Show that an implicit solution of 2x sin2(y) dx − (x2 + 12) cos(y) dy = 0 is given by ln(x2 + 12) + csc(y) = C. Differentiating ln(x2 + 12) + csc(y) = C we get 2x x2 + 12 + dy dx = 0 or 2x sin2(y) dx + dy = 0. Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) y =

Which transformations could have occurred to map △abc to △a"b"c"? a rotation and a reflection a translation and a dilation a reflection and a dilation a dilation and a rotation

Bob’s bank charges him a $3.15 service fee every time he uses an out-of-network atm. if bob uses an out-of-network atm an average of three times every two weeks, how much will he pay in service fees over the course of a year? a. $327.60 b. $109.20 c. $491.40 d. $245.70 select the best answer from the choices provided a b c d

Graph red beads cost $1 an ounce and gold beads cost $3 an ounce. juanita wants to purchase a 12-ounce mixture of red and gold beads that she can sell for $2 an ounce. the solution of the system shows the number of beads needed for juanita to break even. x + y = 12, x + 3y = 24 how many ounces of red beads will juanita buy to break even? how many ounces of gold beads will she buy?