Solve the ODE: (3e3a sin y - 10y² sin(5x)) dx + (e³ cos y+ 4y cos(5x)) dy = 0 Entry format: Write your solution equation so that: (1) The equation is in implicit form. (2) The highest degree term containing only has a coefficient of 1. (3) Constants are combined and moved to the RHS of the equation.

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 72 students, requires 5 chaperones, and costs $1,400 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $120 to rent. Since there are 432 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 432 students. Since only 50 parents have volunteered to serve as chaperones, the officers must plan to use at most 50 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs? The officers should rent buses and The minimal transportation costs are $ vans to minimize the transportation costs.

Luke Thorndike, founder and current president of Thorndike Sports Equipment, had guided the business through 34 successful years and was now interested in bringing his favorite grandson Ted into the company. The elder Thorndike, possessed of a sharp but fading wit, begins the meeting with, “Great to see you, Ted. You always were a high-strung kid. Thought you might like to join our tennis racquet division.” Ted counters, “Not quite, but you’re getting warm, Luke.” The Thorndikes have always been a strange bunch. “Seriously, Ted, I’m getting a little up in years, the microcomputer I bought myself for Christ- mas is collecting dust, and I think you and your business degree could bring some new blood to the company. I’d like you to be my executive vice president. I’ve been running this outfit by the seat of my pants for a lot of years now, and the world just seems to be getting too big and too complicated these days. I’ve got index cards and file folders just about piled up to the ceiling…