Arc Definition and 485 Threads

So sorry if this has been discussed elsewhere before. I know it may be trivial but for some reason I just can't get it. I simply can't seem to integrate the square root of (1 + 1/4x). This problem has been highlighted for a reason, but I'm missing the point. Any input is much appreciated.

There are line integral with respect to arc length and line integral with respect x/y. I know \int_C Pdx+Qdy is useful to calculate the work. When do we need the line integral with respect to arc length?

Homework Statement Determine the arc length of the function on the given interval x = (y^4)/8 + 1/(4y^2) from 1 to 2 The arc length formula \int (f'(x)2 + 1).5 dx The Attempt at a Solution I used the arc length formula but don't know where to go from here. Usually these...

Dear all, I feel this should be a simple problem but I can't solve it. Could you give me a hand? Imagine if an arc is bounded by a rectangle of dimensions width and height. The arc starts in the bottom left corner of the rectangle, and ends in the bottom right corner. The apex of the...

This is an engineering problem that involves geometry so I thought this would be the best forum to post in. I am attempting to interpolate elevations of roadway lines offset from a baseline (center line of a roadway) between two points. The coordinate system used is a combination of stations and...

First of all hello, I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry. My background is computer science but I am not a student. I am only now starting to learn about diff...

Would really appreciate help with the following: Firstly, could someone answer this (simple?) question for something I am trying to make? Secondly, could you give me the most straightforward formula for working it out if I change the length? Hope this makes sense. I have a cylinder. I have an...

Experiments are being carried out on a new ‘high-tech’ swing in a playground, the motion of which follows the model of y=(e^(-ct))*cos(at) Where y is the distance in meters from the equilibrium point of the swing, t is the time in minutes from midday on Sunday, and a, c are real constants...

Seeing the other thread about "How I view AC" and the talk of drift velocity reminded me of a question I had a number of years back, and never found an answer to ... what is the electron drift velocity of an electric arc? I'd be interested in the wide scope of everything from lightning strikes...

Homework Statement Let c be the path c(t)=(2t,t^2,logt), defined for t>0. Find the arc length of c between the points (2,1,0) and (4,4,log2) I just have a problem with the limits for the integral...what limits so I set for it after finding the derivative and using Pythagorean...

Common Temperature ranges from a welding arc can range from 3000-8000 Degrees Celsius. I would like to know the direct relationship of a resultant arc temperature based on the amount of current (amps) flowing. Let's say common steel for the base metal (Electrical Resistivity: 1.74e-005...

Homework Statement Equation of a circle is: x^2+(y+a)^2=R^2 x intercepts are +/-\sqrt{3} and arclength above x-axis is \frac{4\pi}{3} Find a and R.

Homework Statement Find coordinates of a piont on an arc from beginning coordinates at the arc distance of 6.6821. Given Radius of 25 at (100,100), Begining coordinates at (125,100), Ending Coordinates at (115.6994,119.6301), with an overall arc length of 22.4472. Homework Equations...

Homework Statement Confirm that th definition of th arc length ds^{2}=dr.dr leads to the formula L=\int_{C}\frac{dr}{dt}dt Homework Equations \frac{dr}{dt}=\frac{dx}{dt}+\frac{dy}{dt}+\frac{dz}{dt}dt The Attempt at a Solution I am really unsure of what to do here. I have tried starting at...

Homework Statement I previously calculated the electric field for the the arc of the circle and got Ex= Q/2pi^2 e_0 a^2 sin(theta) Ey= Q/2pi^2 e_0 a^2 (1-cos(theta)) I need the electric potential Homework Equations The Attempt at a Solution V=Edr i got an answer interms of theta and since I...

Hi all, Let me state up front that I'm a math idiot. I minored in it in college 20+ years ago and haven't needed it as a software engineer...until now. I'm trying to solve a problem for work that's got me pulling my hair out, mostly because I'm having to relearn so much math I'd forgotten...

Homework Statement The ring (m), which weighs 5Kg, is sliding along a frictionless arc (Shown in the draw). Arc radius - 1.2 meters. There are 2 forces applied on the ring: 1) F - 40N and always tangent to the circle. 2) F' - 150N, 30 degrees above the horizon. Calculate the total...

Homework Statement Find the exact length of the curve x=e^t + e^-t , y=5-2t , 0≤ x≤ 3 Homework Equations ∫ √ ( (dx/dt)² + (dy/dt)² )dt The Attempt at a Solution My attempt at the solution is hopefully in the attachment. I could use Simpson's and get an approximate length but...

