Curve Definition and 1000 Threads

Homework Statement A heat-seeking missile is located at (2,-3) on a plane. The temperature function is given by T(x; y) = 20-4x^2-y^2. Find the equation of the curve along which the missile travels, if it continuously moves in the direction of maximum temperature increase. Express your...

Hello! I'm just asking for a clue on how to make a unit hydrograph Reservoir Level - Storage Curve for a Dam. I have been searching information on internet, but I could not find anything about that. I would appreciate any idea or suggestion. Thanks!

Homework Statement A curve with a 200-m radius on a level road is banked at the correct angle for a speed of 60 km/h, i.e. a car traveling at this speed would remain on the road, even if the surface were frictionless. a) If a car travels around this curve at a speed of 90 km/h, what is the...

Hello, I'm trying to do exercise number 20 from chapter 6 of this http://www.people.vcu.edu/~rhammack/BookOfProof/index.html, it asks to show that the curve x2 + y2 - 3 = 0 has no rational points. In the answer it has this tip: first show that a2 + b2 = 3c has no solutions, other than the...

Homework Statement Find the length of the parabolic segment r = \frac{12}{1+cos(θ))}, 0\leqθ\leq\frac{∏}{2}. Homework Equations L = ∫\sqrt{f(θ)^{2}+f^{'}(θ)^{2}}dθ The Attempt at a Solution I got up to here and didn't know whta to do L = 12 ∫^{0}_{\frac{∏}{2}}...

Hi, I want to verify if my answer to this problem I made up is correct? Suppose we have a plane z=x+y Lets find the magnitude of the volume of the space underneath the plane and over the REGION in the xy plane defined by y=sin(x), from 0<=x<=2pi. So for example, my definition of the...

Hi everyone, First of all I am not sure if I have chosen the right category for this posting but this looked the most reasonable out. I have a problem that I would like to solve but I am not sure where to look for answers. It seems like something other people might have worked with before...

Homework Statement A particle moves along the curve of intersection of shapes y = -x2 and z = x2 in the direction in which x increases. At the instant when the particle is at the point P(1,-1,1), its speed is 9cm/s and that speed is increasing at a rate of 3cm/s2. Find the velocity and...

Homework Statement Find the area inside the inner loop of the limacon curve : r = 1 + 2cos(θ) Homework Equations A = ∫\stackrel{α}{β}(\frac{1}{2}r2)dθ The Attempt at a Solution i have the solution, my question is : how do you find α and β ? here α = 2π/3 and β = π A =...

Reparametrize the curve R(t) in terms of arc length measured from the point where t = 0 R(t) is defined by x = et, y = \sqrt{2}t, z = -e-t Arc length S = ∫ ||R'(t)||dt ||R'(t)||= sqrt{\dot{x}2 + \dot{y}2 + \dot{z}2}The attempt at a solution Getting R'(t) ==> x = et, y = \sqrt{2}, z = e-t...

Homework Statement Find area of curve using area formula of Greens theorem Homework Equations r(t)=(t-sin t) i +(1- cos t ) j for 0 <= t <= 2 pi. The curve is y = sin x The Attempt at a Solution Do i let x(t)=t...?

Homework Statement find the total area of the region between the curve and the x- axis Homework Equations 1) y=2-x, 0≤x≤3 2)y=3x^2-3,-2≤x≤2 3)y=x^3-3x^2+2x, 0≤x≤2 4)y= x^3-4x, -2≤x≤2 The Attempt at a Solution I've tried using my graphic calculator to see what the graphs looked...

I decided to write my problem and attach as a separate document so that everything was included and would leave room here to discuss my problem. From what I understand from the equations is that for each value of u I calculate the value of the basis function for each basis function i. Then...

Homework Statement What assumptions do we make to rule out vertical or horizontal indifference curves when slope is zero? Homework Equations There are several assumptions: completeness reflexivity transitivity being continuous strong monotonicity diminishing marginal rates of...

Homework Statement Find an equation of the tangent line to the curve at the given point. y = tan x at point (pi/4,1) Homework Equations The Attempt at a Solution step 1. find the derivative of tan x, which sec^2 x step 2. find the slope. this is where I mess up. I assume...

Hi. In order to measure the I-V curve of a normal diode in pulsed mode, I set up the following experimental kit. The experimental results do not change with pulsewidth, which is quite long (us regime), and low frequency (200hz and less). An HP pulse generator is connected via BNC cable to an...

Hi there, To find the gradient of a curve, we draw a chord on the curve and then makes the 2nd coordinates ( B ) tends to A ( 1st coordinates ). To find the gradient of the chord, i.e, ΔY/ΔX, we replace the two coordinates into the equation of the curve. But my question is why do we...

