Suppose s(t) is the arc-length parametrization of a space-turd flying through space. What is the arc-length...
Question 9 1 pts Suppose s(t) is the arc-length parametrization of a space-turd flying through space. What is the arc-length of the space-turd's path between time t = 1 and t = 70 ?
asap Inue False Question 9 1 pts Suppose s(t) is the arc-length parametrization of a space turd flying through space. What is the arc-length of the space-turd's path between timet - 1 and t = 70?
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...
You need to find vector r(t) first. 1. Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder a21 and the plane z2. Use s as the arc-length parameter wih s 0 corresponds to the point (1,0,-1). Specify the limits for
eparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s. r(t) = cos 7ti +2j+et sin 7tk (t(s)) = (2+1)0001( a + 1)) +25+(vs + 1}sin(in( tz +1]] x
1) For this problem use the following space curve: F(t) =< t, 3 sin(t), 3 cos(t) > a) Determine the unit tangent vector: T. b) Determine the unit normal vector: Ñ. c) Determine the curvature of this space curve at the point: (0,0,3). d) Determine the arc length of the curve between t = 0 and t = 1.
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
The path integral of a function f(x, y) along a path e in the xy-plane with respect to a parameter r is given by 2. fex,y)ds= f(x),ye) /x(mF +y(t" dr , where a sr sb. (a) Show that the path integral of f(x, y) along a path c(0) in polar coordinates where r=r(0), α<θ<β, is Sf(r cos 0,rsin e) oN+( de. (b) Use this formula to compute the arc length of the path r 1+cos0, 0<0 27 The path integral...
The Implicit Function Theorem and the Marginal Rate of Substitution (4 Points) 3 An important result from multivariable calculus is the implicit function theorem which states that given a function f (x,y), the derivative of y with respect to a is given by where of/bx denotes the partial derivative of f with respect to a and af/ay denotes the partial derivative of f with respect to y. Simply stated, a partial derivative of a multivariable function is the derivative of...
what is the answer for number 4 1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...