Curves Definition and 778 Threads

Homework Statement Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. Homework Equations The Attempt at a Solution My result gave me an...

Hello, given a parametric curve \mathbf{r}(s)=x(s)\mathbf{i} + y(s)\mathbf{j} + z(s)\mathbf{k}, my textbook says that tangent vector having unit-magnitude is given by \mathbf{r}(s)=x'(s)\mathbf{i} + y'(s)\mathbf{j} + z'(s)\mathbf{k} I don't understand the proof that it has unit magnitude...

Homework Statement Find the gradient of the function at the given point, then sketch the gradient together with the level curve that passes through the point. f(x,y) = y - x (2,1) Homework Equations gradient of f = (df/dx)i + (df/dy)j The Attempt at a Solution df/dx = -1...

Homework Statement "Find the area of the region which is inside the polar curve r=5cos(theta) and outside the curve r=4-3cos(theta)." Homework Equations The Attempt at a Solution I keep coming up with 18.708, but it says that's incorrect. I don't know what I'm doing wrong...

1. A roller coaster of mass 320 kg (including passengers) travels around a horizontal curve of radius 35 m. Its speed is 16 m/s. What is the magnitude and direction of the total force exerted on the car by the track? Homework Equations The Attempt at a Solution

Hello all. This is not homework, i stumbled upon it looking for information for my physics.. I have some background in calculus and am just wondering if anyone would have any idea on how you'd solve this area problem.. all i have is a picture of it and not any equations of the lines. Thanks.

dear all, Hello, I need your help in this matter, the discription of the subject is: we have two input vectors ( included in one vector): T ( temperature ) and H ( humidity ), there is a corresponding one output P ( power demand ), and all these data are normalized I...

Hello everyone, I am working on trying to model a bouncing light ray between two curves, and I would like to model it in Mathematica. However, I do not know what syntax or how to go about typing the code in. I tried to find examples on the Mathematica Documentation Centre but the examples...

Homework Statement We have been shown the probability curve and coresponding density of state curve for a metal only. I am trying to figure the probability versus energy, number of energy levels and density of state curves for a insulator.I have found a few on the internet but they seem...

Hi, I am currently using MATLAB to do some work on simple closed curves in the plane. In order to make this work quite general I have opted to use a matrix which stores (x,y) coordinates of points on my curve (rather than use a function). I want to feed some interesting curves into my code...

Hi guys, I was trying to sketch a polar curve but my curve was different from the curve on maple(I plotted the same curve on maple). Homework Statement Here is the whole question, I am using t as theta. The hyperbolic spiral is described by the equation rt=a whenever t>0,where a is a...

I need something that I can use to draw a few simple 2D images, that don't have to look pretty. I really mean "draw" (with the mouse) and not generate from a formula, and a minimum requirement is that the program can at least let me try to draw a smooth curve with the mouse and then smooth it...

Homework Statement let C1 : y = x - 1/2 x2 and C2 : x = y - 1/2 y2 be curves on the xy plane. 1. find the equation of the tangent to the curve C1 at x = k 2. suppose the line obtained in 1) is also tangent to the curve C2. find all values of k and the equations of the tangents. 3...

Elipse [0,2pi] x=acosT y=bsinT\ by symmetry 4I(y,x) chossing the limits of integration my text is showing 4I(y,x,0,a) T=0=>x=a T=pi/2=>x=0 so wouldn't this be 4I(y,x,a,0) proceeding inthe books case gives pi(ab) while in the later case gives -pi(ab) Also x= (t-1)/t y=(t+1)/t...

Lately I have been going nuts trying to find a definitive answer to this relatively simple question. Why does light curve around bodies of mass? After a bit of digging I have found 3 answers. 1. Light follows the curve of space-time. 2. The mass of a photon is attracted by gravity of the...

Homework Statement Find the area bounded by the curves given by the graphs x = 4 - y^2 and x = y^2 - 2y The Attempt at a Solution I don't know how I can integrate these curves as they are not functions. Can someone tell me to get started on this problem? Thank you

Homework Statement The problem asks to find the shortest distance between two points on Earth, assuming different equatorial and polar radii i.e. the coordinates are represented as: x = a*cos(theta)*sin(phi) y = a*sin(theta)*sin(phi) z = b*cos(phi) Homework Equations The Attempt at a...

