Curves Definition and 741 Threads

Let be a open curve on R^2 so x^{n}-c-ky=0 where k,n and c are integers, are there any methods to calculate or at least know if the curve above will have integer roots (a,b) so a^{n}-c-kb=0 ?? or perhaps to calculate the number of solutions as a sum (involving floor function) over integers of...

Homework Statement Sketch on the same axis the graphs of y = |x| and y = 2 - x^2. For which values f x is the inequality |x| < 2 - x^2 Homework Equations The Attempt at a Solution I don't really understand what it is asking me to do, I've sketched the two curves, y = |x| 45...

Hi all. I have say 5 curves in a 2-D plot and they are of different colors. I would like to label them according to their colors or pattern. Say, --- Sin[[x] ___ Cos[x] What command shall I refer to?

Are there notes on the net or books that give a gentle introduction on Riemann surfaces ( say undergraduate math or math for physicists type level)? Always read of the importance and beauty of Riemann surfaces but can't find surveys or intros for outsiders. Same for elliptic curves...

Doing some extra credit and got stuck on this one. Find the differential equation of the family of curves and of the orthogonal trajectories. y = c - 2x Needing a little help on this one... Thanks

Homework Statement The picture is found here (top picture): http://www.iastate.edu/~statics/examples/centroid/centroida.html#ysubc Homework Equations The Attempt at a Solution I get the wrong sign (ie: negative area) when I integrate to find the area between 2 curves when I...

Homework Statement This is so basic and yet I'm not getting it. Find the volume of the solid when the region enclosed is revolved arond the y axis. x = \sqrt{1 + y} x=0, y=3 Homework Equations The Attempt at a Solution So I first graphed the thing, finding that the...

Ok, I've been trying to work this out for a couple of hours now and I'm completely stumped. Not even Google was helping much. The question is: Find and Sketch the level curves of the scalar field T(x,y) = (x +y)/(x2 + y2) for T = -1, -0.5, 0, 0.5, 1[/size] I know that I should equate the...

Homework Statement I want to show that if the chhord length ||f(s)-f(t)|| depends only on |s-t| then the f is part of a line or circlle. f may not be regular or unit speed. Homework Equations The Attempt at a Solution I'm trying to differentiete it and taking ||f'(t)||, but I...

I'm looking for a program which can draw 3D graphs which can identify the generating curves and ruling. i'm trying to draw up these 2 graphs z = 2x^2 + y^2 x^2/9 + y^2/9 + z^2/16 = 1 any ideas?

hi, hope you can help with this. For your reference I am 16 doing the nationwide 16 year olds exam (GCSE) so please if you can avoid using stuff I havn't done that'd be great :D Homework Statement The x coordinates of the points of intersection of the curve y = x^3 - 2x^2 - 5x and a...

Currently in chemistry, we are doing titrations and buffers for acid base equilibrium. I've noticed that titration curves have the distinct characteristics of sigmoid curves. So, can titration curves be modeled with a sigmoid function?

y = x^2 ,\,\,y = \frac{2}{{x^2 + 1}} It looks obvious from the graph that the intersections are -1 and 1, but just to verify: \frac{2}{{x^2 + 1}} = x^2 \,\, \Leftrightarrow \,\,x^2 \left( {x^2 + 1} \right) = 2\,\, \Leftrightarrow x^4 + x^2 = 2,\,\,x = - 1,\,\,1 So my...

Homework Statement Find the area of the region bounded by: y=cosx, y=sin2x, 0, x=pi/2 Homework Equations The Attempt at a Solution I made a graph. I believe I'm trying to find the area I shaded. red=cos(x), blue=sin(2x) I need to find the intersection point so I will know...

Hi, I have two parametric curves defined in three dimensions, which are functions of a variable t, like so: x1 = f1(t) y1 = f2(t) z1 = f3(t) x2 = f4(t) y2 = f5(t) z2 = f6(t) I am trying to find the intersection of these two curves, but I am having some difficulty with the...

