Given the differential equation y' + y : 3cos(4t l D.785398)u[t). Remember to use obi) in Webworlt answers when the solution is for t 23 0. For differential equations, angles are given in radians. a. Find the complementary solution, ya {it}, with constants denoted Cl, (32, yea) = ' meet-6t} ' help[formulas} b. Find the particular solution, yE). yp) : ' 1.591cosi4t} ' help(formulas} c. Find the total solution, y} forthe initial condition y(0) = 1. y(t} = l ' help (formulas) This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, RUS= {(x, y) E A x B | (x, y) E R or (x, y) = S) RnS = {(x, y) E A x B | (x, y) = R and (x, y) = S). Let A = {-4, 4, 7, 9) and B = {4, 7), and define relations R and S from A to B as follows. For every (x, y) E A x B, x Ry = |x| = ly| and xSy = x - y is even. Which ordered pairs are in A x B, R, S, R US, and R n S? (Use set-roster notation to enter your answers. ) A xB = R = S = RUS= ROS =IQ scores are normally distributed in a population with a mean of 100 and a standard deviation of 15. Two persons are selected from the population, what is the probability that at least one ofthem has an IQ score between 90 and 105? Calculate the heat release rate required for flashover using the Babrauskas Method in a compartment that is 6 meters wide, 5 meters long, and 3 meters tall, and has a single door that is 1 meters tall and 1.2 meters wide. The compartment is constructed of 12 inch gypsum plaster. (assume t>tp) Danielle received an invoice for $6,000 that had payment terms of 3,00 n/45. He made a partial payment of $2,400 during the discount period. a. Calculate the amount credited b. Calculate the balance on the invoice after the partial payment was made. Round all the answers to the nearest cent please get it right since this work will be rated. In terms of paying less in interest, which is more economical for a $150,000 mortgage: A 30-year fixed rate at 7% or a 20-year fixed- rate at 6.5%? How much is saved in interest