Arc Definition and 478 Threads

A circle has a radius of 10cm. Find the length s of the arc intercepted by a central angle of 124° . Do not round any intermediate computations, and round your answer to the nearest tenth. How do I do this?

Hello everyone, I have a rather simple question. I have the curve ## C(t) = \begin{cases} 1 + it & \text{if}~ 0 \le t \le 2 \\ (t-1) + 2i & \text{if }~ 2 \le t \le 3 \end{cases} ## which is obviously formed from the two curves. This curve is regarded as an arc if the functions ##x(t)## and...

Homework Statement My class is working through chapter 2 of Newman's Analytic Number Theory text (on partitions). We have come to a part where he states that "elementary geometry gives the formula" (for the length of arc A) 4r\text{arcsin}\frac{\sqrt(2)(1-r)}{\sqrt(r)} We are attempting to...

Homework Statement Given that the circular arc wire with radius 'r' has a linear charge density ##\lambda##. What is the Electric field at the origin? Homework Equations ##\vec{E}=\frac{kq}{r^2}## where ##k=9\times10^9## is a constant. 3. The Attempt at a Solution I took a small segment dy...

Hi, So I'm working through a bunch of problems involving gradient vectors and derivatives to try to better understand it all, and one specific thing is giving me trouble. I have a general function that defines a change in Temperature with respect to position (x,y). So for example, dT/dt would...

Homework Statement Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) . Homework Equations s(t)=integral of |r'(t)| dt The Attempt at a Solution I was able to get the integral of the magnitude of the velocity vector to simplify to: s(t) = integral of...

I am working on an algorithm which requires the coordinates for the center point of an offset circle. Dimensions available to find this are shown in the image below and the dimension required is labeled as X: The point at the very left of the arc is a quadrant therefore, the circle center also...

Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360 Where: A: Central Angle C: Circumference Is this correct? Thank you for your help.

Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...

Homework Statement A curve has the equation y2 = x3. Find the length of the arc joining (1, - 1) to (1, 1). Homework Equations The Attempt at a Solution I took the integral of the distance and tried to evaluate from -1 to 1. L = [intergral (-1 to 1) sqrt (1+(dy/dx x^3/23/2)2 dx] Evaluated I...

Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0Homework Equations Arc length =...

find the length of an arc of a helix r(t)=(sint,cost,t) from the point (0,2,0) to (0,5,2pi) would the interval when integrating be from 0 to 2pi because t in the case is (z=t)? please say yes. please say yes.

let C be the curve of intersection of the parabolic cylinder $x^2=2y$ and the surface $3z=xy$. find the exact length of C from the origin to the point (6,18,36). please help! this is the last question i have left from this assignment and i have no idea how to do it. i have grading to do and a...

Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...

Electric Field from Arc of Charge - NEED HELP WITHIN AN HOUR I have literally been working on this all day and I am finally turning it over to someone better at physics then myself. This is due within two hours and I'm starting to doubt my ability to finish this, any help will be beneficial...

Of course, I need to find the first derivative and integrate its norm. α'(t) = (1, 0, (1/2)t^2 - (1/2)t^-2) ∫ [1 + (1/4)t^4 + (1/4)t^-4]^(1/2) dt, t = 1 to t = 3. Have I simply forgotten useful integrals? α'(t) = (e^t, -e^-t, root2) ∫ [e^2u + e^-2u + 2]^(1/2) du, u = 0 to u = t.

I am not sure if this is the right forum for this question, but I arrived at the question while studying the principle of stationary action so here it is: Consider the problem of finding the shortest path between two non-antipodal points on a sphere. Usually one solves this by using calculus of...

EDIT: Okay now that the admin has cleaned up my mess, please scroll down to see the correct image and the question on the 3rd post in this thread.

find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far. $y'=3\sqrt{x}$ $1+(3\sqrt{x})^2=9x+1$ $\int_{a}^{b} \ \sqrt{9x+1},dx$ what's my a and what's my b?

how do i use the nspire to find arc length?

