Curve Definition and 1000 Threads

Homework Statement The question is- What is the minimum coefficient of static friction that would keep the car from sliding off the curve? The Cars mass is 13500KG and it is traveling at 50.0hm/hr(13.9m/s) and the curve has a radius of 2.00 x102 m. I know the centripetal acceleration of the car...

I have a calculus question and I am not sure where to get started. The question states:"Find the value of c>0 such that the line y=x+1 is the tangent line to the curve c√x (i.e. intersects the curve at one point and shares the same slope at that point)." Thanks

Homework Statement f(x,y) = x^2 + xy + y^2 and z=2x+y intersect, find a parameterization of the curve where they intersect. Homework EquationsThe Attempt at a Solution I am lost. I know that z is the partial derivative of the original function, if that's of any use. I can visualize it but not...

a) Find the roots of the equation $$x^{2}+5x-6$$ b) Sketch the graph of the function $$x^{2}+5x-6$$ labeling the points at which the graph crosses the axes and the co-ordinates of the maximum and minimum of the curve c) Find the equation of the tangent at the point where $$x=2$$ on the curve...

Homework Statement I have data of an experiment to find absorbtion coefficent of a sample. one curve shows intensity of original beam, the other one is intensity with sample (with wavelenght). Here is the data : Homework Equations Where: I = the intensity of photons transmitted across...

I need to perform geometry matching of curves (see http://www.tiikoni.com/tis/view/?id=c54d9b8 ). As it can be seen, the big problem is that curves might be rotated, though they have similar shape. Do I need to make curve fitting and look at the parameters of analytical models? But, I guess...

There is a 2D array of x and y positions of a vehicle measured at an interval of one second, e.g.: [FONT=Courier New]x y 1, 5 1, 6 1.5, 6.8 ... I need to somehow quantify how a given driver approaches curves (i.e. driving style - does he/she drives aggressively or not). For this, I divided...

Is normal force on moving car on a track a component of weight or vice versa.

A problem states " For a banked curve, ignoring friction, prove that tan θ = ν^2/rg". I tried to prove but I thought that as the normal force is at right angle to track then how could be the component of normal force provide the centripetal force as my book is saying. Please someone help. I...

I'd appreciate advice on the correct statistical method to analyse a dataset - Dataset is basically a titration curve consisting of [0.5, 1, 2, 3, 4, 5, 6] pg of starting material and 8 replicates in each 'pg bin'. In 'stage 1' of the process each bin is labeled separately, in 'stage 2' all...

Homework Statement Let C be the curve given parametrically by x = (t^3) - 3t; y = (t^2) - 5t a) Find an equation for the line tangent to C at the point corresponding to t = 4 b) Determine the values of t where the tangent line is horizontal or vertical. Homework Equations dy/dx =...

According to the documents I have read, Plank made two changes to Rayleigh-Jeans approach in order to produce an equation that matched the black-body radiation, experimental curves: 1) As a mathematical convenience he assumed that the oscillators in the walls of black-body cavity could only have...

Hi Folks, I have a curve that varies sinusoidally calculated from a numerical program as attached "Trace.png". I would like to fit this amplitude modulation expression to it. f(t)=A[1+B \cos(\omega_1 t+ \phi)] \cos(\omega_2 t+ \theta) I managed to adjust the parameters manually to get a very...

Homework Statement Calculate ##\int_C z^{1/3} dz##, where ##C## is the circle of radius ##1## centered at the origin oriented in the clockwise direction. Use the branch ##0 \le \arg z \le 2 \pi## to define ##z^{1/3}##. Homework Equations The Attempt at a Solution [/B] I was hoping that...

Hey I am new here and not exactly sure how it works. I am stuck on this problem from my professor and would love any help anyone has!When one thinks of the normal distribution the first thing that comes to mind is the bell curve and grades. While this is one example of a normal curve that is...

