Curve Definition and 1000 Threads

[FONT=Times New Roman]If the line $x=k$ is tangent to the curve $$\large y\:=\:x+\sqrt2\,e^{\frac{x+y}{\sqrt2}}$$ what is the value of $k$?

Hello all, I am trying to build a simulation to understand what power is required by an electric car in order to accelerate from 0-50kmh. As per my understanding the total power required by engine is calculated using Total Power required at given velocity formula as stated below. I am...

I've been in discussions on another board with a physicist and he contends that a pilot in a plane will need to put a 1 degree downward direction input to the controls to account for the 1 degree of curvature rate at 500mph. as small as those control inputs are required, he says that the...

Homework Statement Find a piecewise smooth parametric curve to the astroid. The astroid, given by $\phi(\theta) = (cos^3(\theta),sin^3(\theta))$, is not smooth, as we see singular points at 0, pi/2, 3pi/2, and 2pi. However is there a piecewise smooth curve? Homework Equations $\phi(\theta) =...

Hi folks, My query is that... As one can see that in the IF response curve the picture carrier is placed 6db down the amplitude curve. Such a placement modifies the output of video detector in such a way that the picture carrier lies at half point or 50 % of the total amplitude. Now this whole...

I understand that the centripetal force on an object of mass 'm' is (mv2)/r However, isn't this for an object going around in a circle? Suppose I have a curve (0.0033x2+−1.0038x+98.2331). What would be the fastest speed around this curve on the bounds x -> Please note that we would...

So, I've been studying some tensor calculus for general theory of relativity, and I was reading d'Inverno's book, so out of all exercises in this area(which I all solved), this 6.30. exercise is causing quite some problems, so far. Moreover, I couldn't find anything relevant on the internet that...

Homework Statement a man is driving around a curve rather quickly one day at 21.2m/s. He has an object hanging from his mirror that makes an angle of 36.4 wih respect to vertical as he goes around the curve. What is the radius of the curve? Homework EquationsThe Attempt at a Solution I set up...

Homework Statement [/B] Find the definite integral formula for the length of the curve for $$0 \leq t \leq \frac \pi 2$$ $$x = 2*cos^k(t)$$ $$y = 2*sin^k(t)$$ for general $$k \gt 0$$2. The attempt at a solution I don't understand why this is wrong: $$\int_0^\frac \pi 2\...

Dear community, For one of the projects which I am currently working on, I want to quantify my three phase AC induction motor in the following ways: 1. Find Torque vs RPM Curve 2.Find Efficiency vs RPM Curve Now since I don't have the industrial "Torque Sensor" to plot Torque vs RPM curves, I...

Question: Question: Find the point on the curve y=x^2 +1 that is closest to the point (18,1). Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot.

Mod note: Thread moved from the Precalc Homework section 1. Homework Statement So I am designing a machine. the issue is I have to calculate like 8 things and the maths is floating in my head but I can't get there. the requirements are that X axis squared + Y axis Squared = 75 Squared. then...

Homework Statement [/B] Sketch the curve z = x2 + 2y2Homework Equations None[/B]The Attempt at a Solution : [/B]The easiest thing to do is to sketch the traces at x, y and z = 0. I'm 95% sure its an elliptic paraboloid, but the 2 in front of the Y is really throwing me off. Should we...

Homework Statement Homework Equations The Attempt at a Solution I'm confused avout questions 2-3. The answers for 2-2 is 1 So the answer for 2-3 is $$\frac{1}{3}$$ But, how the area looks like? Because $$ x^2 $$ will be an open curve upside? There's no boundary for above side.

What lead to the equality of the, rate of change of area under curve f(x) = f(x). Was it, they were just compared(OR believed to be equal) and mathematically found to be equal. Or when one was integrated or differentiated the other appeared. Also I knew, integration was being used since...

Homework Statement Homework EquationsThe Attempt at a Solution Line integral of a curve ## I = \int_{ }^{ } yz dx + \int_{ }^{ } zx dy + \int_{ }^{ } xy dz ## with proper limits. ## I = \int_{\frac { \pi }4}^{ \frac { 3 \pi} 4} abc ( \cos^2 t - \sin^2 t ) dt = -abc ## |I| = abc...

