Consider the problem u_tt + u_t = u_xx + u, u(0,t) = u(1,t) = 0, u(x,0) = 3 sin(phix) + sin (2phix), and u_t(x,0) = -sin(2phix) + 7 sin(11phix). perform separation of variables on the pde and determine the resulting odes with boundary conditions. also determine what the eigenvalues are. no need to find the solution to the odes or the pde after finding the eigenvalues.

Which graph shows a function with a range of all real numbers greater than or equal to -1

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

If f(x) = 4x - 3 and g(x) = x + 4, find (f - g) (x)