :/

Hello, I am wondering how to make a standard additions curve for this experiment. In this experiment, we used cyclic voltammetry to determine the original concentration of an elixir. We diluted the elixir to 0.75mM based on a claimed concentration of acetaminophen (instructed) and an elixir...

THe parametric equations of the curve C are: x = a(t-sin(t)), y = a(1-cos(t)) where 0 <= t <= 2pi Find, by using integration, the length of C. \dfrac{dx}{dt} = a (1-\cos t) \dfrac{dy}{dt} = a\sin t \left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2 = a^2 (1 - 2\cos t +...

Homework Statement The tangent of any point that belongs to a curve, cuts Y axis in such a way, that the cut off segment in Y axis is twice as big as the X value of the point. Find the equation of the curve, if point (1,4) is part of it.Homework Equations The ultimate solution is y =...

Homework Statement For whoever does not want to read the attached problem: Firstly, I need to express the arc-length from given x=r\cos\theta, y=r\sin\theta z = f(r), \text{ where } f(r) \text{ is an infinitely differentiable function and } r=r(\theta) \text{ i.e. parameter is } \theta I...

Hi I am doing some problem in Hibbeler's Engineering Dynamics (12 ed.). I have posted the problem as an attachment. I think the author has not given the x coordinate of the point B. Once that is given we can use the radius of curvature formula \rho = \frac{[1+(dy /...

Can anyone describe a tangency of Bezier curve such as below image?

I wonder how many degree of this curve where the endpoints are A0, A3, and A6? Is it degree of 6?

Homework Statement Compute ∫C (z+i)/(z3+2z2) dz Homework Equations C is the positively orientated circle |z+2-i|=2 The Attempt at a Solution I managed to solve a similar problem where the circle was simply |z|=1, with the centre at the origin converting it to z=eiθ with 0≤θ2∏. I'm...

Hi everyone, I would like to ask about the continuity of the cubic Bezier curve. There are two cubic Bezier curves, A and B, shown as below two images: The coordinates of the A curve are: A0 = (x0,y0) = (0,0) A1 = (x1,y1) = (2,3) A2 = (x2,Y2) = (5,4) A3 = (x3,y3) = (7,0)...

Homework Statement Find the length of the curve between x=0 and x=1. [SIZE="4"]Note: can this be done without a calculator?Homework Equations y = sqrt(4-x^2) The Attempt at a Solution x=2sin∅ dx = 2cos∅ d∅ sqrt(4-4(sin∅)^2) ---> 2cos∅integral (0 to 1) sqrt(1+(-2sin∅)^2) integral (0 to 1)...

Homework Statement At what points on the curve y = (x^2)/(2x+5) is the tangent line horizontal? Homework Equations Quotient rule The Attempt at a Solution I figured out the derivative which is 2x(2x+5) - 2x^2 ----------------- (2x+5)^2 I also know that for the equation of...

Homework Statement Just wondering if my output seems wrong. The interpolating polynomial looks like it's way off, though I've looked over my code many times and it seems right (?). [FONT="Courier New"]clc clear all format long x1=[1:1/10:4]; y1=zeros(1,length(x1))...

Hello everyone, I've been googling how to find the angle of a curve but the results are not the kind I'm looking for. Let's say I have a shape that has a curve in it at some point. Something like this. I'm curious what I need to be reading in order to find the angle of the curve. what...

So I have a function \(f(x,y)=\sqrt{2x+3y}\) and need to find the gradient at the point (-1,2). I got this part already, its \(\frac{1}{2}\hat{i}+\frac{3}{4}\hat{j}\). The part I'm having trouble with is when it asks me to sketch the gradient with the level curve that passes through (-1,2). The...

Homework Statement A car travels around a circular curve on a flat, horizontal road at a radius of 42meters. the maximum frictional force between the tyres and the road is equal to 20% of the weight of the car calculate the maximum speed at which the car can travel around the curve at a...

Homework Statement The hypocycloid is the plane curve generated by a point ##P## on the circumference of a circle ##C##, as this circle rolls without sliding on the interior of the fixed circle ##C_0##. If ##C## has a fixed radius of ##r## and ##C_0## is at the origin with radius ##r_0## and...

