Imagine you build a house and for heating systems you have a choice between solar and air heated by natural gas. the solar heating system costs $30,000 to install, with annual operating of cost of $150 per year afterwards. the gas heating system costs $6,250 to install, with an expected annual operating cost of $1100 per year afterwards. how could you use a system of equations to solve for the time when both systems would be the same cost? how many years would that be and what is the common cost? which system would you want?

(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.