*3. Show that a diffeomorphism φ: S S is an isometry if and only if the arc length of any paramet...
Prove a) Let a : 1R be a curve parametrized by arc length. If the torsion of a is 0, then the trace of a is contained in a plane of R. b) Let a : 1 R3 be a curve parametrized by are length such that Trace(a) not contain 0. If there is to € I such that aſto) has the maximum distance to the origin, show that k(a)(to) ||a(to) || 1
(a) A diffeomorphism : S1 S2 is area-preserving if the area of any region Rc S is equal to the area of 4(R). Show that if is area-preserving and conformal, then is a local isometry (b) Show that the Mercator's projection (defined in do Carmo, chapter 4-2, exercise 16) is not area ea-preserving (c) Lambert's cylindrical projection projects L = S2 \ {N,S}, the unit sphere minus the north pole N and the south pole S, into a the unit...
5. Let ф: S1 S2 be a diffeomorphism. a. Show that S is orientable if and only if S2 is orientable (thus, orientability is preserved by diffeomorphisms). b. Let S, and S2 be orientable and oriented. Prove that the diffeomorphism ф induces an orientation in S. Use the antipodal map of the sphere (Exercise 1, Sec. 2-3) to show that this orientation may be distinct (cf. Exercise 4) from the initial one (thus, orientation itself may not be preserved by...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016)
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
2. (20 marks) A rose by any other name... () (5 arks) The equation for arc length we have seen in lectures is: dr Convert this to an arc length of a curve that is given in polar coordinates (b) (5 marks) Investigate 'rose curves' and summarise what they are. (c) (5 marks) Determine the integral that should be used to determine the arc length of a rose curve and explain why a solution will not be possible (d) (5...
3 of 14 7x Instructor-created question Find the length s of the arc of a circle of radius 14 meters subtended by the central angle 270°. Find the exact length as a fractional multiple of and the approximate length to three decimal places. Exact arc lengthmeters (Enter a simplified fraction) s (arc length) = 65.973 meters (Round to three decimal places.)
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(a) Show that any set S in Q" is Z-linearly independent if and only if it is Q-linearly independent. (b) Let A be a non-trivial subgroup of Zn and φ : Zn → Zn Cz Q be the Z-module homomorphism given by a H> a&1. Using and Part (a), show that A is isomorphic to Zk where k .
(a) Show that any set S in Q" is Z-linearly independent if and only if it is Q-linearly independent. (b)...
Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s | |vIdT. Then find the length of 0 the indicated portion of the curve. The arc length parameter is s(t) (Type an exact answer, using radicals as needed.) Find T, N, and k for the plane curve r(t) (2t+9) i+ (5-t2) j T(t)= (Type exact answers, using radicals as needed.) (Type exact answers, using radicals as needed.)
Find the arc length parameter...
Find the exact length of the curve given by
Area and Arc Length: Problem 3 Previous Problem List Next (1 point) (1 point) Find the exact length of the curve given by I=t,y= - (0<=<5). Length = Preview My Answers Submit Answers You have attempted this problem 4 times. Your overall recorded score is 0%
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1. Find the arc length of the curve given by: r(t) = sinh t i – (t+2) j + exp(-) k in (0, 2).