Howard is designing a chair swing ride. The swing ropes are 4 meters long, and in full swing they tilt in an angle
of 23º. Howard wants the chairs to be 3.5 meters above the ground in full swing.
How tall should the pole of the swing ride be?
Round your final answer to the nearest hundredth.

Find the solutions for a triangle with a =16, c =12, and b = 63º

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."

Which functions shave a maximum and are transformed to the left and down of the parent function ,check all that apply f(x) = x2? p(x) =14 (x+7)2 + 1