A group of students were experimenting with building electromagnets in science class. To do this, the students wrapped a piece of insulated copper wire around an iron nail and then connected the two ends of
the wire to a battery, making the nail magnetic. The number of wraps of the wire around the nail affected the
number of metal paperclips that the electromagnet could pick up at one time. The results of the students’
experiment are shown in the data table below. Predict how many paperclips the electromagnet would have picked up if the students had wrapped the wire
around the nail only five times.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i. e., a subspace of r 3 ). explain your reasoning

Aperson gives a shopping cart an initial push along a horizontal floor to get it moving, and then lets go. the cart travels forward along the floor, gradually slowing as it moves. consider the horizontal force(s) on the cart while it is moving forward and slowing. which of the following statements is correct? (a) both a forward and a backward force are acting on the cart, but the forward force is larger. (b) only a forward force is acting which diminishes with time. (c) both a forward and a backward force are acting on the cart, but the backward force is larger. (d) only a backward force is acting, no forward force.

If the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 27 in. beyond its natural length?