Solve the initial value problem for the following inhomogeneous heat equation ut − 1 4 uxx = e −t in − [infinity] < x < [infinity], t > 0, u(x, 0) = x 2 . Write your answer as a linear combination u = C1 f1(t) g1(x)+· · ·+Cn fn(t) gn(x) computing fj , gj . Do not compute the constants C1,...,n.

Fiona and her friends are playing a game by guessing where a coin will land when it is randomly dropped inside the square shown below. fiona guesses that the coin is likely to land in the blue area. which explains whether or not fiona is correct and why?

Y+ 2/y is it a polynomial in one variable or not? and if so, why?

Aprobability experiment is conducted in which the sample space of the experiment is s={7,8,9,10,11,12,13,14,15,16,17,18 }, event f={7,8,9,10,11,12}, and event g={11,12,13,14}. assume that each outcome is equally likely. list the outcomes in f or g. find p(f or g) by counting the number of outcomes in f or g. determine p(f or g) using the general addition rule.