Numerade

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Consider H2O and CH3CO2H (acetic acid). Draw their acid-base reaction, and add two curved arrows to show the taking of a proton in the reactants: ? +. ? ---> ? +. ? Label these features in your chemical equation, clearly: conjugate base pKa 15.7 acid base pKa 4.74 conjugate acid

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3) Compliments If each person has a favorite month of the year, find the probably that two or more people have the same favorite month from a group of N total people for N = 2, 3, 4, ..., 12, 12+

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$6\frac{3}{8} \div 4\frac{1}{4}$

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Chemical irritants that may cause periotinis are: bile in the peritoneal cavity chyme in the peritoneal cavity foreign bodies in the peritoneal cavity all of the above

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The National Park Service is building a 16 -mile hiking trail. They will post a sign every $ \frac{1}{8} $ mile along the trail, including one at the end. There will not be a sign posted at the beginning of the trail. How many signs will they post along the trail? 2 24 88 128

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22.8g Sr = 22.8g Al2O3 =

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3. Sketch a graph of a function that such that (a) $f$ has a vertical asymptote at $x = 3$. (b) $f'' > 0$ when $x > 3$. (c) $f'(0) = 0$ (d) $\int_{-1}^{1} f(x) dx < 0$. (e) $\lim_{x \to -\infty} f(x)$ does not exist.

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Summer 2020 Charges 1. You have a point charge Q$_1$ C at the origin and Q$_2$ C is at point (x= 5, y=-3, z=0) find the Electric field at the point (x=6, y=7, z=0) knowing that the field of a point charge is $\vec{E} = \frac{q}{4\pi\epsilon_0r^2}\hat{r}$ (for this problem you need to find the field due to each charge and then add the two vectors at the point x=6, y=7, z=0) 2. If you have a surface charge of $k_s = \frac{C}{m^2}$ uniformly spread over surface of -2x+3z=3 and we know that the Electric flux density is $\vec{D} = k_s \frac{c}{m^2}\hat{a}_n$ where $\hat{a}_n$ is normal to the surface.Find $\vec{D}$ for the 2 given points (x=0 z=2) and (x=2, z=0) show your work.

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Derive the Laplace transforms of the following functions (use definition): 1. $f(t) = e^{2t} \cosh t$ 2. $f(t) = t^2 - 2t$ 3. $f(t) = \cos 2\pi t$ Derive the Laplace transforms of the following functions (use Laplace transform table): 4. $f(t) = \cos(\omega t + \theta)$ 5. $f(t) = \sin(3t - 1/2)$ 6. $f(t) = \sin t \cos t$

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Note: in all of the below capital letters are non-terminals, non-grammar symbols are terminals. 0. Given the following grammar, G: S ? A | S # S | S @ S A ? C | C A C ? a | b | c For each production below, state whether it is: In the language G decides - if so, prove it with a derivation and parse tree - if not, explain why If it is ambiguous in G - if so, prove it is with another valid parse tree in G Productions: I. aa ## bb II. a @ b # c III. ab 1. Rewrite grammar G so that: - no string in it is ambiguous - # has higher precedence than @ - # and @ are both left-associative (i.e. a # b # c should mean (a # b) # c)

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gabriel h.