Curve Definition and 1000 Threads

So I have two equations that intersect: z=x2+y2 which I know is a paraboloid, and z=x2+(y-1)2 which I know is also a paraboloid shifted one unit in the positive y-direction. However I attempted to find the intersection curve and only way I could think to do that was by setting the two equations...

Homework Statement Find the values of m for y = mx that enclose a region with y = \frac{x}{x^2 + 1} and find the area of this bounded region. Homework Equations The Attempt at a Solution So I set the two functions equal to each other to solve for x in terms of m: mx = \frac{x}{x^{2}...

Hi, I recently learned that to find the tangent at a point on any curve, you can simply place a mirror on that point and reflect the part of the curve on one side of that point such that the reflection flows smoothly into the other part of the curve on the other side. Once this is done, draw a...

Homework Statement Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Homework Equations x = t \\ y = e^{-4t} \\ z = 5t - t^5 \\ P = (0, 1, 0) The Attempt at a Solution \vec{r}(t) = < t, e^{-4t}, 5t - t^5 > At the point...

Homework Statement Let ##\gamma(t)## be a path describing a level curve of ##f : \mathbb{R}^2 \to \mathbb{R}##. Show, for all ##t##, that ##( \nabla f ) (\gamma(t))## is orthogonal to ##\gamma ' (t)##Homework Equations ##\gamma(t) = ((x(t), y(t))## ##\gamma ' (t) = F(\gamma(t))## ##F = \nabla f...

(a) Suppose \kappa is a clockwise circle of radius R centered at a complex number \mathcal{z}0. Evaluate: K_m := \oint_{\kappa}{dz(z-z_0)^m} for any integer m = 0, \pm{1},\pm{2}, ,... Show that K_m = -2\pi i if m = -2; else : K_m = 0 if m = 0, \pm{1}, \pm{2}, \pm{3},... Note...

"Find the area of the surface of the curve obtained by rotating the.." 1. Find the area of the surface obtained by rotating the curve y= 1+5x^2 from x=0 to x=5 about the y-axis. 2. I thought to find surface area, we would need to use this formula: SA= ∫2\pi(f(x))√(1 + (f'(x))2)]dx...

Homework Statement Find the equation of the curve which passes through the point (-1,0) and whose gradient at any point (x,y) is 3x2-6x+4. Find the area enclosed by the curve, the axis of x and the ordinates x=1 and x=2. . The attempt at a solution I integrated and got the equation...

Could anyone mind to help me how to calculate and draw the curve such as below image? http://s9.postimage.org/ksup6knwv/curve.png There are two handles, the red and blue. Also, is this everyone called by a Bezier curve? Give me the equations and let me try to calculate by myself.

Homework Statement x(t) = (t^2 -1) / (t^2 +1) y(t) = (2t) / (t^2 +1) at the point t=1 Homework Equations Line equation = y-y1 = m(x-x1) chan rule = (dy/dt) / (dx/dt) = dy/dx The Attempt at a Solution I find the y1 and x1 values by subing in t=1 to the x(t) and y(t)...

Homework Statement Sketch roughly the curve y = x^2(3-x) between x=-1 and x=4. Calculate the area bounded by the curve and the x-axis . The attempt at a solution I tried to find the area from x=-1 to x=4 I got 1 1/4 answer in the back of my textbook is 6 3/4 When i find the...

Homework Statement Find the area bounded by the curve y= x2-x-2 and the x-axis from x=-2 and x=3. The attempt at a solution I integrated from x=-2 to x=3 using (x^3/3)-(x^2/2)-2x and I got -4 5/6 but the answer is -4 1/2 . I don't really see where I went wrong.

Homework Statement Find the areas enclosed by the following curves and straight lines: c) y= (1/x2) -1 , y= -1 , x=1/2, and x=2 b) y = x3-1, the axes and y = 26 2. The attempt at a solution Okay I sketched the curve and to me it looks like the curve occupies no area at y=-1...

Homework Statement Find the path ##\vec\gamma(t)## which represents the level curve ##f(x,y) = \displaystyle\frac{xy + 1}{x^2 + y^2}## corresponding to ##c=1##. Similarly, find the path for the curve ##x^{2/3} + y^{2/3} = 1## Homework Equations None.The Attempt at a Solution Since the level...

I need to sketch the curve (1/x2) - 1 Is this correct? Excuse the untidiness this was drawn in paint. :S I know the y-axis is an asymptote to the function, I haven't sketch a graph like this before so I'm kind of confused.

