Curves Definition and 778 Threads

Homework Statement i have to create a mathematical forumal from data of high and low tide depths and times. from that predict the next weeks outcome. it has to have sin or cos in the equation. a*COS (bx+c)+d or sin. this is the data given Mon 09/03/2009 Tue 10/03/2009 Wed 11/03/2009...

Homework Statement A 1200 kg car rounds a curve of radius 67 m banked at an angle of 12 degrees. If the car is traveling at 95 km/hr, will a friction force be required? If so how much and in what direction? Homework Equations F=ma a=v2/r The Attempt at a Solution I don't know what...

Homework Statement A car rounds a slippery curve. The radius of curvature of the road is R, the banking angle is theta and coefficient of friction is mu. What should be the cars speed in order that there is no frictional force between the car and the road? Homework Equations F=mv^2/r...

x^{2}-y^{2}-2x+4y+5; let x^{2}-y^{2}-2x+4y+5 \ = \ c; To sketch this as a level curve, I'm not sure how to proceed. I can't seem to rearrange the function into anything familiar. For the sake of trying to find a reference point, I let x=0 and found y \ = \ 2 \ ^{+}_{-}\sqrt{9-c}...

I have a function: y=e^x the tangent line at the point (1,e) would be x*e? in order to find the area between the tangent line, the y-axis and y=e^x i equate these functions and solve for x? I got this far (e^x)/(x)=e how do i solve for x

Homework Statement z=f(x,y)= -\sqrt{9-2x^2-y^2} Sketch the level curves for f(x,y) Homework Equations The Attempt at a Solution I am really poor at this. I let z = c (a constant) . Substituting c into the equation and rearranging it, I got this 9-c^{2}=2x^{2}+y^{2} From this, I...

To the moderator: I'm not sure if this should go here or in the Computational Physics forum. Please shift it there if you think that's the appropriate place for it. Hi everyone Merry Christmas! I'm writing a computer program in C, to explicitly compute the band structures for a 1D...

I encountered a few problems for a few questions while doing my homework. 1. Angular measure problem: A Ferris wheel with a radius of 25.3m makes 2 rotations every minute. a) Find the average angular speed of the Ferris wheel in radians per second. b) How far does a rider travel if the ride...

This is my last annoying post here, probably. :) Homework Statement I have a curve \alpha: I \rightarrow \Re^3 parametrized by arclength. \kappa(t) \neq 0 for all I. Given the surface \psi (s,t) = \alpha (t) + (s-t) v(t), where v(t) = \frac{d \alpha}{dt}, t is in I, and s > t, I want to...

I've attempted to solve this problem but I'm not really sure if I'm doing it right. I've looked up other threads containing the same question, but they just don't have the answers I'm looking for. Thank you in advance to anyone who helps. Homework Statement A race-car driver is driving her...

Homework Statement Alright so the problem: Find the reigon in the xy plane that is bounded by the curves: x = y^2 and 2y + x = 3 quickly solving for the y coordinates of intersection, i get y = -3 and 1 so using horizontal components i got: \int^{1}_{-3} 3-2y - y^2 and...

Are there surfaces that have a geodesic curve which completely covers the surface, or (if that's not possible) is dense in the surface? In other words, if you were standing on the surface and started walking in a straight line, eventually you would walk over (or arbitrarily close to) every...

I know its a really dumb question and if i reached this far in math i should know but..how do you draw the diagrams for this topic? Like they give you a region in a plane defined by some kind of inequalities such as (x-2y^2 greater than or equal to 0), (1-x- IyI greater than or equal to 0) and...

Hello, I am an amateur developing the math to describe the motion of a robot of sorts. At this stage I'd like to use http://en.wikipedia.org/wiki/Bézier_curve" as user input to describe the motion path/s that it will make over time... (imagine it sitting flat on the cartesian 'floor')...

I must demonstrate in two ways that if c(t) is an integral curve of a smooth vector field X on a smooth manifold M with c'(t_0)=0 for some t_0, then c is a constant curve. I found one way: If \theta denotes the flow of X, then because X is invariant under its own flow, we have c'(t)=X_{c(t)} =...