This is a problem I thought up. If I'm correct as far as I've gone, the answer is rather surprising. A thin but 'massive' rope lies coiled on a floor. Treat the coil as a point. One end passes vertically up and over a smooth cylindrical drum radius r. The centre of the drum is height h...

There are tons of different explanation for each of them in internet. Could someone please confrim the explanation below which I gathered from different places; If the electrical field in a fluid reaches the fluids dielectrical strenght, dielectric collapses and corona happens, but since the...

I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope I'm using the term arc...

1.) The problem is: Find the arc length of f(x)= x^3/3-1/(4x) from x=1 to 2 2.) Relevant formulas: ds = √(1+(dy/dx)) abs(L) = ∫ds 3.) My work so far: f'(x)= x^2+1/(4x^2) abs(L) = ∫(from 1 to 2) √(1+(x^2+1/(4x^2))^2 dx = ∫(from 1 to 2) √(1+(x^4+1/2+1/(16x^4)) dx = ∫(from 1...

Hello all I was hoping someone could help me with a geometry problem. Firstly this is not a homework question – this is work related I am just not very good with Maths. I have been asked to set out an arc for a wall. I have been given all the values I need but I do not know how the...

So here's a little background for the question: I have an arc that covers 3/4s of a circle (so it's not quite a full circumference) such that the radius from the center of the arc varies with respect to the angle (dR/d(theta)) (and it can be either positive or negative, but not constant). I am...

Homework Statement Find the length of the curve x = 3 y^{4/3}-\frac{3}{32}y^{2/3}, \quad -64\le y\le 64Homework Equations Integral for arc length (L): L = \int_a^b \sqrt{1 + (\frac{dy}{dx})^{2}} dx The Attempt at a Solution Using symmetry of the interval and the above integral for arc length...

Homework Statement I don't know the radius of the circumference. I could only measure the arc lenght, and the height. I know the guidelines say we should not post images, but this is a geometric problem and I think it is something logic to show it with a picture. So the variables are the...

Homework Statement Find the area of the region in the first quadrant, which is bounded by the x-axis, the line x = 2 and the circular arc x^2 + y^2 = 8Homework Equations The Attempt at a Solution I didn't use the hint given in the question but does my answer still makes sense. Did I set up the...

∫sqrt(x^4/4 + 1/(x^4) + 1/2) dx from x = 1 to 4 Could someone help me solve this? I can't seem to find a substitution that works, or find the square root of (x^4/4 + 1/(x^4). Any help would be very appreciated. Thanks in advance!

This may seem like a dumb question, but is finding the "arc length" of a curve and finding the "length" of a curve the same thing? Just worded differently?

Homework Statement image attachment Homework Equations The Attempt at a Solution i have the solution , but in it , he assumes the center of mass is on the vertical and thus the distance of the vertical from the center is rsin(1/4∏)/(1/4∏) where r is the radius , so why did he...

Hello, I solved the arc length for a particular problem. However, what is the unit of arc length if the units of the velocity vs time graph are m/s vs s? I am really confused.

1. The problem statement, all variables and given/known If C is a smooth curve given by r(s)= x(s)i + y(s)j + z(s)k Where s is the arc length parameter. Then ||r'(s)|| = 1. My professor has stated that this is true for all cases the magnitude of r'(s) will always equal 1. But he wants me...

Find the length of the positive arc of the curve y=cosh^{-1}(x) (for which y≥0) between x=1 and x=\sqrt{5}. My attempt: x=cosh(y) → \frac{dx}{dy} = sinh(y) → (\frac{dx}{dy})^{2}=sinh^{2}(y), so ds=dy\sqrt{1+sinh^{2}(y)}, therefore the arc length is S=\int_{y=0}^{y=cosh^{-1}(\sqrt{5})} cosh(y)...

hello frnz i m aiming to provide a compensation scheme for electrical arc furnance but i don't have practical data to deal with.Is there anyone who could provide me rating of electric arc furnace (KVA rating n power factor).

