Below you are six Cartesian equations and four polar equations. For each polar equation, identify the corresponding Cartesian equation. a. (x - 1)^2 + (y - 1)^2 = 2
b. y = 1
c. x^2 + y^2 =4
d. x = 1
e. x^2 = y x^2+(y - 3/2)^2 = 9/4
1. r cos(theta) = 1
2. r = 2 sin(theta) + 2 cos(theta)
3. r = 3sin(theta)
4. r = csc(theta)

The floor plan of a room has a scale of 2.5 in.: 35 ft. in the drawing, the length of the room is 8 in. and the width of the room is 6 in. what is the perimeter of the actual room?

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."

Need an artist designed a badge for a school club. figure abcd on the coordinate grid below shows the shape of the badge: the badge is enlarged and plotted on the coordinate grid as figure jklm with point j located at (2, -2) and point m is located at (5, 4). which of these could be the coordinates for point l? a. (2, 4) b. (8, 4) c. (5, 1) d. (5, 7)