Homework Statement A conservative force F(x) acts on a 3.0 kg particle that moves along the x axis. The potential energy U(x) associated with F(x) is graphed in Figure 8-60. When the particle is at x = 3.0 m, its velocity is -1.0 m/s. The "kinks" in the graph occur at (1, -2.8), (4, -17.2)...

Homework Statement I was wondering if there was a general method for finding a function that fits a set of data for a damped harmonic oscillator I'm currently writing up a presentation on the experiment for the gravitational constant and the way i did the experiment was to use a torsion...

Homework Statement "Find the equation of the plane tangent to the surface (x^2-y^2)(x^2+y^2)=15 at the point (2,1) " If only it really were a plane and a surface, I could do that. I have a formula for that. Unfortunately, this is a curve and I'm looking for tangent line. Homework Equations...

Homework Statement Homework Equations L[c]:=\int_{a}^{b}(\sum_{i,j=1}^{2}g_{ij}(c(t))c_{i}'(t)c_{j}'(t))^{1/2}dt The Attempt at a Solution So g_{ij}(x,y)=0 for i{\neq}j, c_{1}'(t)=-Rsin(t), c_{2}'(t)=Rcos(t) so...

Homework Statement Hello, So i was just doing a few past papers for an upcoming exam and i got stuck on this one. i have got to the stage where i have 1/p all in term of x and y, but i can't see how you would go about getting the maximum acceleration just from x and y values...

I have a physics exam soon and i would just like to know, which method would be best for me to use to estimate the area under a curve to estimate work done when the force-extension graph is not linear. I know you could draw bars to estimate the area of the curve and you could draw a line so...

Homework Statement http://s2.ipicture.ru/uploads/20120107/67Ag24Qb.jpg The attempt at a solution So, i plotted the graphs of the circle and the curve: http://s2.ipicture.ru/uploads/20120107/x32KTV6y.jpg The shaded area is what i need to find. My plan to solve this problem is to find...

This is another question from last year's calculus exam that I'm a bit stuck on. " Let f be the real function given by f(x) = −x4+2x2+3x. (a) Determine the tangent line to the curve y = f(x) at x = 1. (b) Show that the tangent line to the curve y = f(x) at x = 1 is also the tangent line to...

Simply put, does space actually curve or is it only the perception of space that curves? I've always thought space actually curved, but I'm not sure if this question is even valid since empty space isn't tangible in any real way. (This is in reference to both length contraction and the...

Homework Statement Solve the following PDE's: \frac{\partial u }{\partial t }+c \frac{\partial u }{\partial x} with u(x,0)=h(x). (1) \frac{\partial u }{\partial t }+u \frac{\partial u }{\partial x} with u(x,0)=h(x). (2) Hints: Specify the characteristic field of directions associated to each...

Hey all, In one of my textbooks, there is a passage in the thermodynamics section that states that: For a closed cycle where the system returns to its initial state, the work done is the area enclosed by the curve (when looking at a Pressure-Volume graph). Shouldn't the work done by...

Homework Statement Find area of regions bounded by x^2 + y^2 = 9, y = 2x, x-axis in the first quadrant The attempt at a solution So, i drew the graph of y against x in my copybook, and circle with origin (0,0), radius = 3 units. The line y = 2x cuts through the circle. Transforming to...

I want to remove the oscillation from the curve In one of the variable i have oscillation values and i want to take avg of them so that i can plot the straight line e.g. X Y 100 80 110 20 120 70 130 19 140 84 120 26 I want to post process my data to...

How do I know which function is the upper boundary curve and which is the lower boundary curve. For example find the area between the curves e^x and x bounded on the sides x=0 and x=1. We can draw it and we know that e^x is the upper curve and x is the lower curve. Thus the area is ∫e^x-∫x...

Homework Statement Consider three systems of equations: x^2 + y^2 + z^2 = 1 y^2 + z^2 = 1 x^2 + y^2 + z^2 = 1 x = 0 y^2 + z^2 = 1 x = 0 Which of these define the same curve and which define different ones? Homework Equations x^2 + y^2 + z^2 = R^2 is a sphere x,y, or z =...

Homework Statement What does the area under a Maxwell Boltzmann Distribution curve represent Homework Equations The Attempt at a Solution So I know that the y-axis is no. molecules x-axis is energy of molecules I also know that the area under the graph is proportional to the...