Hi All, Having plotted a cell growth curve (fluorescence vs days), I have found that during the lag phase, the fluorescence values decrease. I haven't come across this previously during lectures and can't seem to find any examples online to help explain it. My only thought was that cell death...

Homework Statement Attached Image Homework Equations this is not a simple plane curve or a close plane curve so I use the formula: ∫ F ⋅ dr/dt dt The Attempt at a Solution From the point (0,0) to (2,4) Direction Vector v(t) = <2-0, 4-0> Parametric Equation: r(t) = (2t + 0) i + (4t + 0) j...

Homework Statement Evaluate the line integral over the curve http://webwork.math.ttu.edu/webwork2_files/tmp/equations/33/92ca0e3b907f876e5a974ad1457d1f1.png from to http://webwork.math.ttu.edu/webwork2_files/tmp/equations/6f/bccf9dd59b9c22450c590a042bb77d1.png . ∫-ydx+3xdy (over the curve C)...

Homework Statement Consider a mass sliding down a frictionless curve in the shape of a quarter circle of radius 2.00 m as in the diagram. Assume it starts from rest. Use Euler’s method to approximate both the time it takes to reach the bottom of the curve and its speed at the bottom. Hint...

Homework Statement ##C(t) = t =it^2##, where ##-2 \le t \le 2##. Re-parametrize the curve from ##t## to ##\tau## by the following transformation: ##\tau = \frac{t}{2}##. Homework EquationsThe Attempt at a Solution So, the variable ##\tau## is half of every value ##t## can be. Therefore, I...

Relative equations: F = ma a = v^2/r Fcent = mv^2/r ωf^2 – ωi^2 = 2αs s = θr ω = v/r Problem statement and work so far are all included: (I am having trouble with 5 and no clue how to start on 7-9) You are designing a roadway for a local business, to include a circular exit ramp from the...

Hello, I was working on a textbook problem that was referencing a paper regarding the mechanism for the production of Terephthalic acid (TPA). It piqued my interest so I found the original paper and did some reading. At least in 1987 when this paper was published, the intermediate reactions were...

Homework Statement Let A be a set of critical points of the function f(x). Let B be a set of roots of the equation f''(x)=0. Let C be a set of points where f''(x) does not exist. It follows that B∪C=D is a set of potential inflection points of f(x). Q 1: Can there exist any inflection points...

Hi all, I want to know the why the Braking force coefficient is increasing first and then decreasing with respect to wheel slip. I attached the graph for your reference

A point moves along the curve y=2x^2+1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x=(3/2)?Ok here's what I've done... Dy/dt=(4x)(dx/dt) -2 = (4*3/2)(dx/dt) So dx/dt=-1/3 (ie decreasing by 1/3 units per second) First, is...

The question I've been given this question by a teacher and I'm clueless as to what b) and c) are. Could you please help? I would really appreciate it. The prize is a place to see a lecture on quantum simulation at our local University. Thank you :)

Hy, I wonder which is the good solution for this problem: Nonlinear least square problem: function: y = x / (a + b.x) linearization: 1/y = a/x + b substitution: v = 1/y , u = 1/x >> model v = b + a.u What we did in school: x = [1 2 4 7]; y = [2 1 0.4 0.1]; v=1./y; u=1./x; n = length(x)...

I'm confused trying to understand the previous steps that lead to the formula for the angle of an ideally banked curve. In absence of friction, this is the angle where the Centripetal Force is provided by the horizontal component of the Normal Force. I understand that the Normal Force is...

In john oprea's differential geometry book he discusses the notion of a rectifying curve. where the difference of the position vector along the curve and some constant vector lies in the rectifying plane defined by the tangent and binormal vector of the Frenet Frame. I'm having a hard time...

Hi, I'm building a fluid model and using the method of characteristics to solve it. I'll not go into the details as they aren't necessary. Basically I have two points $(-\epsilon,70)$ and $(\epsilon, 0)$ and need to create an exponential curve between them. Could someone please tell me of a way...