Homework Statement find the length of the curve. Homework Equations x=y^3/15 + 5/4y on 3<=y<=5 The Attempt at a Solution (dy/dx)^2 = Y^4/25 - 1/2 + 25/16y^4 integral (3,5) y^2/5 + 5/4y^2 however, i got the wrong answer. the answer is 67/10.

Homework Statement find the length of the following curve. Homework Equations y=(2/3)(x^2 +1)^(3/2) from x=3 to x=9. The Attempt at a Solution f'(x) = 2x^3 + 2x f'(x)^2 = 4x^6 + 8x^4 + 4x^2 L = integral (3,9) sqrt(1+4x^6 + 8x^4 + 4x^2)

Homework Statement for the curve x= sqrt(64-y^2), -4<=y<=4 (identify from multiple choice 1. setup an integral for the curve. 2. identify the graph 3. find the length of the curve.Homework Equations x = sqrt(64-y^2), -4<=y<=4The Attempt at a Solution 1. dx/dy = y*sqrt(64-y^2) 2. (dx/dy)^2 =...

Homework Statement Find a vector function that represents the curve of intersection of the two surfaces: The cone z = sqrt( x^2 + y^2) and the plane z = 1+y. Homework Equations z = sqrt( x^2 + y^2) and the plane z = 1+y. The Attempt at a Solution This problem can be solved as...

Ok, so for a give function f(x) it's curve length from a to b is supposed to be ∫(1+(f '(x))^2)dx evaluated from a to b. However even wolfram alpha had a hard time solving that, plus the results were wrong. What am I missing? PS: With f(x)= sqrt(r^2-x^2)

How can space know how to curve from a black hole. My understanding is that the no information can escape a black hole so how can space know how much to curve? Duordi

\int_{\gamma (t) }\, f(z) dz \int_{\alpha}^{\beta} \, f(\gamma (t))\, \gamma '(t) \, dt \text{Use the substitution : } \gamma (t) = \xi \int_{\gamma (\alpha) }^{\gamma (\beta)} \, f(\xi )\, d \xi \text{If we integrate around a closed loope : }\gamma (\alpha) = \gamma(\beta)...

Hi I have been having a hard time visualizing how a car must turn in a curve we know 2 things: 1. if the steering wheel is held at an angle, the front wheels must be at a certain angle relative to the car frame as well as the back wheel at all time. 2. the wheels cannot have any...

Homework Statement Find a vector-valued function f that parametrizes the curve (x-1)^2 + y^2 = 1Homework Equations (x-1)^2 + y^2 = 1The Attempt at a Solution The equation is the graph of a circle that is 1 unit to the right of the origin, therefore a parametrization would be x(t) = cos(t) +...

Homework Statement Sketch the regions enclosed by the given curves. y = 3 cos 6x, y = 3 sin 12x, x = 0, x = π/12 Find the area as well.Homework Equations The sketch of the curve is given too which I uploaded. The Attempt at a Solution Trouble finding intersection points 3cos(6x)=...

how can rcosθ in a banked road be equal to mg; since r is equal to normal reaction which is equal to mgcosθ. rcos is even smaller than r. so mg>mgcosθ mgcosθ=r r>rcosθ so mg>rcosθ then how can mg=rcos when banking in curved road?

Is there a general way to find a vector valued function that parametrizes a curve? I'm reading through a textbook and it says nothing in depth about parametrization and suddenly there's a question... Find a vector valued function f that parametrizes the curve in the direction indicated...

Some experimental covariance curve for entangled photons gives abs(Cov(0)) less than 1. For example : Violation of Bell inequalities by photons more than 10km apart by Gisin's group in Geneva. Does this mean that experimentally we can't predict with certainty in this case ? In order to...

Homework Statement Find the volume generated by revolving the regions bounded by the given curves about the x-axis. Use indicated method in each case. Question 11: y = x^3, y = 8, x = 0 Question 15: x = 4y - y^2 - 3, x = 0 Homework Equations for question 11: Shells for Question 15...

I know most salts' have increased solubility in 100g of water with an increase in temperature, a few have an inverse relationship, but why does NaCl flatline regardless of temperature? Like is there a mechanism that explains this phenomenon? Thanks in advance.

I am studying for my undergraduate Astrophysics module and the lectures notes say that that all abundances are measured relative, in terms of H = 12.00 by mass or number of atoms. Is this correct? I thought it was all based off of Carbon = 12. Am I missing something?

Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.

