Use separation of variables to find, if possible, product solutions for the given partial differential equation. (Use the separation constant −λ ≠ 0. If not possible, enter IMPOSSIBLE.) k∂^2u/∂x^2 - u = ∂u/∂t, k>0

James wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would james need to keep the website for site a to be a better choice than site b? define a variable for the situation. write an inequality that represents the situation. solve the inequality to find out how many months he needs to keep the website for site a to be less expensive than site b. using words, describe how many months he needs to keep the website for site a to be less expensive than site b.

Anyone know? is appreciated! will mark brainliest if correct!

Someone this asap for a group of students attends a basketball game. * the group buys x hot dogs at the concession stand for $2 each. * the group buys y drinks at the concession stand for $3 each. the group buys 29 items at the concession stand for a total of $70. how many hot dogs did the group buy?