$\begin{align*}\displaystyle f(x)&=\ln(\sin{x})\\ \frac{\pi}{6}& \le x \le \frac{\pi}{2}\\ \end{align*}$ $\begin{align*}\displaystyle f^\prime(x)&=\cot{x} \end{align*}$ so $\begin{align*}\displaystyle L&=\int_{\pi/6}^{\pi/2} \sqrt{1- (\cot{x})^2} \,dx \\ \therefore...

Homework Statement Homework Equations First derivative=maxima/minima/vertical tangent/rising/falling When f'(x)>0 ? the function rises The Attempt at a Solution Deriving relative to x: $$10x-6(yy'+x)+10yy'=0~\rightarrow~y'=-\frac{x}{y}$$ What do i do with that?

Hey guys, I've got this question in my book, and I think that I may be misunderstanding the concept. The book is somewhat lacking on this particular question, and has left me in the dark to some degree. The question is Find the area between the curve y=2/(x-1)dx and the x-axis over the...

Homework Statement A car giving a turn on a curve with 88m of radius, traveling at a speed of 95km/h, the curve is perfectly banked for a car traveling at 75 km/h, meaning that the curve has an angle θ of 26.7º. Homework Equations μ = ? r = 88m v = 26.38 m/s θ = 26.7º Ff = μ · g · m Fc = m...

Hey! :o We consider the space $D$ that we get if we remove from the square $[-2,7]\times [-3,6]$ the open discs with center the point $(0,0)$ and radius $1$ and with center $(3,3)$ and radius $2$. I want to calculate $$\sum_{j=1}^3\oint_{\sigma_j}\left...

Homework Statement I am stuck on finding ##W^u## Homework Equations [/B] I have computed the christoffel symbols via comparing the Euler-Lagrange equations to the form expected from geodesic equation. geodesic equation: ##\ddot{x^a}+\Gamma^a_{bc}\dot{x^b}\dot{x^c}=0## covariantly constant...

$\textsf{12 Find the length of the curve $y=\ln(e^x-1)-\ln( e^x+1 )$ from $x=\ln{4}$ to $x=\ln{5}$}$ ok I thot that curve lengths were done with parametric equations but didn't know how to convert this

Homework Statement I tried to answer the following questions is about the curve surface z= f (x, y) = x^2 + y^2 in the xyz space. And the three questions related to each otherA.) Find the tangent plane equation at the point (a, b, a^2+ b^2) in curved surface z . The equation of the...

I'm trying to guess when my hot tub will be ready for use. If an ideal body of water is insulated and has a constant source of heating applied to it, can its temperature be expected to rise linearly? (No. Even as I write this I see it can't be true. As the water temp rises, it will approach...

Hello everyone, A question about curve fitting. Hope you can share some helpful hints. Given some data we plot a graph y versus x. How do we approach the problem from a curve fitting standpoint? For example, using Excel, if the data "looks" linear from the graph, we choose a linear fit and...

For this nonlinear hardening stress strain curve, how do you express strain in terms of stresses ?

1. Homework Statement I have problem solving the bending moment and shear force of a conduit with a curve end. The conduit is lifted in the mid-air with 2 slings and assume it is in equillibrum. I have attach a drawing for reference. Homework Equations What i know, there is a UDL somewhere...

hi, I am aware that stress strain curve involves some function which begins with linear part and continues with non linear part after a while. I consider that it is so complicated, but I really wonder how a stress strain curve is derived, what kind of tests are applied and how those tests are...

Hey! :o I want t calculate $\int_{\sigma}(ydx+zdy+xdz)$ when $\sigma$ is the curve that traces once the intersection of the surfaces with equations $x+y=2$ and $x^2+y^2+z^2=2(x+y)$ with positive direction while we look the traces from the point $(0,0,0)$. We have that...

$\textit{$13.4.7$ Find the curvature of the curve $r(t).$}$ \begin{align*}\displaystyle r(t)&=(5+9 \cos 8t) i - (4 + 9 \sin 8t)j + 6k\\ v&= -72\sin(8t)+72\cos(8t)\\ |v|&=\sqrt{(-72\sin(8t))^2 +(72\cos(8t))^2}\\ &=5184\\ \frac{v}{|v|}&=\frac{-72\sin(8t)+72\cos(8t)}{5184}\\...

