The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t2). (a) Find the speed of the particle at time t0 = 4π. (b) Is c'(t) ever orthogonal to c(t)? Yes, when t is a multiple of π. Yes, when t = 0. No (c) Find a parametrization for the tangent line to c(t) at t0 = 4π. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (d) Where will this line intersect the xy-plane?

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".

Avector of magnitude 2 cannot be added to a vector of magnitude 3 so that the magnitude of the resultant is a. zero b. 1 c. 3 d. 5 e. 7

Ne way in which elements differ from each other is the structure of the electron cloud in each element's atoms. in an electron cloud, an electron that is farther away from the nucleus has