Passwords for a certain computer system are strings of uppercase letters. a valid password must contain an even number of x’s. determine a recurrence relation for the number of valid passwords of length n. note: 0 is an even number, so abbc is a valid password. this counting problem is pretty tricky. here’s a good way to think about it: to make a good password of length n you can either (a) add any non-x to the end of a good password of length n − 1, or (b) add an x to the end of a bad password of length n − 1. for (b) you can use the good = total-bad trick to count the number of bad passwords of length n−1.

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α. part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part b suppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i. e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part c now try a numerical problem. what is the direction of the vector w = < -1, 6 > ?