The smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1 is

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."

Find cot x if sin x cot x csc x = √2

In the diagram, bc¯¯¯¯¯∥de¯¯¯¯¯ . what is ce ? enter your answer in the box.