The sum of the cubic powers of three rational numbers is -1009. The ratio between the first number and the second number is 2/3, and the ratio between the first number and the third number is 4/9. Find those numbers

In the diagram, the ratio of ab to ae is (1/2) . what is the ratio of the length of to the length of ?

In the 30-60-90 triangle below side s has a length of and side r has a length

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."