Match each parametrization with the corresponding surface.(i)(u, cos (u), sin (v))Z(iv)(u, v³, v)(ii)Answer Bank(u, u + v, v)(cos (u) sin (v), 3 cos (u) sin (u), cos (v))(v)(iii)(u, u (2+ cos (v)), u (2+ sin (u)))

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Answered: Match each parametrization with the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = (v1, v2, V3) has parametric equations x = xo + tV1, y = Yo + tv2, z = 20 + tv3, -0
Example Video Example) Find the length of the arc of the circular helix with vector equation r(t) = 6 cos(t) i + 6 sin(t) j + tk from the point (6, 0, 0) to the point (6, 0, 2π). Solution Since r'(t) = Ir' (t) = √(-6 sin(t))² + (6 cos(t))² + 1² 2 L = L = The arc from (6, 0, 0) to (6, 0, 27) is described by the parametric interval 0 ≤ t ≤ 2π, and so from the formula -SD 1² Ja we have the following. -2π 1.²5 I \r'(t)\ dt, |r'(t)\ dt = Need Help? we have 2π 16² (1 JO Read It = ]) at dt
Let R(r, theta) = (r*cos(theta))er (polar coordinates) How do I find v (velocity) for r = 2, theta = pi/4, dtheta/dt = 2, and dr/dt = 3?
4) For the following vector functions, identify the shape of graph they would represent: a. r(t) = (2+ 3t, 5, -2-t) b. r(t) = (2, cos(3t), sin(3t)) c. r(t) = (t,5, t²)
3) (a) Eliminate the parameter of the parametric equation x = 4 sin and y =1+ 2 cos (b) Write parametric equations describing the motion of a particle moving under uniform linear motion from point A(-3, 2) to point B(9, -6) in 4 sec.

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Match each parametrization with the corresponding surface. (i) (u, cos (v), sin (v)) (iv) (u, v³, v) (ii) Answer Bank (u, u + v, v) (cos (u) sin (v), 3 cos (u) sin (v), cos (v)) € (iii) (u, u (2+ cos (v)), u (2+ sin (u)))