Homework Statement Find equations of the tangents to the curve x=3t^2+1, y=2t^3+1 that pass through the point (4,3). The Attempt at a Solution I was able to find the equation y=x-1 as a tangent line through the point (4,3) for the part of the curve above the x-axis since (4,3) is on...

I learned that vertifcal tangents occur at a parametric curve if the derivative of the curve is undefined. That is given dy/dx = dy/dt / dx/dt, a vertical tangent occurs when dx/dt = 0. I don't understand why this is so. I know that vertical tangents occur when the slope is infinite, but...

Show that for all values of t, the point P with the equation x=2t^2, y=t^3 lies on the curve 8y^2=x^3 Find the equation of the tangent to the curve at point P. The tangent meets the curve once again at point Q. Find the coordinates of point Q. I can find the equation of the tangent. After...

Homework Statement Find the area of the region enclosed by the following curves: f(y)=1-y^2 g(y)=y^2-1 Homework Equations The Attempt at a Solution I'm confused by the graph because the region enclosed has positive and negative parts, and I can't determine whether f(y)>g(y), g(y)>f(y), or...

We were given a graded assigment and one of the question asks. Prove that all curves in the family y1=-.5x^2 + k (k any constant) are perpendicular to all curves in the family y2=lnx+ c (c any constant) at their points of intersection. I found the derivatives of y1 and y2 and they are...

I just finished learning the fundamental theorem of curves in 3 dimensions. As a reminder, this is the theorem that states that a continuous, C infinity, unit speed curve in 3d is uniquely determined by its curvature and torsion (up to actions by SE(3), that is rotations and translations)...

I am trouble with problems that don't list each function f(x) or g(x). The book sets them equal to y. Every time I do these I'm getting them wrong. When I check the solution, I'm mistaking f(x) for g(x) or vise versa. So is there a way to tell which y is f(x) or g(x)?

A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.84. at what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction...

I have three points on a Y= -ax^2 + bx + c graph (negative parabola). I don't know how to find the equation with this information. Tangent lines? Help.

A thought occurs... In a world devoid of curved lines, can we create a circle using only straight rigid lines? If we take a square as our starting block, then use 4 straight lines to cut off its 4 corners at 45 degree angles, we now have a perfect octagon. If we now take 8 straight lines...

Hello, are all Oval Shaped Cartesian Curves" +/-(x^2) " or we can have it with other degrees??

Hi, I am having a little trouble with this one, how do you do them when no boundaries are given? y=sin \frac{\pi x}{2} and y=x how do i find the boundaries?

How would one go about finding an analytical solution to the following ODE note that we are trying to find y(x) subject to... (x*y'')^2 - (1 + (y')^2) = 0

Hi all, I'm having a problem with this subject and I was wondering if anyone could confirm/comment on my understanding. As I understand it, in a typical transformer, an AC current is supplied to a primary coil which induces an oscillating flux within the core. If the core is made of a...

I need to find the area that's inside both of the following curves: r = \sin\theta r = \cos\theta I know that I should have to subtract the area of the one curve from the other and I know the area formula for polar coordinates, but I just can't see how to set this one up any help or...

Find the area of a figure bounded by the equilateral hyperbola xy = a^2, the x-axis, and the lines x = a, b = 2a. My work: The equations of the lines and curves involved here are: xy = a^2 y = 0 x = a I don't know how b=2a is treated as an equation of a line here & hence I am puzzled as how to...

Hi Could someone please give me an idea on how to go about this problem Find the volume of the curve genereated by revolving the area between the curve y =(cos x)/x and the x-axis in the interval pie/6 to pie/2 Thanks a lot..

Write, but do not evaluate the integral that will give the area between y = cos x and y = x/2 - 1 , bounded on the left by the y-axis I've sketched the graphs, so I know that y = cos x is above y = x/2 - 1 , so the indefinite integral to solve would be \int (cos x) - (x/2 -1) dx I...

Good morning to all. By laboral reasons I am reading about digital signatures and "public key" cryptography. The most popular of the cryptographic methods related to digital signatures (RSA) is only an application of the "little Fermat theorem". This theorem belongs to "baby" number theory...

