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…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.1: Parabolas

Problem 24E

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Find parametric equations for the tangent line to the helix with parametric equations x = 2 cos(t), y = 4 sin(t), and z = t at the point ( 0, 4, 4,7). Solution The vector equation of the helix is r(t) = (2 cos(t), 4 sin(t), t), so r'(t) = (0,4,7) is t (7²) = 2 , so by the equations x = Xo+at, y = Yo + bt, and z = Zo + ct, its parametric equations are the following. The parameter value corresponding to the point 0, 4, to the vector (x(t), y(t), z(t)) = = so the tangent vector there is r' I The tangent line is the line through (0,4, 1) ₁ paralle
Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u, cos (v) , sin (v)) (u, u (2 + cos (v), u (2 + sin (v))) (u, u + v, v) (cos (u) sin (v), 3 cos (u) sin (v), cos (v)) , COS (u, v³, v)
The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =
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Vector equation of the circle (x + 2)² + (y – 3)² = 16 is: (A) ř(t) = (B) r(t) = (C) 7(t) = (D) r(t) = (E) ř(t) =
3. What is the parametric equation for the line through the point (1,2, 3) parallel to the x- axis? (a) x = 1+ 2t, y = 0, z = 0 (c) x = 1+ 3t, y = 0, z = 0 (b) x = 1+ 5t, y = 0, z = 0 (d) a, b, & c
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Find parametric equations of the line that is perpendicular to both i = (1,0,0) and v = (1,1,1) that passes though the point P(1, -2, -1).
The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function F(t) = 4(26t – sin(26t))i + 4(1 – cos(26t))3 Find the velocity vector of the point. ü(t) = | 4(26 – 26 cos(26t))i + 4(26 sin( 26t ))j Find the acceleration vector of the point. ä(t) = | 2704 sin(26t )i + 2704 cos( 26t)j v| Find the speed of the point. s(t) = 2704 sin(26t)i+ 2704 cos( 26t)j x syntax error. Check your variables - you might be using an incorrect one.

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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)))