Homework Statement So the curves are: y = \frac {x^{4}}{x^{2}+1} and y = \frac {1}{x^{2}+1} The Attempt at a Solution So first the limits of integration are: \frac{x^{4}}{x^{2}+1} = \frac{1}{x^{2}+1} (x^{2}+1)\frac{x^{4}}{x^{2}+1} = \frac{1}{x^{2}+1} (x^{2}+1)...

Homework Statement The curves are: f(x)= x^{2/3} and g(x)=x^{3/2} Homework Equations I am assuming that: x^{2/3} = x^{3/2} is going to give me the limits of integration but I don't know how to solve for x on this equation. Could also put it this way...

I've always admired the way Einstein approached gravity, -which had previously been treated as an a attraction, that is, a determined kinematics that had to be accounted for by a force-,from a completely different point of view, looking at it as the curvature that matter-energy produces in the...

Homework Statement find the Area Bounded by the two curves, y=|x+1|, y= - ( x+1)2 + 6 Homework Equations y=|x+1|, y= - ( x+1)2 + 6 The Attempt at a SolutionA= Integration of | f (x) - g(x) | x+1= f(x) -(x+1)2 + 6= g(x) getting the limit of integration: x+1= - (x+1)2 + 6 x2 + 3x - 4=0...

Homework Statement Let S be the solid region bounded by the paraboloid z = x^2 + y^2 - 4 for z \le 0 , 0 \le x \le \sqrt{4 - y^2} and 0 \le y \le 2 . Find the Cartesian equations of the curves if the surface S intersects the xy,xz , and yz planes. The Attempt at a Solution...

Hi there If possible can someone please review my understanding of this question. Homework Statement At what point on the Parabola y= 2x^2-7x-15 will a normal to the parabola have a gradient of -1/2 Homework Equations The Attempt at a Solution We are given the gradient of the...

Homework Statement I am working on a Calculus I project and the last question has me stunned. I would really appreciate some assistance in this. Maybe a push in the right direction. So here is the problem word for word. There is also an attachment containing a picture of the problem...

Please give geometrical desciption of what are characterstic curves and domain of dependence of a PDE. Please help. Thanks.

Homework Statement Is there a curve on a regular surface M that is asymptotic but not principal or geodesic? Homework Equations The given definitions of asymptotic, principal, and geodesic: A principal curve is a curve that is always in a principal direction. An asymptotic curve is a...

Homework Statement A particle of mass m = 3.0 kg moves along the x-axis through a region in which its potential energy U(x) varies as shown in the Figure. When the particle is at x = 8.5 m, its velocity is 2.273 m/s. http://i118.photobucket.com/albums/o...yfe42/phys.gif D.) What...

Hi everyone..Can anyone help me to solve this problem. Consider a scaler field T(x,y) = (2x+2y) / (x2+y2) How can i find the level equations.

Homework Statement Find the total length of the cardioid r=a(1-cos theta) Homework Equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta The Attempt at a Solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d...

Homework Statement What is the area between y=x3 and its tangent at x=1The Attempt at a Solution The first derivative of y=x3, which is 3x2, tells me that the slope of the tangent at x=1 is 3. That (1,1) is a point on the tangent line tells me that the equation of the tangent line is y=3x-2...

Hi, Is it true to say on a topological manifold one can always find a unique metric such that a set of non intersecting curves become its geodesics? Is there any way to find that metric? Thanks, Owzhan

Homework Statement Find the area of the region between the two curves. y=\sqrt{x} y=\frac{1}{2}x x=9 Homework Equations The Attempt at a Solution The domain of the region is [4,9]: \int\frac{1}{2}x-\sqrt{x}dx with limits of integration [4, 9]...

When going through topics on melting and freezing, i came across 2 graphs of slightly different curvature for both the heating and cooling of naphthalene. The ending part of the graphs are the ones that confuse me, whether slope upwards or downwards. Most graphs in the internet just show...

