Water is flowing in a channel at a rate of Q = 30 m/s. The critical depth x for such a channel must satisfy the equation 0 = 1-B Q2 gA3 = where g=9.81 m/s2, A = the cross-sectional area (m), and B = the width of the channel at the surface (m). For this case, the width and the cross-sectional area can be related to depth x by B = 3 + x x2 A = 3x + 2 Solve for the critical depth using (a) Bisection with the initial guesses of x= 1.0 and Xu = 3, (b) False position with the initial guesses of x= 1.0 and Xu = 3, and (c) Newton-Raphson method with the initial guess of xi= 1.0. In all these three cases, iterate until the approximate error falls below 10%. Discuss your results