Assume that children is an integer variable containing the number of children in a community and that families is an integer variable containing the number of families in the same community. write an expression whose value is the average number of children per family.

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?