Homework Statement You want to rest on a hammock where the cords are damaged. a) If you don't want to the cords to break during your nap, do you have to place the hammock at the horizontal or, on the contrary, put the knot of the first rope higher than the other ? b) What is the curve made by...

I understand why when deriving the formulas for cars on banked curves, the net force in the Y direction is zero. However, when I google how to derive them, people say that there is a net force greater than zero in the X direction. This is not what my professor says in his explanations however...

Hi everyone! I'm a student of electrical engineering. At my math class, we were given a problem to solve at home. Now, from what I've managed to gather, this is a trick question, but I would like to get someone else's opinion on the task. It's also worth mentioning that parametrization is a...

Homework Statement Homework Equations Force * time = mass * change in velocity[/B]The Attempt at a Solution What I did was I converted the y-axis from kilograms to Newtons, since the "mass" reading is the force that the scale experiences. Then, the area under the curve will be the change...

Does a car on a banked curve have a component of gravity that accounts for the centripetal force ( along with the normal force)?

Homework Statement In this first photo , we can see that the adjusted is found by extending the longer portion of straight line . The line is extended to the upper part of the graph.( We can see that there's a break in the line , the longer portion of the line is extended , and taken as...

I am having a difficult time communicating about concepts without the math. And I have some very specific questions. So here we go with one of them. Regarding a crank mechanism, say with a throw of 10 centimeters, how can I calculate what percentage of a given constant force that is applied...

Homework Statement After plotting a graph with frequency (f) of a wire on the y-axis and tension (C-Clamps) on the x-axis, a root curve was obtained. If the trend of the line is maintained, does it pass through the origin? Should it? Note: graph attached Homework Equations f is proportional...

Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...

Homework Statement This is Pytels Dynamics 2nd edition problem 13.16 13.16. Pen P of the flatbed plotter traces the curve y=x3/80000, where x and y are measured in mm. When x=200mm, the speed of slider A is 60 mm/s. For this position, calculate (a) the speed of P; and (b) the normal component...

A particle moves in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equation of the trajectory, and identify the curve.

1 The attempt at a solution: For part a) I got the following: I'm stuck on part b). I've tried to take the maclaurin series of coth x to see what the function does when T→0 and T→∞

Homework Statement What is the equation of a straight line passing through (1,2) and normal to ##~x^2=4y## Homework Equations Slopes of perpendicular lines: $$m_2=-\frac{1}{m_1}$$ The Attempt at a Solution $$x^2=4y~\rightarrow~m_1=y'=\frac{x}{2}$$ $$m_2=-\frac{2}{x}$$...

Hi all, I'm currently in the middle of performing an experiment for the final project of my MSc, and I have a question about how I should go about weighting the data when fitting a curve to it using the MATLAB fitting tool. Firstly, a bit of background about the problem. I am seeing how low...

friction is causes the circular motion in the car around a curve, and if we draw free body diagram we will see the friction force must be opposite the car motion so the force of friction not toward to the center of the curve ,so the force of friction must be not the centripetal force ,mustn't it?

Homework Statement A bicycle of mass m is traveling at constant speed v around a curve of radius r without slipping. You can take the acceleration due to gravity as g. Calculate the angle of tilt, θ, that will enable it to balance. Homework Equations R=mg Rsintheeta (Length)=Fcostheeta...

I was doing some integral exercises for getting area under the function. I was doing only more simple stuff, like functions that don't go over the same "x area" multiple times, like a quadratic function. My question is how to calculate area of a loop in an equation x^3+y^3-3axy=0 if let's say...

Homework Statement Homework EquationsThe Attempt at a Solution Every small part of the trajectory can be taken as a circular arc. Then, $$\frac { m v^2} R ≤ kmg $$ But how to find out R from the sine-curve?

Hi all, I am a student trying to figure out the system curve for a pipe line system. I know how to calculate friction loss for just one flow, but not for a system of branched flow! I read a short article online saying that for parallel pipes the friction head is the same for all branches, so...