What are (a) the x component, (b) the y component, and (c) the z component of r = a - b +c if a= 7.8 + 6.6 - 7.1 , b= -2.9 + 7.4 + 3.9 , and c = 7.6 + 8.8 + 2.2 . (d) Calculate the angle between r and the positive z axis. (e) What is the component of along the direction of b? (f) What is the magnitude of the component of a perpendicular to the direction of b but in the plane of a and b?

Which fact supports the conclusion that there will be fewer farm managers in the future? a) a farmer manager’s duties vary by the type of farm. b) farm technology is replacing some administrative jobs c) farm managers often need experience but not education. d) administrative duties include budgeting and training staff.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm

A6.0-kilogram cart initially traveling at 4.0 meters per second east accelerates uniformly at 0.50 meter per second squared east for 3.0 seconds. what is the speed of the cart at the end of this 3.0 second interval? (1) 1.5 m/s (3) 3.0 m/s (2) 5.5 m/s (4) 7.0 m/s