hi tutor i need a handwritten solution of this basic calculus real life problems please include the illustrations and the detailed solution handwritten or clean typewritten subject: calculus

6. On a certain day, a scientist had 1 kg of a radioactive substance X at 1:00 pm. After six hours, only 27 g of the substance remained. How much substance X was there at 3:00 pm that same day?A cold drink is taken from a refrigerator and placed outside where the temper ature is 32"0. After 25 minutes outside its temperature is 14"C. and after 50 minutes outside its temperature is 200C. assuming the temperature of drink obeys Newtons Law of Heating, what 1was the initial temperature of the drink?I Two men can},F a 14v]? ft. ladder down a IDs/5- ft. wide corridor. They turn into a second corridor. perpendicular to the rst one. while keeping the ladder horizontal. Find the minimum possible width of the second corridor. Answer: feet. A horizontal tank of length 25 feet has parabolic cross-sections (vertex down) 8 feet across at the top and 4 feet deep. The work done in pumping out the tank from an outlet 2 feet above the top of the tank if it is filled with oil weighing 60 pounds per cubic foot is 11 00 foot-pounds.A conical tank is 20 ft. tall and the diameter of the tank at the top is 20 ft. It is filled with a liquid whose density is 12 1b. /ft.3. What is the work done in lifting the liquid to a trough 5 ft above the top of the tank? Answer: I ft-lbs.A falling stone is observed to be at a height of 171 feet. Two seconds later it is observed to be at a height of 75 feet. From what height was it dropped? (Use 32 ft./sec.' as the magnitude of the acceleration due to gravity.) Answer: ft