Homework Statement Find all x coordinates of points (x, y) on the curve y = (x − 2)5 /(x − 4)3 where the tangent line is horizontal Homework Equations Quotient Rule - Differentiation The Attempt at a Solution So I could guess, that if tangent line is horizontal, the equation of...

\int_\alpha\frac{1}{z^2}dz I can't figure out how to integrate this over a closed circle which contains the origin on its interior. I'm assuming it is equal to 2πi; is there a way to apply Cauchy's Integral Theorem? If I set f(z)=1/z then that is not analytic on the interior, so I don't see...

Homework Statement Show that the gradient of the curve \frac{a}{x}+\frac{b}{y}=1 is -\frac{ay^2}{bx^2}. The point (p,q) lies on both the straight line [itex]ax+by=1[/tex] and \frac{a}{x}+\frac{b}{y}=1 where ab =/= 0. Given that, at this point, the line and the curve have the same gradient...

Homework Statement http://imageshack.us/photo/my-images/703/dfdfu.jpg Homework Equations To find the x coordinate 1. Make both equations equal, expose e and take logs. I'm not sure how to do this and I've tried but keep getting the wrong answer. 2. To find the area, subract the...

f= x^2 f' = 2x f'> 0 in (0, ∞)... f = y increases on this interval f' < 0 in (-∞,0) f = y decreases on this interval I don't understand... it is saying that f decrease on (-∞,0) but obviously its not because (∞)^2 = ∞ which is increasing... Does this mean that the function is...

Homework Statement I am in the process of studying integration and finding the areas under curves. So far, I know of two methods of finding the area under a curve: the limit method and the direct integral method. Could someone explain the relationship between these two methods? Homework...

Hi, I have implemented the cardinal spline curve. ref link:- http://www.ibiblio.org/e-notes/Splines/Cardinal.htm My requirement is to get the Y Value along the spline curve for a given x.Please look at the image attached below. Here P1,P2,P3,P4 are my Points and cardinal spline passes...

Homework Statement a.) A hiker is climbing a mountain whose height is z = 1000 - 2x**2 - 3y**2. When he is at the point (1,1,995) in what direction should he move in order to ascent as rapidly as possible? b.) If he continues along a path of steepest ascent, obtain the equation of the curve...

Hello, I have the following points that need to be fitted with a curve: (1,20);(2,4);(5,3) I'm wondering how to use the http://en.wikipedia.org/wiki/Lagrange_polynomial to do this. If possible, can these points be fitted with a cubic function? I tried to fit a cubic to this, but...

Homework Statement Given xz^2-yz+cos(xy)=2 which defines z implicitly in terms of x and y, find the directional derivative of z in the direction of the tangent to the curve y=x^2+2x-1 at the point (0,1) in the direction of decreasing x Homework Equations The Attempt at a Solution...

Homework Statement The question gives a transfer function. and we are asked to put it into pole zero form and then we are asked to sketch the positions of the poles and zeros of the system on the complex plane and then sketch the impulse response corresponding to each pole. i have...

I have two curves 1+m1*log(x) and 4.5+m2*log(x) [please see the attached picture]. I want to fit a third curve (which might of any equation), which should actually 'balance' the first two curves, so that the error is minimum. My problem is I am not able to get a initial reduced slope in the...

Hello all Please note: This is not a homework question. I work in Engineering. Firstly Thank you for reading my post. I am trying to learn a technique called Hallade which is used on the Railway to design curves. I have some notes (attached). The bit I fail to understand is on...

Homework Statement f(x,y) = \sqrt{1+9xy}, y = x^{3} for 0≤x≤1 Homework Equations The Attempt at a Solution I don't even know how to start this problem. I thought about c(t) since that's all I have been doing, but there isn't even c(t). I only recognize domain. Can anyone help me...

Find the length of the curve given by the parametric representation... Homework Statement Calculate the length of the curve given by the parametric representation r(t) = t2(cos t; sin t; cos 2t; sin 2t) for 1≤ t ≤+1: Homework Equations The Attempt at a Solution I know that...

Given the following sets of data, find the curve of best fit x = -4, -6, 5, -6, -9, -2, 5 y = -4, -7, 3, -12, -2, 5, 7 a) y = a + bx b) y = a + bx + c cosx I can do part a by using the formula for least square methods for straight line. But what about part b? One way I can think of is...

Homework Statement Let c(s) = \left( \begin{array}{ccc} \cos(s) & -\sin(s) & 0 \\ \sin(s) & \cos(s) & 0 \\ 0 & 0 & 1 \end{array} \right) be a curve in SO(3). Find the tangent vector to this curve at I_3 . Homework Equations Presumably, the definition of a tangent vector as a differential...