MAE 300 SP 2023 HW# 5 (40 points) Due: 8AM Monday 3/6/2023 Review the lecture note #5 and # 6 and perform uncertainty analysis with the use of partial derivatives for the following problems. Show your work to receive full credit. 1. The maximum shear stress S of a rectangular beam is defined as S = F bh3 4 (h y4\ b Where S is the shear force, b is the width of the section, h is the length of the beam and y is the distance from the neutral axis. Find the uncertainty equation for S assuming b, h, F, and y are variables. (20 pts) 2. Find the uncertainty equation for the following function f. Assuming x, y, and z are variables. xz4 f(x, y, z) = x (4-3/27) y (20 pts) Uncertainty equation: R = R(x1, x2,..., x,) X, OR X2 R UR U + -U = X X2 R Ox R ax2 +...+ x n R R Oxn -U X Xn