Homework Statement Draw a contour map of the function showing several level curves. f(x,y) = x^3 - y Homework Equations f(x, y) = x^3 - y The Attempt at a Solution I think I should be finding the domain and range, but other than that I am not sure what else I need to do.

Homework Statement Find the area of the region enclosed by the asteroid: x=a*cos^{3}\theta y=a*sin^{3}\theta Homework Equations A = \int\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}The Attempt at a Solution \frac{dy}{d\theta} = 3asin^{2}\theta(cos\theta) \frac{dx}{d\theta} =...

Homework Statement At what point do the curves r1(t) = <t, 1 - t, 3 + t^2> and r2(s) = <3 - s, s - 2, s^2> intersect? Find their angle of intersection correct to the nearest degree. Homework Equations The Attempt at a Solution I set t = 3 -s 1 - t = s - 2 3 + t^2 = s^2 I got...

for a graph that has the velocity as the x-axis and the number of molecules as the y axis, i know that as the number of molecules increases, the average velocity will become lower and lower, but what if the molecules being tested are in relative amounts? for example you have air which is...

for a graph that has the velocity as the x-axis and the number of molecules as the y axis, i know that as the number of molecules increases, the average velocity will become lower and lower, but what if the molecules being tested are in relative amounts? you have the equation speed = sqrt...

I've been reading a bit on these, not in a rigorous way yet, and it's an enjoyable read. But now I've a few questions. As I understand it, they allow for a continuous index set in \Re to completely cover a higher dimensional \Re^{n}. Everywhere continuous, but nowhere differentiable, so it...

Homework Statement An automobile club plans to race a 740 kg car at the local racetrack. The car needs to be able to travel around several 175 m radius curves at 85 km/h. What should the banking angle of the curves be so that the force of the pavement on the tires of the car is in the normal...

1. Two curves on a highway have the same radii. However, one is unbanked and the other is banked at an angle theta. A car can safely travel along the unbanked curve at a maximum speed Vo under conditions when the coefficient of static friction between the ties and the road is ms=0.81. The banked...

Homework Statement Solve for the vector function that represents the curve of intersection in the following two surface: z = sqrt(x^2 + y^2) and z = 1 + y Homework Equations The Attempt at a Solution Through blind trial and error, I managed to get the book-specified answer of x =...

Homework Statement Compute the area between the graphs of f(x) = 8sin(2x) and g(x) = 5sin(x)+3sin(2x) on the interval [0,pi/2] Homework Equations Area = Integral of [f(x)-g(x)]dx The Attempt at a Solution I first did f(x) - g(x) = 5sin(2x)-5sin(x)...after integrating, I got...

Sketch the following function, showing all work needed to sketch each curve. y = \frac{1}{3 + x^2} The question is asking for all the work done to find x and y intercepts, vertical, horizontal and slant asymptotes; critical points and points of inflection, i have completed the question...

I have three questions that I'm going to roll into one. I'm going insane trying to figure these out. 1. Find the unit tangent vector T to the cycloid. Also find the speed at theta=0 and theta=Pi, if the wheel turns at dtheta/dt=1. that dtheta/dt is the speed, right? I'm a little...

I've been involved for a long time going over astronomical influences on climate. My job is to be an astronomer and I don't know about climate. Maybe you think this is impossible, but I think it would be too complex to say whether a record of some sort within the ice was the driving force of all...

Need help checking if my reasoning is sound for this. Homework Statement Isobars are lines of constant temperature. Show that isobars are perpendicular to any part of the boundary that is insulated. Homework Equations u(t,\underline{X}) is the temperature at time t and spatial...

I'm really having trouble with these three problems. I'd post my attempts but most of it is in graph from. 3. David subjects a cylindrical can to a certain transformation. During this transformation the radius and height vary continuously with time. The radius is increasing at 4 in/min...

i was going over some relativity search online and came across what is called a closed timelike curve and that i actually allows time travel, am i right?

On galaxy rotation curves, the velocities of stars (or gas) rotating about their galactic centre remain fairly constant as the distance from the galactic centre increases. But these rotation curves show a drop in rotation velocity towards the centre of the galaxy...

im doing my project for school on this a need help.

