Consider a rectangle with dimensions x and y in cm. if x is growing at a rate of 2 cm/s and y is growing at a rate of 3 cm/s, find the rate at which the length of the diagonal is changing when x= 5 cm and y= 8 cm.

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.