At what point on the curve $$y = e^x$$ is the tangent line parallel to the line $$y = 2x$$ The derivative of y is $$\frac{dy}{dx} = e^x$$ But I'm unsure how to proceed from here.

Homework Statement A highway curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road? r = 80m \theta = 45^o g = 9.8m/s^2...

NB. first time using Latex so apologies if something came out wrong, I've done my best to double check it. Consider the curve y = \frac{1}{x} from x=1 to x=\infty. Rotate this curve around the x-axis to create a funnel-like surface of revolution. By slicing up the funnel into disks with...

Homework Statement A civil engineer is asked to design a curved section of roadway that meets the following conditions: With ice on the road, when the coefficient of static friction between the road and rubber is 0.12, a car at rest must not slide into the ditch and a car traveling less than 70...

For finding fan performance curve where better to put static pressure probes - near the surface or near the center of the duct ?

how to prove Any curve in space can be written as for a parameter

Hi there, I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic. Here are my questions 1) Can both optical and acoustic branch of phonon can simultaneously exist in crystal? 2)Why there is a band gap between optical and acoustic phonon...

How do I find the polar coordinates of the points on the polar curve r=cos(theta)+sin(theta), 0(greater than or equal to)(theta)(less than or equal to)(pi), where the tangent line is horizontal or vertical? I know that I need to convert the coordinates to x & y and then take the derivative of...

Hi, We all know everyone's favorite "exception" to the speed of light limit...that space itself can expand faster than C. My question is whether space can curve faster than C? I understand that gravity travels at the speed of light...but can space itself move faster than this limit in other...

Homework Statement Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) . Homework Equations s(t)=integral of |r'(t)| dt The Attempt at a Solution I was able to get the integral of the magnitude of the velocity vector to simplify to: s(t) = integral of...

Hello I'm having trouble wrapping my head around finding things from stress strain curvesI need to find: Elastic modulus (Young’s modulus) •Yield strength •Tensile strength •Uniform and total elongation (ductility) elastic modulus I think is 1240/0.02 = 62000 but I'm unsure of how to find...

Hello! I would like to learn finding genus of my curve $x^2-x+y-y^5$. Also, I want to know how to apply Falting's Theorem to conclude finitely many rational points of my curve. Thanks in advance!

Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...

Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0Homework Equations Arc length =...

Dear all, here is my animation of a simple plot: Animate[ ParametricPlot[ {Sin[tf], Cos[tf]}, {tf, 0, t}, PlotStyle -> {{Thickness[0.002], Red}, {Thickness[0.002], Blue}}, PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, AspectRatio -> Automatic], {t, 0.01, 100, 0.01}, AnimationRate -> 2...

I am trying to calculate the area under the curve of a projectile for a school project. A simple way to do this is to integrate the following equation of the trajectory: However I've tried to use another method. Since we have the two equations for the horizontal and vertical displacements...

Eh. I'm not quite sure how to find the curve γ(t). I think that the problem is probably a bit easier being given the parametrization of M. I do know that the point P lies in the xy-plane.

Why curvature of a plane curve is k = \frac{d\phi }{ds} ? I know that curvature of a plane is \frac{\left | r'(t) \times r''(t) \right |}{\left | r'(t) \right |^3} , and that led to this. k = \frac{\left | \frac{d^2s}{dt^2} \right |sin\phi }{\left | \frac{ds}{dt}\right |^2} But I can't go...

I've spent hours on this question: A truck of mass 4500 kg is traveling in a fog due north at 20 m/s. Suddenly, at point A, the driver notices a wall straight ahead. He makes a sharp right turn along path AB, which is one-quarter of a circle of 50 m radius. He does this without any change in...

Homework Statement Find the slope to the tangent line to the polar curve r^2 = 9 sin (3θ) at the point (3, π/6) Homework Equations dy/dx = (r cos θ + sin θ dr/dθ)/(-r sin θ + cos θ dr/dθ) The Attempt at a Solution So I have no issues with taking r^2 = 9 sin (3θ) and taking the...