1. You are the manager of a cemetery. Your client wants a new tombstone for an ancestor who fought in World War II. They have ordered 36 cubic feet of cement. The tombstone must be exactly 1 foot thick and must have the shortest perimeter possible. What should the dimensions of the tombstone be?
2. Another client wants to set up a booth in your cemetery so that he can sell BBQ. He gives you 48 feet of fencing and asks you to use the fencing to mark off the largest possible rectangular plot of land that he can use for his booth. One of the sides is the existing fence that marks the territory of your cemetery, so you only need to use the fencing to erect three more sides. What is the largest possible area you can carve out?
3. A team of archaeologists has stumbled upon a grave and they wish to determine its depth. If they fold a rope over itself halfway and align it directly with the grave's side wall, the length of rope outside the grave is 4.5 feet unfolded. If they fold the rope into four, the grave is 4.5 feet deeper than the length of the folded rope. How long is the rope, and how deep is the grave?
4. It takes 20 days for the dead body of a cow to completely decompose. Every day, the amount of the cow's body mass that has decomposed is twice as much as that amount of the previous day. After how many days will the cow be 1/4 decomposed?
5. You're a tattoo artist. Your client wants a tattoo with ink made from the ashes of his late wife, who worked long hours as a nurse during the pandemic and got infected after the hospital was unable to secure a vaccine for her. You begin with 75 mL of a solution that is 20% ashes and the rest water, only to realize it's too thick. In order to reduce the ash concentration to 15%, how much water should you add?