Homework Statement Find $$\int_{C} z^3 ds $$ where C is the part of the curve $$ x^2+y^2+z^2=1,x+y=1$$ where$$ z ≥ 0 $$ then I let $$ x=t , y=1-t , z= \sqrt{2t-2t^2}$$ . Is it correct? Or there are some better idea? Homework Equations The Attempt at a Solution

Homework Statement Please evaluate the line integral \oint dr\cdot\vec{v}, where \vec{v} = (y, 0, 0) along the curve C that is a square in the xy-plane of side length a center at \vec{r} = 0 a) by direct integration b) by Stokes' theoremHomework Equations Stokes' theorem: \oint V \cdot dr =...

Homework Statement For some scalar field f : U ⊆ Rn → R, the line integral along a piecewise smooth curve C ⊂ U is defined as \int_C f\, ds = \int_a^b f(\mathbf{r}(t)) |\mathbf{r}'(t)|\, dt where r: [a, b] → C is an arbitrary bijective parametrization of the curve C such that r(a) and r(b)...

[b]1. if y(t)= (a/t, b/t, c/t) [b]2. Prove that this curve is a straight line. Find the equation of the line [b]3. i found the first part without a problem, i just am not sure how to find the equation f the line.

are both of the equations i posted flux equations. one of them is for a surface of a solid and the other is for a curve?

http://store3.up-00.com/Nov12/fWJ65017.jpg http://store3.up-00.com/Nov12/kpS65017.jpg

Hi All, I'm not a math guy so I am coming to you for help. I am trying to come up with an equation to graph any 180 degree curve that is comprised of: a 135 degree radius, and a 45 degree ellipse (135 + 45 = 180). The two curves being the same curvature (slope?) where they meet. The portion...

Homework Statement Let C be a simple closed plane curve in space. Let n = ai+bj+ck be a unit vector normal to the plane of C and let the direction on C match that of n. Prove that (1/2)∫[(bz-cy)dx+(cx-az)dy+(ay-bx)dz] equals the plane area enclosed by C. What does the integral reduce...

Hello .. I have problem understanding how to decide which material is more elastic based on stress strain curve.. my understanding is as follows 1)if a material has big youngs modulus.. then it is more stiff 2)a material with a big youngs modulus may be or may not be very elastic (elasticity...

Homework Statement a)x=cos2ωt, y=sin2ωt b)x=cos2ωt, y=cos(2ωt-∏/4) c)x=cos2ωt, y=cosωt draw the graphs of Simple Harmonic Motions.Homework Equations parametric and complex harmonic motion equation is needed.The Attempt at a Solution No attempt to solution.I can't do anything,because I can't...

Homework Statement A certain curve on a freeway has a radius of 200m and is banked at an angle of 25°. A 200-kg car moves around the curve at constant speed. 1. If the speed of the car is 35m/s, what friction force is needed to keep the car moving in a circle? 2. If the speed of the car...

Homework Statement For a gas obeying Dieterici's equation of state: P(V-b) = RTexp(-a/RTV) for one mole, prove that the equation of the inversion curve is P = ((2a/b^2) - (RT/b)) * exp((1/2) - (a/(RTb))) and hence find the maximum inversion temperature.Homework Equations N/A The Attempt...

Let's say I have a parabola that I know the equation of. I then asked myself the question "how do I calculate the length of the curve between two values of x, for example. After thinking about it, I realized I could use pythagoras: √δx + δy will give me a length, and then I could find the...

Hi friends. I want to fit my x datas and y datas with a function in the most exact way.my data is: x=[0.3 0.5 0.7 0.9 1 1.3 1.4 1.5 2 3 5 7 9 10 30 50 70 90 100]; y=[13.4347 8.3372 6.3107 5.27 4.93 4.28 4.14 4.0199 3.6349 3.3178 3.1282 3.0691 3.0432 3.0354 3.0043 3.0016 3.0008 3.0005...

I've been fooling around in MS Excel trying to reconstruct this fractal: I haven't had any issues here making it. I totally understand the algorithm for generating the left turn/right turn ordering. What I really want to know is how this version is generated: Original image...

Hi all! I would like to extrude a 2d curve in the X-Y plane along the Z direction,thereby wanting to obtain a plane of Z units long.How should I proceed? Is there a tool especially for this in MATLAB?

Hi, I m unsure whether or not this should perhaps be in the homework forum, however one might say this is more of a technical issue. I recently conducted an experiment for a report I intend to write up promptly, and I wanted to find the best fitting curve for these values. I tested how different...

My math is a little weak, so I'm having a hard time finding the elastic and plastic regions on this curve. Any further help will also be appreciated!