You work at a canning factory that's producing cans for a new brand of soup. you need to decide what size the cans should be. the soup cans can have a radius of either 2 in, 2.5 in, 3 in, or 3.5 in. the cans need to hold a volume of exactly 90 in3. the company wants the cans to be no more than 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it can print more information on the side of the cans. to solve this problem, you will fill in this table with the surface area and volume of each cylinder: first, calculate the height each can must be, given the radius and volume. b. now calculate the lateral surface area for each possible can. c. based on the requirements for the can, which can should you make?

For problems 7–10, state a reasonable domain for the problem statement, find the inverse function f –1(x), and identify the independent and dependent quantities of the inverse. 7. gary is jogging. the total distance he has traveled, in miles, can be estimated using the function f(x) = 9x, where x is his jogging time in hours. 8. camryn sells computers. she earns commission for her computer sales plus a fixed wage for each day she works. her daily earnings, in dollars, can be estimated using the function f(x) = 0.15x + 50, where x represents her computer sales in dollars. 9. the distance a motorboat travels, in meters, can be estimated using the equation f(x) = 1.9x2, wherexisthetimeinseconds,for0≤x≤10. 10. a rock band is selling tickets to a concert at a theater. the band earns money for each ticket sold, but has to pay some of the earnings to the theater. the total money earned by the band can be estimated using the function f(x) = 7.5x – 300, where x is the number of tickets sold.