Evaluate the following integrals. $\int \frac { z + 1 } { z \left( z ^ { 2 } + 4 \right) } d z$

The leaves of a tree lose water to the atmosphere via the process of transpiration. A particular tree loses water at the rate of $3 \times 10^{-8} \mathrm{m}^{3} / \mathrm{s}$; this water is replenished by the upward flow of sap through vessels in the trunk. This tree's trunk contains about 2000 vessels, each $100 \mu \mathrm{m}$ in diameter. What is the speed of the sap flowing in the vessels?

Write as powers of 3: $\frac{1}{9}$

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. $2^{x+1}=5^{1-2 x}$

Suppose $\int_{1}^{3} f(x) d x=10 \text { and } \int_{1}^{3} g(x) d x=-20$. Evaluate $\int_{1}^{3}(2 f(x)-4 g(x)) d x\$and$\int_{3}^{1}(2 f(x)-4 g(x)) d x$

Find each quotient. $\frac{2-3 i}{2+3 i}$

What is the mean of 4.2, 4.8, and 5.1?

Express each union or intersection in simplest interval form. $(4, \infty) \cup(9, \infty)$

A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least equal to the cost C (in dollars) of producing it. Suppose that the cost to produce x units of carpet is C=50x+5000, while the revenue is R=60x. For what values of x is R at least equal to C?

Let the universe be the set U={1,2,3,...,10}. Let A={1,4,7,10}, B={1,2,3,4,5}, and C={2,4,6,8}. List the elements of each set.

$$(A\cup B)-(C-B)$$

What events does Angier describe at the beginning of the article?

Use a spreadsheet program to represent the data for each table. $$ \begin{matrix} \text{Abigail's Summer Earnings }\mathrm{($)} \\ \text{Month} & \text{Carnival Ride Operator} & \text{Lawn Mowing}\\ \text{May} & \text{40} & \text{72}\\ \text{June} & \text{65} & \text{80}\\ \text{July} & \text{75} & \text{60}\\ \text{August} & \text{100} & \text{70}\\ \end{matrix} $$ Represent the data by making a double-bar graph and a double-line graph. On a separate sheet of paper sketch the displayed graphs.

Assume that $\exists x \forall yP(x,y)$ is true and that the domain of discourse is nonempty. Which must also be true? Prove your answer.

$$\forall x\forall yP(x,y)$$

When a drip coffeemaker on-off switch is turned to the on position, how is cold water in the water reservoir converted to hot water and sent upward to drip down into the coffee grounds in the filter?