Hello, my name is Calleigh and i am new to the forum! I am in Calculus II and have a few questions on some problems. I am using the textbook Calculus 8th edition by Larson, Hostetler and Edwards. Could someone please help me? The problem is on pg 950 in chapter 13.7 in the text, number 46. It...

Hey all, This question stems from Scorpan, "The Wild World of 4-Manifolds", pg 302 (and all through that chapter). He states that a random homogeneous polynomial of degree d in CP^2 with coordinates [z_0:z_1:z_2] defines a complex curve C, with homology class [C]=d[CP^1]. So I understand...

Hello! Homework Statement Well,I'm having a problem drawing level curves for piecewise functions. The problem is, how do I know which value the constant k will hold? Homework Equations The functions is the following: f(x,y)=4 if x^2+y^2<=16 sqrt(32-x^2-y^2) if...

Hi, this is a question to the members with some knowledge in algebraic geometry: 1. what are rational curves with self-intersection -2? How do they look like? 2. do you know why these correspond to the vertices of some of the Dynkin diagrams? 3. just something that's bothering me...

I'm trying to figure out how to best interpret multiple shifts in a supply/demand curve. Suppose that a new law requires every firm to provide its workers with free cell phones. The cell phones are worth $200 a year to the works and cost the firms $500 a year to provide. On a labor...

I've been doing some analysis on isotope data for a paper, and I've obtained some results which don't seem to appear in the literature. Have you come actross this? Here's the first one.

I'm stuck on a problem on vector calculus. Given a surface S defined as the end point of the vector: \mathbf{r}(u,v) = u\mathbf{i} + v\mathbf{j} + f(u,v)\mathbf{k} and any curve on the surface represented by \mathbf{r}(\lambda) = \mathbf{r}(u(\lambda),v(\lambda)) and it mentions the...

Homework Statement y=x^2-2.x y=x^3 Homework Equations none The Attempt at a Solution I have no idea how to do this so please help me. Thank you.

I'm trying to find patterns for polar curves. I just reviewed and feel comfortable with taking advantage of symmetry, but I still have trouble with some type of curves. Limacons: Two types 1) inner loop 2) no inner loop Is there a general formula that tells me whether there will be an...

The problem is related to polar curves. most of the topics i need to do are easy (finding the slope, finding the area etc.) What I'm facing problems with is that when I find the area, I don't know how to find the limits. Homework Statement Sample problem: Find the area of the region in...

Find the area of the region between the following curves for x in [0, 3]. Give the answer to three decimal places. y=x y=4e^x I understand how to do these types of problems but I always get confused when there is an e involved. If someone could explain how to arrange it before the anti...

Homework Statement The curves `bar r_1(t) = < 2t,t^(4),5t^(6) >` and `bar r_2(t) = < sin(-2t),sin(4t),t - pi >` intersect at the origin. Find the angle of intersection, in radians on the domain `0<=t<=pi`, to two decimal places. The Attempt at a Solution Well, I tried to do it in...

Homework Statement Homework Equations r=sinx r= cosx Ok , i need help how to properly select the integral to evaluate the area they make. Can someone please show me how , i know how to evaluate it just having hard times with integrals The Attempt at a Solution

Various problems in my textbook ask me to sketch the level curves for a Hamiltonian system, but they don't suggest how to go about it. I know that I need to determine the eigenvalues for each equilibrium point in the given system, and these values hint at the behavior of solutions near each...

Suppose the area of the region between the graph of a positive continuous function f and the x-axis from x = a to x = b is 4 square units. Find the area between the area between the curves y = f(x) and y = 2f(x) from x = a to x = b. Attempt: Since 2 f(x) is greater than f(x) we can call it...

I am curious to know whether in a real physical situation a cooldown curve (temperature vs. time plot for a given point) can exhibit inflection. Why or why not? Let me point out that there is no phase change involved during the cooling process...

Homework Statement Identify and sketch the curve represented by the parametric equations: x=1+cost y=1+sin^2t Homework Equations The Attempt at a Solution I have to isolate t in one of these equations and sub whatever t equals into the other equation right? So how do I get rid of the...