Consider the equation utt = c 2uxx for 0 < x < l, with the boundary conditions ux(0, t) = 0, u(l, t) = 0. (a) Find all eigenfunctions. (The answer is cos[(n + 1 2 )πx/l], which n?) (b) Write the series expansion for a solution u(x, t) in terms of the initial data and (·, ·)L2 .

Find the perimeter of the figure shown above. a. 18 yds c. 20 yds b. 10 yds d. 24 yds select the best answer from the choices provided

Solve each equation using the quadratic formula. find the exact solutions. 6n^2 + 4n - 11

Adecibel is a logarithmic unit that can be used to measure the intensity of a sound. the function y = 10logx gives the intensity of a sound in decibels, where x is the ratio of the intensity of the sound to a reference intensity. the reference intensity is generally set at the threshold of hearing. use the graphing utility to graph the decibel function.a whisper has a sound intensity of 30 decibels. use your graph to you complete the following statement. the sound intensity of a whisper is times the reference intensity.