Makena, who works for Costco's corporate office, is helping to construct an open top box from a 14 by 30-inch piece of cardboard. To do this, Makena is going to cut out squares from the four corners so that the four sides can

be bent upwards. She is trying to create a rectangular box with the largest possible volume.

a.) Write the formula that you will be typing into Desmos (this should be the formula you are optimizing in terms ofone variable)

b.) What should be the dimension of the square cuts? remember your units!"

c.) What is the largest possible volume for the box? "remember your units!"

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Based on the figures as marked, /\rqs = —

Which shows the correct lengths of side c in both scales? scale 1: 45 m; scale 2: 60 m scale 1: 60 m; scale 2: 45 m scale 1: 36 m; scale 2: 27 m scale 1: 27 m; scale 2: 36 m mark this and return save and exit