Show that u(x, t)=cos(a*pi*x)e^-a^2*pi^2*t is a solution of the heat equation with k=1, on any interval [0,l].

Apple pie is removed from 350 degree oven. temperature of the pie t minutes after being removed id given by the function t(t)=72+268e-0.068t

(05.03 mc) part a: explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) part b: make tables to find the solution to 4x = 2x−2. take the integer values of x between −3 and 3. (4 points) part c: how can you solve the equation 4x = 2x−2 graphically? (2 points)

Eden has a part time job. she is paid ? 7.20 an hour the week she worked 18 and a half hours how much is she paid