Solve the non-homogeneous diusion equation ut = 2uxx + 4x ux (0, t) = 0 u (1, t) = 1 u (x, 0) = x 2 (a) Separate the problem into boundary and interior parts. (b) Find all the eigenfunctions, and transform the interior PDE. (c) Solve the resulting ODEs and invert to write the solution as a series. (d) Plot a 5-term series solution for times t = {0.0, 0.1, 0.4, 0.9, 1.6, 2.5} . For a bonus point, create and upload a 51-frame movie spanning the time domain t ∈ [0, 2.5].

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.

Tatiana reads 40 pages of her book every night for x number of nights. write an expression that shows the number of pages she has read

Change negative exponents to positive, then solve