Show how you would synthesize 2-phenylhex-3-yn-2-ol, starting with acetophenone $\left(\mathrm{PhCOCH}_{3}\right)$ and any other reagents you need. (“2-ol” means there is an OH group on C2.)

Integrate

$$\int \sec x \tan x d x$$

What are the products of reaction of (E)-3-methyl-3-hexene with each of the reagents in the indicated problem?

Find $y^{\prime}$.

y=ln sec x

Starting with acetylene, show reagents that you would use to prepare each of the following compounds: (a) 1-Butyne (b) 2-Butyne (c) 3-Hexyne (d) 2-Hexyne (e) 1-Hexyne (f) 2-Heptyne (g) 3-Heptyne (h) 2-Octyne (i) 2-Pentyne

In this exercise,, suppose that f(u, v)=ue$^v$, where u=rs and v=r+s.

What is the value of f(u, v) at(r, s)=(1,1)?

What products would you expect to obtain from the reaction of benzene with the following reagents? (a) $\left(\mathrm{CH}_3\right)_3 \mathrm{CCl}, \mathrm{AlCl}_3$ (b) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COCl}, \mathrm{AlCl}_3$

A car under surveillance accelerates at a constant rate from 0 mph to 60 mph in 30 sec. How far has it traveled after 30 sec?

Find $y^{\prime}$.

$$y=e^{x \sec x}$$

For the following exercise,

Find the exact value of each trigonometric function.

$$\sin \frac{\pi}{2}$$

Karl ralses his hand and Informs Ms. Rhombi that he has discovered another property related to the angles of an inscribed quadrilateral. He claims that the measure of any exterior angle of the quadrilateral is equal to the measure of the opposite interior angle in the quadrilateral. In other words, $m \angle A W Z=m \angle Y$. Explain Karl's reasoning.

In this exercise, use a calculator to find the value of the trigonometric function to four decimal places.

$$\csc 1$$

Outline efficient syntheses of each of the following alkynes from acetylene and any necessary organic or inorganic reagents: (a) 1-Heptyne (b) 2-Heptyne (c) 3-Heptyne

Consider a right rectangular prism:

a. Edge AF is perpendicular to (makes right angles with) which of these? (The bar notation is common for line segments.)

edge FE, or $\overline{F E} \quad$ edge AD, or $\overline{A D} \quad$ edge AB, or $\overline{A B}$

segment AG, or $\overline{A G} \quad$ segment BF, or $\overline{B F} \quad$ segment FH, or $\overline{F H}$

b. Name the endpoints of three edges that are parallel to edge AD.