In a cooling curve of a single substance there is a thermal arrest point where the liquid turns into solid. My laboratory manual mentions that in a cooling curve containing two liquids (A + B), in addition to the arrest there is a second point called a "break". It says the point at which solid A...

"The temperature of space is given by \phi (x,y,z) = xy + xz . A fly is flying in space and at each point (x,y,z) of its journey it flies in the direction \mathbf{F} (x,y,z) in which the rate of increase of temperature is maximum. (a.) Calculate F(x,y,z). (b.) Find the curve along which the fly...

Hello, thank you for helping. My Question: On a banked race track, the smallest circular path on which cars can move has a radius r1 = 107 m, while the largest has a radius r2 = 163. The height of the outer wall is 18 m. Find the smallest speed and largest speed at which cars can move on...

I have been asked to find the area between the following curves f(x)= x^3 -9x^2 +18x and g(x)= (-x)^3 +9x^2 -18x I started out by finding the points of intersection, which I found to be 0, 3, and 6. I then integrated |f(x)-g(x)|and evaluated between 6 and 0. I got an answer of zero but it...

I'm stuck on this problem. I am hoping someone can walk me through it or get me past my choking point. The problem states: Two equations have two shared tangent lines between them. Find the equations of these tangent lines analytically. g(x)=x^2 f(x)=-x^2+6x-5 The first step I took was to...

hi! Thanks for the advice, I managed to find the intersection points, but I seem to have run into a problem. I set up the integral as follows: (4-x^2) (for 1 to 2) + (4 - 1/x) (for 1/4 to 1) this worked out to ((8-8/3) - (4 - 1/3)) + (4 - (1 - ln1/4)) (16/3 - 11/3) + (3 + ln1/4) 5/3 +...

hi, the question goes as follows: y = x^2, y=1/x, y=4 for the first quadrant. This may be a dumb question :blushing: but how do I figure out the points at which these three intersect? Do I first set the first two equal to each other and then set the resulting equation equal to 4? Thanks...

I know how to do this graphically, but I can't remember how to set it up the long way. The equations are: y^2=x and y=x-2 I know it should be easy, but it's late and I can't think...

Hi. I'm new here. :) I was wondering if anyone could help me out with this problem... i'm supposed to find the region bounded by: y=x+1 y=e^-x x=1 i think i should find the other point of intersection but i forgot to do that (i haven't taken a math course for about 4 years). please help!

A curve of radius 170 m is banked at an angle of 22°. At what speed can it be negotiated under icy conditions where friction is negligible? Can someone explain how to get the answer for this question? Thanks

1. I am given a curve defined parametrically by x= 2/t , y=1-2t i have found the equation of tangent at t=-2 to be y=4x+9, they have asked whether it cuts the curve again. how do i find that, since i don't know the original equation of the curve and can't solve them simultaneously. 2. Also...

Hi, I'm having trouble drawing the level curves of a function because I can't really visualise what's going on. f\left( {x,y} \right) = \frac{{2xy}}{{x^2 + y^2 }} In polar coordinates (x,y) = (rcos(phi),rsin(phi)) I get:f\left( {r\cos \phi ,r\sin \phi } \right) = \sin \left( {2\phi }...

What other curves are there that cannot be described by the above? Are trigonometric functions actually a special case of exponentials with complex powers?

Titration Curves - Help needed I really need some help in this, I don't understand how to make a titration curve. I have 50ml of a 0.1 M solution of formic acid with a 0.1 M solution of NaOH. I know that the pKa of the formic acid is 3.74 but i don't know how to get the pH or H+. I've hit a...

Find an equation of the tangent line to the curve with parametric equations x=tsint, y=tcost at the point (0,-π). went dy/dt / dx/dt --> cost - tsint/sint + tcost t not given so figured it could be: x=t(sin(1)) --> t= x/sin(1) or y=t(cos(1)) --> t= y/cos(1) wondering if...

Could anyone explain to me how to go about solving these problems? Example: A Car is driven around a circe with a radius of 200m, bank angle 10 degrees. The static frictional coefficient is 0.60. Calculate the maximum velocity the car can travel (Vmax). Please help! I did this, but am not...