Hi all, I'm trying to develop a model of the magnetic field observed from electrical arcing. To start, I want to consider the example of arcing that sometimes occurs when you unplug a device (inductive load, for example) from a 120V, 60Hz outlet. I searched for a while elsewhere online...

Homework Statement Find the length of the curve y=x^3 using P(1,1) as the starting point Homework Equations f(x) = \int_{a}^{x} {\sqrt 1 + {f'(t)}^2} The Attempt at a Solution So far all I've done is found my y' and plugged it in, giving me 1+9t^4 inside the square...

Homework Statement r = e^θ find arc length from (1,0) to origin Homework Equations ∫ab sqrt (r^2 + (dr/dθ)^2) dθ The Attempt at a Solution ∫10 sqrt ((e^θ)^2 + (e^θ)^2) dθ ∫10 sqrt (2(e^θ)^2) dθ ∫10 sqrt (2) (e^θ) dθ sqrt (2) ∫10 (e^θ) dθ need help converting limits in...

Homework Statement find the length of the curve x = 1/3√y(y-3) 1 ≤ y ≤ 9 Homework Equations L = ∫ √(1 + (dx/dy)^2) The Attempt at a Solution x = 1/3√y(y-3) 1 ≤ y ≤ 9 x = 1/3 (y^3/2 - 3y^1/2) dx/dy = 1/2(y^1/2) - 1/2(y^-1/2) dx/dy = 1/2(y^1/2 -...

Find the arc length of [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP595419ebfac4cg3g1925000036iede4e50653655?MSPStoreType=image/gif&s=4&w=65&h=36 from 0 to 8Formula for Arc Length: integral from a to b of sqrt(1+[f(x)]^2) Attempt: f'(x) = 2/3 * 3/2 * x ^(1/2) f'(x) = x^(1/2) integral...

consider the curve r(t)=<5sin(t),4cos(t),3cos(t)> where 0<t<2*pi. Find a formula for this curve's arc length function: s(t). Also, compute the total arc length. Reparameterize this curve with respect to arc length (find r(s)) Don't forget to specify the range for the arc length parameter...

Homework Statement Homework Equations E = k*Q/r^2 The Attempt at a Solution I tried to get the factor through integrating, but it was wrong.I ended up with (k*lambda*2)/R multiplied by the integral of cos(theta) dtheta. Limits were 10pi/21 and 0. I then divided by k*Q/r^2.

Homework Statement Suppose you are headed toward a plateau 60 m high. If the angle of elevation to the top of the plateau is 25*, how far away from the plateau are you in meters? Homework Equations S = (theta)r The Attempt at a Solution In my head this translates as I am given...

Homework Statement Homework Equations l = int( sqrt( 1 + (dy/dx)^2) dx) from a to b The Attempt at a Solution So far I'm stuck at the R^2 thing. I know if it was just R it would mean the set of all real numbers, but I'm not sure as to what R^2 means and I don't know how to google...

Homework Statement find arc length of curve over the interval t(0,2pi) r(t) = 10cos3t i + 10sin3t j The Attempt at a Solution i apply the formula integral ||r'(t)|| over the interval 0,2pi i get integrate sqrt((-30cos2tsint)2 + (30sin2tcost)2) and then finally get 15sin2t |0 to 2pi and i...

Homework Statement When I use Biot-Savart law to calculate the magnetic field at a distance from an arc, I get the well known B=\frac{i\mu_{0}\phi}{4 \pi R} Why can't I use Amperes law for this? I could imagine that the arc instead to be a complete loop of current. Then I could find...

Homework Statement Today we went over finding the arc length s of a circle with a given radian and radius... Thus s = radian*radius... Thats easy to remember but I think it will be more memorable for the long run if I knew the proof and understood it... can some one please post a website...

Homework Statement Just got done reading the chapter... Want to make sure I have this right... IF Circumference = 2(pi)r Let cir = 360 deg. So that 360 deg = 2(pi)r And 180 deg = (pi)r IF r = 10 then 180 = (pi)10 Hence half of a cirlce with radius of 10 has an arc measure of...

