Suppose that a plate is immersed vertically in a fluid with density p and the width of the plate is w(x) at a depth of x meters beneath the surface of the fluid. if the top of the plate is at depth a and the bottom is at depth b, show that the hydrostatic force on one side of the plate

Describe the symmetry of the figure. identify lines of symmetry, if any. find the angle and the order of any rotational symmetry.

Which fraction below is equivalent to 10/12?

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."