Homework Statement Area between curves y=((e^x)-(e^-x))/2 and y=2e^-x for -1 < x < 2 Homework Equations I know the formula is the integral of ( u(x)-l(x) )dx, but I'm having a lot of trouble trying to integrate this. integral from -1 to ln(5)/2: (((2e^-x)-((e^x)-(e^-x))/2))dx + int...

i know if every simple closed curve in D can be contracted to a point it is simply connected as in the case of|R^2 Domain or R^3 it is simply connected but i am not feeling uncomfortable with |R^3 especially with the domains like when x =! 0 and y =! 0 why it is not simply connected? how...

Hi, I'm reading this piece from George Cain & James Harod's multivariable calculus material. Section 4.3, which is about Torsion, says this: I don't understand how he deduces dB/ds is perpendicular to T? Where did I get lost? Following the paragraph, it seems to me that T and N...

Homework Statement The region bounded by the given curves is rotated about x = 10 x=1-y^{4}, x=0 Find the Volume V of the resulting solid by any method. Homework Equations The Attempt at a Solution I'm using the washer method. Not sure if it is being setup properly as I'm getting the...

I looked this up but couldn't find sufficient information on it. What I know is that calibration curves are used to find the concentration of an unknown compound by graphing a series of measurements of a property like light absorbance from standard solutions of that compound. What I don't get is...

Homework Statement A concrete highway curve of radius 60.0 m is banked at a 11.0 degree angle. What is the maximum speed with which a 1500 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.) Homework Equations...

find the area of the region shared by the curves r=6cosx and r=6sinx i know that if you graph those two functions you get two circles, both with radius 3, the first one has its center on the cartesian x-axis and the other has its center on the y axis. i also know that if you draw a line...

I understand that we could think of a null curve in Minkowski space as being the curve c(s) such that the tangent vector dc(s)/ds = 0 at all s. So suppose that we have a curve c(s) = (t(s), x(s), y(s), z(s)) and we want to ask ourselves what conditions would make c a straight line. I guess...

Homework Statement sketch and find the area of the region bounded by the given curves. Choose the variable of integration so that the area is written as a single integral y = x, y = 2, y = 6 − x, y = 0 Homework Equations the usual integral fx - gx from a to b The Attempt at...

Can anyone direct me to a good source of graphs of galaxy rotation curves. I need graphs that show both the observed curve data points and the expected curve along with the names of the galaxies and labeled axis. Thanks

Homework Statement Anyone familiar with orthogonal families of curves? They're not that difficult to understand. If you have a differential equation \frac{dy}{dx} = F(x, y) you can find it's orthogonal family of curves by solving for \frac{dy}{dx} = \frac{-1}{F(x, y)} Homework...

Homework Statement Find the area of the bounded region enclosed by the curves: 6x+y^2=13, x=2y Homework Equations Integration The Attempt at a Solution Finding the area shouldn't be too much of a problem. In this particular problem, integrating with respect to y is the better...

Homework Statement The curves with equations x" + y" = 1, n = 4, 6, 8, , are called fat circles. Graph the curves with n = 2, 4, 6, 8, and 10 to see why. Set up an integral for the length S(2k), the arc of the fat circle with n=2k. Without attempting to evaluate the integral, state the...

Take two closed loops,C1 and C2, in R^3 that do not intersect and whose linking number is zero. Chose two manifolds D1 and D2 whose boundaries are C1 and C2 and which intersect in their interiors transversally and do not intersect anywhere along their boundaries. The intersection is a...

Homework Statement Find the area bounded between the two curves y=34ln(x) and y=xln(x) Homework Equations Integration by parts: \intudv= uv-\intvdu The Attempt at a Solution First I found the intersection points of the two equation to set the upper and lower bounds. The lower...

hi... I am new to this topic and frustrated. I have a curve f(x,y)= -3y/(x2 +y2 + 1) I was asked to draw a level curve of this and I'm not getting anywhere with it. If anyone has any pointers, or can help me with solving this question I would be gretfull. The only other thing this...

Homework Statement After plotting log(I/A) vs E/mV, you get a tafel curve. calculate the exchange current density, Io, the cathodic transfer coefficient ac and the rate constant of the reaction k. Homework Equations The Attempt at a Solution Is it simply, the exchange current...