(a) In what state is the washwoman when she arrives at the author's home? (b) What has she endured to get there, and how is that situation more difficult when she leaves? Explain.

Write the logarithmic expression as one logarithm.

$$3 \log _ { 2 } x - 5 \log _ { 2 } y + 7 \log _ { 2 } z$$

Based on rate constant considerations, explain why the equilibrium constant depends on temperature.

For each polynomial function, use the remainder theorem and synthetic division to find f(k). k=3; $f(x)=x^{2}-4 x+5$

Why is the washwoman's job so difficult?

(a) Which words does Mrs. Johnson repeat in the third paragraph? (b) What is the effect of that repetition? Explain.

Perform the indicated operations. If possible, reduce the answer to its lowest terms.

$$\left( \frac { 1 } { 2 } + \frac { 1 } { 4 } \right) \div \left( \frac { 1 } { 2 } + \frac { 1 } { 3 } \right)$$

Verify each identity.

$$\sec \theta \cot \theta=\csc \theta$$

What overall idea is Mrs. Johnson communicating by describing the pain and grief of "people who are really not at the center of the tragedy"? Explain.

(a) Show that, for any square matrix A,

$$A ^ { T }$$

and A have the same characteristic polynomial and hence the same eigenvalues. (b) Give an example of a

$$2 \times 2$$

matrix A for which

$$A ^ { T }$$

and A have different eigenspaces.

Solve for $0\leqslant x \leqslant 2 \pi$ giving your answers as exact values: $2 \cos ^{2} x+\cos x-1=0$

The work function $(\phi)$ of a metal is the minimum energy needed to remove an electron from its surface,

Is it easier to remove an electron from a gaseous silver atom or from the surface of solid silver $( \phi = 7.59 \times 10 ? 19 \mathrm { J }$; IE = 731 kJ/mol)?

Find $y ^ { \prime }$ , where a and b are constant.

$$y = e ^ { a x } \cos ( - b x )$$

In a constant-pressure process,

$$\Delta H = 0$$

What can you conclude about

$$\Delta E$$

q, and w?