homework4: Problem 2 Previous Problem Problem List Next Problem (1 point) Suppose r(t) = costi + sint j + 4t k represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? no If the particle is moving downward, when is this? When t is in |none (Enter none if it is never moving downward; otherwise, enter an interval or comma-separated list of intervals, e.g., (0,3], [4,5].) (b) When does the particle reach a point 12 units above the ground? When t = 3 (c) What is the velocity of the particle when it is 12 units above the ground? U = (d) When it is 12 units above the ground, the particle leaves the helix and moves along the tangent. Find parametric equations for this tangent line (pick t so that it is continuous through the time when the particle leaves the helix). x(1) = -sin 3 y(1) = cos 3 + t z(t) = 4+ 4t Note: You can earn partial credit on this