Many years ago, the towns of Franklin and Chester agreed to begin posting their populations on signs just outside of their towns. They also agreed to update their signs once per year at the beginning of the year. During year 1ranklin's sign read " Franklin: Population of 20,000\text{Franklin: Population of } 20{,}000 Franklin: Population of 20,000 start text, F, r, a, n, k, l, i, n, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 20, comma, 000 ", while Chester's sign read " Chester: Population of 25,000\text{Chester: Population of } 25{,}000 Chester: Population of 25,000 start text, C, h, e, s, t, e, r, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, ". Each year, the populations grew ". Each year, the populations grew. Specifically, Franklin's population grew by each year, and Chester's population grew by people each year. What is the first year in which Franklin's sign shows a larger number than Chester's sign?

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.