Consider crho ∂u ∂t = ∂ ∂x k0 ∂u ∂x ! + αu, where c, rho, k0 and α are functions of x, subject to u(0, t) = 0, u(l, t) = 0, u(x,0) = f (x). assume that appropriate eigenfunctions are known according to the results included in the box on p.157. (a) show that the eigenvalues are positive if α < 0. (b) solve the initial-boundary value problem. (c) discuss lim t→[infinity] u(x, t).

With this question substitute t=3 and t=5 to determine if the two expressions are equivalent. 4(t + 3) 4t+12 which statements are true? check all that apply. a. the value of both expressions when t =5 is 32. b. the two expressions are not equivalent. c. the value of both expressions when t=3 is 15. d. the value of both expressions when t=5 is 23. e. the two expressions are equivalent. f. the value of both expressions when t=3 is 24.

Solve the following system of equations express your answer as an ordered pair in the format (a, b) with no spaces between the numbers of symbols 5x+2y=22

If f(x)=1/x and g(x)=x+4 which of the following is the graph