Related questions with answers

The following table gives the total world emissions of $\mathrm{CO}_{2}$ from fossil fuels, in billions of tons per year.

\begin{array}{c|c|c|c|c|c|c|} \hline {\text { Year }} & {1981} & {1986} & {1991} & {1996} & {2001} & {2006} & {2011} \\ \hline \mathrm{CO}_{2(\mathrm{bn}\text { tons per year) } } & {20.1} & {21.3} & {21.9} & {23.4} & {24.2} & {29.1} & {34.7} \\ \hline \end{array}

Use this data to estimate the total world $CO_2$ emissions between 1981 and 2011 using a right sum with n=3.

An insulation company is examining a new material for extruding into cavities. The experimental data is given below for the speed U of the upper plate, which is separated from a fixed lower plate by a 1-mm-thick sample of the material, when a given shear stress is applied. Determine the type of material. If a replacement material with a minimum yield stress of 250 Pa is needed, what viscosity will the material need to have the same behavior as the current material at a shear stress of 450 Pa?

\begin{matrix} \text{}{\tau(\mathrm{Pa})} & \text{50} & \text{100} & \text{150} & \text{163} & \text{171} & \text{170} & \text{202} & \text{246} & \text{349} & \text{444}\\ \text{U (m/s)} & \text{0} & \text{0} & \text{0} & \text{0.005} & \text{0.01} & \text{0.025} & \text{0.05} & \text{0.1} & \text{0.2} & \text{0.3}\\ \end{matrix}

For the following two-dimensional partial differential equations, find the dispersion relation: $(\mathrm{a})\ \frac{\partial^{2} u}{\partial t^{2}}=c^{2}\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}\right); (\mathrm{b})\ \frac{\partial^{2} u}{\partial t^{2}}=c_{1}^{2} \frac{\partial^{2} u}{\partial x^{2}}+c_{2}^{2} \frac{\partial^{2} u}{\partial y^{2}}.$