The Latin root-vis-means "see." The root appears in the word improvised, which literally means "not seen before." It also appears in these words and phrases:

$$\begin{array}{ll}{\text { visitor }} & {\text { revise }} \\ {\text { supervisor }} & {\text { visual aid }} \\ {\text { invisible }} & {\text { envision }}\end{array}$$

Identify the word or phrase above that matches each clue. Not able to be seen

The degree of dissociation, $\alpha,$ of $\mathrm{CO}_{3}(\mathrm{g})$ into CO(g) and $\mathrm{O}_{2}(\mathrm{g})$ at high temperatures and 1 bar total pressure was found to vary with temperature as follows:

$$\begin{matrix} \text{$T / K$} & \text{1395} & \text{1443} & \text{1498}\\ \text{$\alpha / 10^{-4}$} & \text{1.44} & \text{2.5} & \text{4.71}\\ \end{matrix}$$

Assume $\Delta_{r} H^{0}$ to be constant over this temperature range, and calculate K, $\Delta_{r} G^{0}, \Delta_{r} H^{0},$ and $\Delta_{r} S^{0}$ at 1443 K. Make any justifiable approximations.

Evaluate each expression for the given values of the variable.

$$\frac { y ( y - 3 ) } { y - 2 }$$

y=4

Explain whether the given equation defines an exponential function. Give reasons for your answers. Write the base for each exponential function. $y = x ^ { x }$

Find an SVD of each matrix.

$$\left[ \begin{array}{ll}{7} & {1} \\ {5} & {5} \\ {0} & {0}\end{array}\right]$$

Find the perimeter of a triangle with vertices located at (2, 1), (2, -5), (-6, -5).

In a certain state, it is found that the distribution of income for lawyers is given by the Lorenz curve $y=L_{1}(x),$ where $L_{1}(x)=\frac{4}{5} x^{2}+\frac{1}{5} x$ while that of surgeons is given by $y=L_{2}(x),$ where $L_{2}(x)=\frac{5}{8} x^{4}+\frac{3}{8} x.$ Compute the Gini index for each Lorenz curve. Which profession has the more equitable income distribution?

Prove that a conjugate of a glide reflection in M is a glide reflection, and that the glide vectors have the same length.

Rank the following compounds in order of increasing strength of intermolecular forces:

$$\begin{array} { l } { \text { a. } \mathrm { CH } _ { 3 } \mathrm { NH } _ { 2 } , \mathrm { CH } _ { 3 } \mathrm { CH } _ { 3 } , \mathrm { CH } _ { 3 } \mathrm { Cl } } \\ { \mathrm { b } . \mathrm { CH } _ { 3 } \mathrm { Br } , \mathrm { CH } _ { 3 } \mathrm { I } , \mathrm { CH } _ { 3 } \mathrm { Cl } } \\ \mathrm { c } . \left( \mathrm { CH } _ { 3 } \right) _ { 2 } \mathrm { C } = \mathrm { C } \left( \mathrm { CH } _ { 3 } \right) _ { 2 },\left( \mathrm { CH } _ { 3 } \right) _ { 2 } \mathrm { CHCOOH } , \left( \mathrm { CH } _ { 3 } \right) _ { 2 } \mathrm { CHCOCH } _ { 3 } \\ \mathrm { d } . \mathrm { NaCl } , \mathrm { CH } _ { 3 } \mathrm { OH } , \mathrm { CH } _ { 3 } \mathrm { Cl } \end{array}$$

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all real-valued functions f defined everywhere on the real line and such that f(1) = 0.

Find each of the following limits: a) $\lim _ { z \rightarrow 0 } e ^ { z }$ b) $\lim _ { z \rightarrow 2 \pi i } \left( e ^ { z } - e ^ { - z } \right)$ c) $\lim _ { z \rightarrow \pi i / 2 } ( z + 1 ) e ^ { z }$ d) $\lim _ { z \rightarrow - \pi i } \exp \left( \frac { z ^ { 2 } + \pi ^ { 2 } } { z + \pi i } \right)$

Sketch the region bounded between the given curves and then find the area of the region.

$$y=\sin x, y=\sin 2 x, x=0, x=\pi$$

Draw a voltage-amplifier model. Is the gain parameter measured under open-circuit or short-circuit conditions? Repeat for a current amplifier model, a transresistance-amplifier model, and a transconductance-amplifier model.

What effect would an increase in the cost of productive resources have on the aggregate supply curve and on the equilibrium prices of products?