Sharyn needs 3.5 yards of fabric to make a dress for herself and 2.25 yards of the same fabric to make a matching dress for her daughter. if she buys 6.5 yards of fabric, how much will she have left over?

Given (1+cosx)/(sinx) + (sinx)/(1+cosx) =4, find a numerical value of one trigonometric function of x. a. tanx=2 b. sinx=2 c. tanx=1/2 d. sinx=1/2

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."

Thee blue triangle has rotated from quadrant i to quadrant iii about the origin. describe the effects of the rotation on the coordinates of the blue triangle.