Draw the resonance contributors of the cyclooctatrienyl dianion. a. Which of the resonance contributors is the least stable? b. Which of the resonance contributors makes the smallest contribution to the hybrid?

Give the symbol and the equivalent in grams for the unit. Dekagram

For a (classical) simple harmonic oscillator with fixed total energy E, find the mean value of kinetic energy $\overline{K}$ and the mean value of potential energy $\overline{V}$. Show that $\overline{K} =\overline{V} =E/2$.

What is the mass in grams of 13.2 amu?

The ________ exocrine gland stores its secretion until the glandular cell ruptures, whereas the ________ gland releases its apical region and reforms. a. holocrine; apocrine b. eccrine; endocrine c. apocrine; holocrine d. eccrine; apocrine

Find the exact value of each expression. Do not use a calculator. $4 \csc \frac{3 \pi}{4}-\cot \left(-\frac{\pi}{4}\right)$

Simplify.

$$y^3\cdot y^6$$

Divide and check:

$$( 18t^3- 24t^2 + 6t) \div ( 3t)$$

Solve the equation. -10|16x + 4| - 3 = -3

Write each expression in the standard form a + bi. $(\sqrt{3}-i)^{6}$

Find the region on which the function is continuous. $f(x, y)=3 x^{2} e^{4 y}-\frac{3 y}{x}$

Calculate.$\int{\tan^{3/2}x\sec^4x}dx$

(a) Write down the scheme using centered differences for the equation $u_{x x}+u_{y y}=f(x, y)$ (b) Use it with $\Delta x=\Delta y=0.5$ to solve the problem $u_{x x}+u_{y y}=1$ in the square $0 \leq x \leq 1,0 \leq y \leq 1$ with $u=0$ on the boundary (c) Repeat with $\Delta x=\Delta y=\frac{1}{3}$ . (d) Compute the exact value at the center of the square and compare with your answer to part (b).

a. State what is meant by the greenhouse effect. b. State the main greenhouse gases in the Earth’s atmosphere, and for each give three natural and three man-made sources.