Question

Suppose β = β(s) is a curve parametrized by arc-length. If β lies on a sphere...

Suppose β = β(s) is a curve parametrized by arc-length. If β lies on a sphere of center c and radius r, prove β −c = −ρn−ρ0σb where ρ = 1/κ and σ = 1/τ.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

the proof is too much tricky and uses too much concepts so if you stuck somewhere in the proof you can ask in comments

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose g : (a,b) ? R^n is a differentiable parametrized curve with the property that at...
Suppose g : (a,b) ? R^n is a differentiable parametrized curve with the property that at each t, the position and velocity vectors are orthogonal. Prove that g lies on a sphere centered at the origin.
A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with...
A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 28°C. The temperature T(r) (in °C) at a distance r (in meters) from the common center of the spheres satisfies the differential equation d2T dr2 + 2 r dT dr = 0. If we let S = dT/dr, then S satisfies a first-order differential equation. Solve it to find an expression for the temperature T(r) between the spheres. (Use...
Write the curve given by r(t)=((3/2)t)i+(t^3/2)j as a function r(s) parameterized by the arc length s...
Write the curve given by r(t)=((3/2)t)i+(t^3/2)j as a function r(s) parameterized by the arc length s from the point where t=0. Write your answer using standard unit vector notation.
Parameterize the curve using the arc-length parameter s, at the point at which t=0t=0 for r(t)=e^tsint...
Parameterize the curve using the arc-length parameter s, at the point at which t=0t=0 for r(t)=e^tsint i+e^tcost j.
A) Use the arc length formula to find the length of the curve y = 2x...
A) Use the arc length formula to find the length of the curve y = 2x − 1, −2 ≤ x ≤ 1. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula. B) Find the average value fave of the function f on the given interval. fave = C) Find the average value have of the function h on the given interval. h(x) = 9 cos4 x sin x,    [0,...
. Let C be the curve x2+y2=1 lying in the plane z = 1. Let ?=(?−?)?̂+??...
. Let C be the curve x2+y2=1 lying in the plane z = 1. Let ?=(?−?)?̂+?? = (a) Calculate ∇×? (b) Calculate ∫?∙?? F · ds using a parametrization of C and a chosen orientation for C. (c) Write C = ∂S for a suitably chosen surface S and, applying Stokes’ theorem, verify your answer in (b) (d) Consider the sphere with radius √22 and center the origin. Let S’ be the part of the sphere that is above the...
Suppose a conducting sphere, radius r2, has a spherical cavity of radius r1 centered at the...
Suppose a conducting sphere, radius r2, has a spherical cavity of radius r1 centered at the sphere's center. At the center of the sphere is a point charge -4Q. Assuming the conducting sphere has a net charge +Q determine the electric field,magnitude and direction, in the following situations: a) From r = 0 to r = r1. b) From r = r1 to r = r2. c) Outside of r = r2 d) find the surface charge density (charge per...
1. a) Get the arc length of the curve. r(t)= (cos(t) + tsin(t), sin(t) - tcos(t),...
1. a) Get the arc length of the curve. r(t)= (cos(t) + tsin(t), sin(t) - tcos(t), √3/2 t^2) in the Interval 1 ≤ t ≤ 4 b) Get the curvature of r(t) = (e^2t sen(t), e^2t, e^2t cos (t))
Let y = x 2 + 3 be a curve in the plane. (a) Give a...
Let y = x 2 + 3 be a curve in the plane. (a) Give a vector-valued function ~r(t) for the curve y = x 2 + 3. (b) Find the curvature (κ) of ~r(t) at the point (0, 3). [Hint: do not try to find the entire function for κ and then plug in t = 0. Instead, find |~v(0)| and dT~ dt (0) so that κ(0) = 1 |~v(0)| dT~ dt (0) .] (c) Find the center and...
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t +...
1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a. Carefully make 2 sketches of the plane curve over the interval . (5 pts) b. Compute the velocity and acceleration vectors, v(t) and a(t). (6 pts) c. On the 1st graph, sketch the position, velocity and acceleration vectors at t=-1. (5 pts) d. Compute the unit tangent and principal unit normal vectors, T and N at...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT