A particle moves along the x-axis so that at time t≥0 its position is given by x(t) = t³-42t²+81t. Determine all intervals when the speed of the particle is increasing.

Create a real-life situation and create a system and show how it might be modeled algebraically with a system of equations (or inequalities) show all work include a few sentences explaining the situation, your variables of choice and what each represents, and how you would set it up and solve it algebraically. !

What is the square root of 45? (step by step working plz)

()1. how do you find range? 2.the following set of data is to be organized into a histogram. if there are to be five intervals on the graph, what should the length of each interval be? 30, 34, 23, 21, 27, 25, 29, 29, 25, 23, 32, 31