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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...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder -+ y1 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.
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
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
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...
ili Quot 12.3.14 Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral s - Sivce)| dr. Then find the length of the indicated portion of the curve. -jwel de r(t)- (5 + 3)i + (4 +31)j + (2-7)k, - 1sts The arc length parameter is s(t)=0 (Type an exact answer, using radicals as needed.)
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem
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 ? Question 10 1 pts Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at the point (4,2, 7).
15. (1 point) Let C be the intersection curve of the surfaces z = 3x + 5 and x2 + 2y2-1, oriented clockwise as seen from the origin. Let F(x, y, 2) (2z - 1)i +2xj+(-1)k. Compute F.dr (a) directly as a line integral AND (b) as a double integral by using Stokes' Theorem
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the parametric equation of the tangent line to C at (1,1.0) (3) Find the plane that carries the tangent line found above and the vector (4) Set up but not solve, a formula that will determine the length of C for 1StS2 Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane....
Find a parametrization of the circle of radius 4 in the xy-plane, centered at (−2,−4), oriented counterclockwise. The point (2,−4) should correspond to t=0. Use t as the parameter for all of your answers.