Which compound forms the higher concentration of hydrate at equilibrium, PhCOCHO or $\mathrm{phCH}_{2} \mathrm{CHO}$? Explain your reasoning

Determine whether the following series converge absolutely, converge conditionally, or diverge. $\sum_{k=1}^{\infty} \frac{(-2)^{k+1}}{k^{2}}$

Use a convergence test of your choice to determine whether the following series converge. $\sum_{j=0}^{\infty} \frac{2 \cdot 4^{j}}{(2 j+1) !}$

Develop expressions for the mole fractions of reacting species as functions of the reaction coordinate for: (a) A system initially containing 2 mol $NH_3$ and 5 mol $O_2$ and undergoing the reaction: $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$ (b) A system initially containing 3 mol $H_2S$ and 5 mol $O_2$ and undergoing the reaction: $2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{SO}_{2}(g)$ (c) A system initially containing 3 mol $NO_2,$ 4 mol $NH_3,$ and 1 mol $N_2$ and undergoing the reaction: $6 \mathrm{NO}_{2}(g)+8 \mathrm{NH}_{3}(g) \rightarrow 7 \mathrm{N}_{2}(g)+12 \mathrm{H}_{2} \mathrm{O}(g)$

Model the situation with a quadratic equation. Then solve. Round answers to the nearest tenth. Find the radius of a circle with an area of $38 \mathrm{ft}^{2}$.

Circle the common root words in each set of three words. Write the meaning of the root word in the blank. Use a dictionary if necessary. sonorous, consonance, dissonant ____

Write C in the blank if the sentence uses commas correctly. _____ Their works are often impermanent, existing for only a few days or a few weeks.

Find (a) the compound amount and (b) the compound interest for the given investment and annual rate. $700 for 15 years at 7% compounded semiannually

Determine whether the following series converge. Justify your answers. $\sum_{k=3}^{\infty} \frac{5}{2+\ln k}$

Determine whether the following series converge. Justify your answers. $\sum_{k=1}^{\infty} \frac{4}{(k+3)^{3}}$

Sketch the graph of the rational function. To aid in sketching the graphs, check for intercepts, vertical asymptotes, and slant asymptotes. $f(x)=\frac{x^{3}}{x^{2}+4}$

Identify a convergence test for each of the following series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test. $\sum_{k=3}^{\infty} \frac{2}{k^{2}-k-2}$

Write the plural form of each word. rodeo

In Bose–Einstein condensation, the ground state becomes macroscopically occupied. What about the first excited state, which might be only a small energy above the ground state; is it also macroscopically occupied?