The length l of a rectangle is decreasing at a rate of 1 cm/sec, while its width w is increasing at the rate of 3 cm/sec. At what rate is the length of the diagonal changing at the instant when l=8 and w=6

If y varies directly as x2 and y=6 when x=6, find the constant of variation.

Amanda went into the grocery business starting with five stores. after one year, she opened two more stores. after two years, she opened two more stores than the previous year. if amanda expands her grocery business following the same pattern, which of the following graphs represents the number of stores she will own over time?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.