Homework Statement The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 3 - x^2 0 \leq x \leq 4 Homework Equations A_{y} =2\pi\int_a^b x \sqrt{1+\left(\frac{dx}{dy}\right)^2} dy The Attempt at a Solution now we need to write x in terms...

Is there a visual way to represent this theorem? Like Riemanns rules with rectangles and trapezoids? I know the clear cut way to evaluate the area under the curve using the rule on a closed set. Soooo any thoughts?CORRECTION THIS IS SIMPSONS RULE*typo...

Dear Members, I would like to ask if we plot the Roll data of a satellite in degrees vs. the time, and if we take the area under the curve of this roll will give something meaningful? Looking forward for your reply. Regards,

here is a geometric proof, similar to the one in my textbook (copied from Aryabhata, from http://math.stackexchange.com/questions/15294/why-is-the-area-under-a-curve-the-integral) : Is this saying: that the A' equals the function. Which is implying, that the integration of A equals F (where F...

"find a unit tangent vector and the equation of the tangent line to the curve r(t) = (t, t^2, cost), t>=0 at the point r(pi/2)." NOW, what I don't get is, how is that a curve? This is not like the example I have studied and I don't really get the question. So I don't know where to start. Once I...

Homework Statement At what point does the curve \vec{r}(t) = <t,0,2t-t^2> intersects the paraboloid z=x^2+y^2 Homework Equations None Known The Attempt at a Solution I assume that it might be easier to parametrize z=x^2+y^2, but I'm not sure how to do that or if there's a more...

Homework Statement Let α(t) be a regular, parametrized curve in the xy plane viewed as a subset of ℝ^3. Let p be a fixed point not on the curve. Let u be a fixed vector. Let θ(t) be the angle that α(t)-p makes with the direction u. Prove that: θ'(t)=||α'(t) X (α(t)-p)||/(||(α(t)-p)||)^2...

Homework Statement Find the number of tangent lines to the curve: y=\frac{3x}{x-2} which pass through the point (-1,9). Find also the points of contact of these tangent lines with the curve.The Attempt at a Solution 1. I found the equation of lines passing through (-1,9) -> y=(x+1)m+9 2. I...

Fig 1 : the blue volume has a lot of very small spherical balls in it. Balls are under pressure from external system (weight or other), the potential energy is always the same because the blue volume is constant. When I move the blue volume from position 1 to position 2, I can understand that...

Homework Statement A car with mass of 1200kg turns sharply with a radius of 40m and at 15/ms. The tires have a static friction of 0.9, rolling at 0.6 and kinetic at 0.3. 1) how long does it take to make a turn at half a circle. 2) what is the magnitude of frictional force on the tires in the...

I seem to recall when taking college Trigonometry my professor saying that the unit circle and sinusoidal curves were basically a mathematical represention of a slinky in that the unit circle was the view of a slinky head on, so that what you saw in the two dimensional sense was a circle, and...

I hope that this is a foolish question and that someone can make quick meat out of it. If \gamma: S^1 \to M is a loop on an arbitrary manifold M, our goal is to analyze the tangent vectors to \gamma when the loop is traversed in the opposite direction. Let \iota: S^1 \to S^1 be the map...

Homework Statement Find the length of the curve: \phi(t)=\left\{(5+\cos(3t))\cos(t), (5+\cos(3t))\sin(t) \right\}\mbox{ with } t\in [0, 2\pi] Homework Equations L_{\phi}= \int_{a}^{b}\sqrt{[x'(t)]^2+ [y'(t)]^2}\qquad (1.1) Where x(t)= (5+\cos(3t))\cos(t) y(t)=...

Homework Statement Given the following curve: y = x^3 Use shell method and rotate around x-axis to determine the volume bounded region: y = 8, x = 0 Homework Equations 2pixyThe Attempt at a Solution x(x^3) = x^4 Integrate x^4 = 1/5 x^5 1/5(8)^5 = 6553.6 *2 = 13107.2 pi the answer should be...