Cones A and B both have volume 487 cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A.

Aline parallel to a triangle's side splits ab into lengths of x - 5 and x + 2. the other side, ac, is split into lengths of x and x + 12. what is the length of ac? a) 12 b) 24 c) 36 d)

Beth took out a $20,000 loan for college she is borrowing money from two banks. bank a charges an interest rate of 8.5% bank b charges and interest rate of 10.5% after one year alice owes $1860 in interest how much money did she borrow from bank a

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."