The "galilean cannon" is a stack of elastic balls that are dropped from a height onto a flat surface. when they rebound, the smallest ball at the top can bounce to incredible heights. imagine a stack of n balls with masses m, , 2m, 3m, … etc. where > 1. the balls are dropped from a height ℎ.

a. assume all the collisions between balls are elastic. derive an expression for the height that the smallest ball bounces to, using m, ℎ, or some subset thereof

b. now assume that the ball-ball collisions are inelastic; when 2 balls collide, their total kinetic energy decreases by some factor i. e. = , with < 1. find such that the topmost ball rises back to the initial height ℎ. assume the bottom ball’s collision with the ground is perfectly elastic.

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

Acar travels 40m in 8 seconds find the car speed

Write a polynomial function with the given zeros x= -1,0,2show your work