7. [-12 Points] DETAILS ROGACALCET3 11.1.033. Find parametric equations for the segment joining the given points....
Find parametric equations for the segment joining the given points. (1, 3) and (3,6) c(t) = { 1 +31, 2+36 ), ostsi
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
7. [-16 Points) DETAILS SCALCCC4 1.7.031. Find parametric equations for the path of a particle that moves around the given circle in the manner described. x2 + (y - 1)2 = 16 (a) Once around clockwise, starting at (4,1). X(t) = (t) = Osts 2017 (b) Four times around counterclockwise, starting at (4,1). x(t) = 4cos(t) (t) = osts (c) Halfway around counterclockwise, starting at (0,5). x(t) = y(t) = osts Need Help? Read it Watch Talk to Tutor
(a) Give a set of parametric equations (with domain) for the line segment from (4, -1) to (5,6). (b) Give a set of parametric equations (with domain) for the ellipse centered at (0,0) passing through the points (4,0), (-4,0), (0,3), and (0, -3), traversed once counter-clockwise. (c) Find the (x, y) coordinates of the points where the curve, defined parametrically by I= 2 cost y = sin 2t 0<t<T, has a horizontal tangent.
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
Find a parameterization for the line segment joining points (0,2) and (4,0) using the angle o in the figure to the right as the parameter. 2 (x,y) . Find parametric equations for the particle's motion along the line segment joining points (0,2) and (4,0), not including these points. X= y =
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (5+?) 1+ (2t - 1)]+(31') k, t=to = 3 What is the standard parameterization for the tangent line? X = y = ZE (Type expressions using t as the variable.)
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2. Problem 3 (12 points) The curve with parametric equations...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...