The solution to this question (whose answer is pi) is eluding me: The radius of a circle is 3 feet. Find the approximate length of an arc of this circle, if the length of the chord of the arc is 3 feet also.

how do i integrate the function sqrt(1 + 1/2(y^1/2 - y^(-1/2))^2) from 0 to 1??

Homework Statement What is the potential at point P due to a point charge Q at a distance R from P? Set V=0 at infinity. The same charge has been spread uniformly over a circular arc of radius R and central angle of 40 degrees. What is the potential at point P at the center of this arc...

Homework Statement The length L or the curve given by \frac{3y^{4}}{2}+\frac{1}{48y^{2}}-5 from y=1 to y=2 Homework Equations The Attempt at a Solution Setting up the formula is easy. First I found the derivative of f(y) which is: f'(y)=6y^{3}-\frac{1}{24y^{3}} Then I plugged...

Homework Statement I am currently reviewing the physics of 'standing waves on a string'. I know that for the nth harmonic, the length of the 'string' is \frac{n\lambda}{2}. Instead of just memorizing these, I have been trying to apply my knowledge of Calculus to figure out why these numbers...

Homework Statement y^2 = x from (0,0) to (1,1) Homework Equations L = ∫√(1+[g'(y)]^2) dy The Attempt at a Solution So this is a problem in my textbook that has been bothering me because I can't seem to come up with the same answer. 1. [bounds 0 to 1] 1/2∫ sec^3θ was obtained...

Homework Statement This is an update to an earlier post. Since then, I now understand that a pendulum stops when its tension force= mg sin(theta)--because then centripetal force will=0, so velocity will be 0. However, now I am trying to determine how a trapeze would work on the moon. Homework...

When an electrical circuit is opened or closed there is an arc between the terminals/buss that the switch or breaker is connecting or disconnecting and the arc is greater depending on the amount of voltage. My question is, is the arc greater when there is a resistance/load on the circuit? I'm...

Ello every one, i have interesting question. Any one who has james stewert 7th edition calc book I am on secotion 8.1 studying for an exam. number 13 of 8.1 says this y= ln(secx) find arc length from 0-pi/4 here is what i do first in my opinion. y`= 1/sec(sectan) y`= tanx...

Homework Statement Calculate the arc length of <2t,t^2,lnt> from 1=<t=<e Homework Equations Arc length=∫√{(x')^2 + (y')^2 + (z')^2} The Attempt at a Solution So I have gotten to this point: ∫√{4 + 4t^2 + \frac{1}{t^2}} Am I on the right track, and if so, how do I integrate that?

http://www.natuurkunde.nl/servlet/supportBinaryFiles?referenceId=1&supportId=606217 Hello everyone, I was wondering if anyone could shed some light on the following problem: While composing a practise test for a chapter about conservation of energy, I made a problem like the one in the...

This is from my course notes http://img28.imageshack.us/img28/2630/ckyl.jpg In line 3, there's the integral \int_0^t ||y'(s)||ds which represents the length of the curve as a function of t (which I am thinking of as time). Here, I think s is a dummy variable for time. The equation in line...

Homework Statement Find the arc length parameterization of r(t) = <(e^t)sin(t),(e^t)cos(t),10e^t>The Attempt at a Solution so I guess i'll start by taking the derivative of r(t)... r'(t) = <e^t*cos(t) + e^t*sin(t), -e^t*sin(t) + e^t*cos(t), 10e^t> ehh... now do I do ds = |r'(t)|dt and...

Hello. What sort of commonly accessible material can block harmful UV from a 150W Xenon arc lamp, without blocking much of visible light? Lamp relative spectrum (a bit around 250nm, growing to a lot at 400nm): Enough UV should be blocked for the lamp to be usable as a regular...