The linear density ρ in a rod 5 m long is 8/sqrt(x+4) kg/m, where x is measured in meters from one end of the rod. Find the average density ρave of the rod.

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the forumula: f'(t) : - 3f(t)(6 + f(t)) If there is 3 grams of solid at time t = 2 estimate the amount of solid 1 second later. grams

Find the center of mass of a unit hemisphere if the density at a point is proportional to the square of distance from the origin.