(Solved): Directions: Use error propagation to calculate the uncertainty and percent uncertainty of the depe ...

Directions: Use error propagation to calculate the uncertainty and percent uncertainty of the dependent quantity in terms of the measured quantities shown (independent variables). Remember, given \( \mathrm{A}=\mathrm{A}(\mathrm{x}, \mathrm{y}, \mathrm{z}, \ldots) \) where the measured quantities have uncertainties \( \delta \mathrm{x}, \delta \mathrm{y}, \delta \mathrm{z}, \ldots \) then \[ \delta A=\sqrt{\left(\frac{\partial A}{\partial x}\right)^{2}(\delta x)^{2}+\left(\frac{\partial A}{\partial y}\right)^{2}(\delta y)^{2}+\left(\frac{\partial A}{\partial z}\right)^{2}(\delta z)^{2}+\ldots} \] 1. \( z=3 x-5 y \quad x \& y \) is measured quantities with uncertainty \( \delta x \) and \( \delta y \) 2. \( I=A / r^{2}, \quad r \) is a measured quantity with uncertainty \( \delta r, A \) is a constant. 3. \( \mathrm{N}=0.5 \rho \pi \mathrm{R}^{4} \mathrm{~h}, \quad \mathrm{R} \& \mathrm{~h} \) are measured quantities with uncertainty \( \delta \mathrm{R} \) and \( \delta \mathrm{h} \), and \( \rho \) and \( \pi \) are constants. 4. \( A=2 L W+2 W H+2 H ; L, W, \& H \) are measured quantities with uncertainty \( \delta L, \delta W \), 5. \( \rho=\frac{M_{1}^{2}}{\left(M_{2}-M_{1}\right)} d^{2} \quad M_{1}, M_{2}, \& d \) are measured quantities with uncertainty \( \delta \mathrm{M}_{1}, \delta \mathrm{M}_{2}, \delta \mathrm{d} \)