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?
Pls do fast and i will rate instantly for sure Solution must be in typed form
Express the given parametric equations of a line using bracket notation and also using i, j, k notation. (a) x = 6t, y = - 4 + 3t O (x, y) = (0, 4) +1 (6,3) ai + bj = -4j + t (6i + 3j) O (x, y) = (0, 4) + t (6, 3) ai + bj = 4j+ t (6i + 3j) O (x, y) = (0, 6) + (-4, 3) ai + bj = − 4j + t (6i + 3j) O(x, y) =(4,0) + t (3,6) ai + bj = −4i + t (3i + 6j) O (x, y) = (6,3)+1(0, - 4) ai + bj (6i + 3j) +t(-4j) (b)x= 4 + 6t,y=4+9t, z = 87t O (x, y, z) = (-4, 4, − 8) +1(-6, ai + bj + ck = 9,7) ( − 4i + 4j - 8 k) + t ( − 6i - 9j + 7k) O (x, y, z) = (4, ai + bj + ck = 4, 8) + t (6, 9, - 7) (4i − 4j + 8 k) + t (6i + 9j – 7k) O (x, y, z) = (6,9, −7) +1(4, - 4,8) ai + bj + ck = (6i + 9j − 7k) + t(4i - 4j + 8k) O (x, y, z) = (-6, 9, 7) + 1 - 4, 4, 8) ai+bj + ck = ( – 6i – 9j + 7k) + t( − 4i + 4j − 8k) O (x, y, z) = (4, 4, 8) + t (6,9,7) ai + bj + ck = (4i +4j + 8 k) + t (6i + 9j + 7k)
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. Triangle DEF Is reflected over the x-axis and then rotated 90° degrees counterclockwise about the origin. What is the x- coordinate of E"? What is the rule for reflecting over the х-аxis: (х, у) -> y Write your new coordinates here: What is the rule for rotating 90° counterclockwise: (x,y) - Use the coordinates from above, apply the rule, and write your new coordinates here: D
Express the given parametric equations of a line using bracket notation and also using i, j, k notation. (a) x = 6t, y = - 4 + 3t O (x, y) = (0, - 4) + t (6,3) ai + bj = −4j + t (6i + 3j) O(x, y) = (0, 4) + t (6, 3) ai + bj = 4j + t (6i + 3j) ○ (x, y) = (0, 6) + t ( − 4, 3) ai + bj - 4j + t (6i + 3j) - (x, y) = (-4, 0) + t (3, 6) ai + bj = − 4i + t (3i + 6j) (x, y) = (6, 3) + t(0, − 4) ai + bj = (6i + 3j) + t ( − 4j)
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)))