You are performing an experiment using ${ }^3 \mathrm{H}$ (halflife $=4.5 \times 10^3$ days) labeled phenylalanine in which the five aromatic hydrogens are labeled. To perform the experiment, the initial activity cannot be lower than $10 \%$ of the initial activity when the sample was received. How long after receiving the sample can you wait before performing the experiment?

In a parallel reaction in which two products can be formed from the same reactant, what determines the extent to which one product will be formed over another?

Consider the schematic reaction A $\stackrel{k}{\rightarrow}$ P. a. If the reaction is one-half order with respect to A, what is the integrated rate law expression for this reaction? b. What plot would you construct to determine the rate constant $k$ for the reaction? c. What would be the half-life for this reaction? Will it depend on initial concentration of the reactant?

What is the steady-state approximation, and when is this approximation employed?

What is meant by the rate-determining step in a sequential reaction?

You are given the following data for the decomposition of acetaldehyde:

$$\begin{array}{cll}\text { Initial Concentration (M) } & 9.72 \times 10^{-3} & 4.56 \times 10^{-3} \\ \text { Half-Life (s) } & 328 & 685\end{array}$$

Determine the order of the reaction and the rate constant for the reaction.

In a sequential reaction, what is an intermediate?

Express the rate of reaction with respect to each species in the following reactions: a. $2 \mathrm{NO}(g)+\mathrm{O}_2(g) \rightarrow \mathrm{N}_2 \mathrm{O}_4(g)$ b. $\mathrm{H}_2(g)+\mathrm{I}_2(g) \rightarrow 2 \mathrm{HI}(g)$ c. $\mathrm{ClO}(g)+\mathrm{BrO}(g) \rightarrow \mathrm{ClO}_2(g)+\mathrm{Br}(g)$

Why is the stoichiometry of a reaction generally not sufficient to determine reaction order?

Express the rate of reaction with respect to each species in the following reactions: a. $2 \mathrm{NO}(g)+\mathrm{O}_2(g) \rightarrow \mathrm{N}_2 \mathrm{O}_4(g)$ b. $\mathrm{H}_2(g)+\mathrm{I}_2(g) \rightarrow 2 \mathrm{HI}(g)$ c. $\mathrm{ClO}(g)+\mathrm{BrO}(g) \rightarrow \mathrm{ClO}_2(g)+\mathrm{Br}(g)$

Without performing the actual calculations, determine to how many significant figures the results of the following calculations should be reported. d. $(6.521)(5.338+2.11)$

Computer graphics frequently use reflections. Reflections can speed up the generation of a picture or create a figure that appears perfectly symmetrical.

(a) For the given $f(x)$, constant $k$, and viewing rectangle, graph $x=k, y=f(x)$, and $y=f(2 k-x)$.

(b) Generalize how the graph of $y=f(2 k-x)$ compares to the graph of $y=f(x)$.

$f(x)=x^4-2 x^2+1, k=-6,[-15,3,1]$ by $[-3,9,1]$

Natsu Company's annual accounting period ends on October 31, 2017. The following information concerns the adjusting entries that need to be recorded as of that date. (Entries can draw from the following partial chart of accounts: Cash; Rent Receivable; Office Supplies; Prepaid Insurance; Building: Accumulated Depreciation Building; Salaries Payable; Unearned Rent; Rent Earned; Salaries Expense; Office Supplies Expense; Insurance Expense; Depreciation Expense-Building.)

Required
1. Use the information to prepare adjusting entries as of October 31, 2017.
2. Prepare journal entries to record the first subsequent transaction in November 2017 for parts c and e.

e. Since the company does not occupy the entire building it owns, it rented space to a tenant at $1,000 per month, starting on September 1, 2017. The rent was paid on time on September 1, and the amount received was credited to the Rent Earned account. However, the October rent has not been paid. The company has worked out an agreement with the tenant, who has promised to pay both October and November rent in full on November 15. The tenant has agreed not to fall behind again.

Vectors are used in computer graphics to calculate the lengths of shadows over flat surfaces. The length of an object can sometimes be represented by a vector a. If a single light source is shining down on the object, then the length of its shadow on the ground will be equal to the absolute value of the component of the vector a along the direction of the ground, as shown in the figure. Compute the length of the shadow for the specified vector a if the ground is level.

Shadow on level ground $\mathbf{a}=\langle 2.6,4.5\rangle$