Homework Statement r(t)=cos(t^2)\hat{i}+sin(t^2)\hat{j}+t^2\hat{k} Compute the arc length integral from t=0 to t=\sqrt{2 \pi}Homework Equations Arclength = \int_{a}^{b}||v(t)||\, dtThe Attempt at a Solution I did the following: \\r'(t)=-2tsin(t^2)\hat{i}+2tcos(t^2)\hat{j}+2t\hat{k}\\...

I always read in applications of integration is to figure out the arc length but they never tell us what is it good for I also couldn't find immediate results by using google, so can anyone tell me its uses?

Hello there, suppose i want to find the arc length of a circle x^2+y^2=R^2 using integration, implicitly differentiating the equation, i find y'=-(x/y) now, arc length (circumference)= (\int \sqrt{1+y'^2}dx putting the value of y'=-(x/y) and substituting for y^2 from the equation of the...

Can anyone please explain or suggest why the arc from video (link below) rises up? http://blog.makezine.com/archive/2010/12/now_thats_a_switch.html zumulko.

Homework Statement This is another problem my teacher game me. Given the Polar function r=6*sin(t/2) where the variable t is the angle theta in radians, and that t is between 0 and 2*Pi inclusive. Find the distance around the perimeter of the graph. Hint: this is arc length , round to the...

Homework Statement I'm attempting to find the orbital radius for a binary system based on the parallax of the system and angular seperation: 1. A visual binary system that is 5 pc away is seen edge-on (i.e. we are in the plane of the orbit). The maximum angular separation of the two stars is...

Homework Statement I appologize if this is in the wrong topic. But, I need help with the. I know you guys don't exactly give out the answer, but I'm looking for a particular rule of something that will help me. My calculus professor told me to use any available resource to solve this problem...

Homework Statement As a pilot comes out of a dive in a circular arc she experiences an upward acceleration of 9.0 gs (i.e. 9 x 9.8). a) Mentions that the Pilot's mass is 60 kg, already solved this b) If the speed of the plane is 330 km/h, what is the radius of the plane's arc...

Homework Statement F(x) = (4/5)*x^(5/4) on the interval of [0,4] Find the Arc Length Homework Equations Arc Length = Integral (sqrt (1 + [f(x)']^2)) dx The Attempt at a Solution F'(x) = x^(1/4) Integral from [0,4] of Sqrt (1 + x^(1/2)) dx I'm not sure where to go with this...

NVM bout the arc length, need help on integrations Homework Statement Integrate sqrt(1+3x)Homework Equations Sqrt (1+3x) The Attempt at a Solution i made it into (1+3x)^(1/2)

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

Homework Statement An 1850 kg car passes over a bump in a road that follows the arc of a circle of radius 40.60 m as seen in the figure below. a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 14.9 m/s? b) What is the maximum...

i have calculated the C.M. of semi-circular arc of radius r and mass m. How can i use this answer to calculate the C.M of semi-circular disk of radius r and mass m? thanks:) ps. how about the converse?

Homework Statement Find the arclength of the section y=x2 between points (-2,2) and (2,4) Homework Equations L = \int\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}The Attempt at a Solution So what I did first is find the derivative of y=x2 which is y'=2x So I put that into the formula and get...

The string in the Figure is L = 118.0 cm long and the distance d to the fixed peg P is 99.1 cm. When the ball is released from rest in the position shown, it will swing along the dashed arc. How fast will it be going when it reaches the lowest point in its swing? What about the highest in its...

hi, i have a home-made high voltage power supply which produces an arc of about 1 inch long maximum, which i assume is about 20KV, how can i generate nitrous oxide with this spark? will you give me more information about what chemicals/gases are produced from an arc, and what the...

Sorry, latex is being weird. I'm currently trying to come up with a way to find an equation that satisfies: s=\int_a^b \sqrt{(f'[x])^2+1} \, dx Which is arc length and G=\int_a^b f[x] \, dx which is area under the curve where A and s are known values, and f[a]=A, f[b]=B...

Getting the "Arc Length Function" Homework Statement I have two problems scanned, one is an in class example and one is from the homework. The book uses the standard arc length of a curve equation to get the answers. Later in the same chapter they introduce the Arc Length Function, using 's'...

Homework Statement Find the arclength of the curve r(t)=(10t^2,2*sqrt(10)*t, ln t) for 1<=t<=8 Homework Equations The Attempt at a Solution i took the derivative of each component of vector r 20t,2sqrt(10),1/t then i square each term and square root it int sqrt( 400t + 40 +...