At what value of x does the quadratic function $f(x)=a x^{2}+b x+c, a \neq 0,$ have a stationary point? Under what conditions is the stationary point a local maximum or a local minimum?

Consider a $15-\mathrm{cm} \times 20-\mathrm{cm}$ printed circuit board $\mathrm{(PCB)}$ that has electronic components on one side. The board is placed in a room at $20^{\circ} \mathrm{C}$. The heat loss from the back surface of the board is negligible. If the circuit board is dissipating $8 \mathrm{~W}$ of power in steady operation, Find the average temperature of the hot surface of the board, assuming the board is $(a)$ vertical; $(b)$ horizontal with hot surface facing up; and $(c)$ horizontal with hot surface facing down. Take the emissivity of the surface of the board to be $0.8$ and assume the surrounding surfaces to be at the same temperature as the air in the room.

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.) -4

What is the chance that the next person I meet will be different from me? The diversity index, from 0 (no diversity) to 100, measures the chance that two randomly selected people are of a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 81 in Hawaii to as low as 11 in Vermont. The bar graph at the top of the next column shows the national diversity index for the United States for four years the period from 1980 through 2010.

The data in the graph can be modeled by the formula

$$D=0.7 x+34 \text {, }$$

where $D$ is the national diversity index for the United States $x$ years after 1980.

How well does the formula model the national diversity index for 2010?

Major home appliances purchased in the United States are labeled with bright yellow "Energy Guide" ${ }^{\mathrm{N}}$ tags showing anticipated energy consumption. The tag on a recently purchased washing machine indicated the anticipated energy use would be $940 \mathrm{~kW}$-h per yeas. Calculate the anticipated annual energy use in kilojoules. (See Question 20 for a definition of kilowatt-hour.) At 8 cents/kW-h, how much would it cost per month to operate this machine?

The wattage of an appliance indicates the average power consumption in watts $(W)$, where $1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}$. What is the difference in the number of $\mathrm{kJ}$ of energy consumed per month between a refrigeration unit that consumes $625 \mathrm{~W}$ and one that consumes $855 \mathrm{~W}$ ? If electricity costs $\$ 0.15$ per $\mathrm{kWh}$, what is the monthly cost difference to operate the two refrigerators? (Assume $30.0$ days in one month and $24.0$ hours per day.)

If you left a board lying on the grass for a few days, what would happen to the grass underneath the board? Why?

Infection that weakens the heart muscle is called _______.

Approximately how many oxygen molecules arrive each second at the mitochondrion of an active person with a mass of $84 \mathrm{~kg}$ ? The following data are available: Oxygen consumption is about $40 . \mathrm{mL}$ of $\mathrm{O}_2$ per minute per kilogram of body weight, measured at $T=300 .\ \mathrm{K}$ and $P=1.00 \mathrm{~atm}$. In an adult there are about $1.6 \times 10^{10}$ cells per kg body mass. Each cell contains about 800 . mitochondria.

Suppose we have a repository of 1000 documents, and we wish to build an inverted index with 10,000 words. A block can hold ten word-pointer pairs or 50 pointers to either a document or a position within a document. The distribution of words is Zipfian; the number of occurrences of the $i$ th most frequent word is $100000 / \sqrt{i}$, for $i=1,2, \ldots, 10000$.

a) What is the averge number of words per document?

b) Suppose our inverted index only records for each word all the documents that have that word. What is the maximum number of blocks we could need to hold the inverted index?

c) Suppose our inverted index holds pointers to each occurrence of each word. How many blocks do we need to hold the inverted index?

d) Repeat (b) if the 400 most common words ("stop" words) are not included in the index.

e) Repeat (c) if the 400 most common words are not included in the index.

You have a 1-m-wide, 2-m-long 14-kg wooden board. If you place a 5.0-kg pot of soup in one corner of the board, where is the center of mass of the board-pot system?

What is the product of two squared and two to the sixth power? express using exponents.

Differentiate between the three types of muscle.

Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value of $f(x)=x^{3}-2 x^{2}-4 x+5,$ for -3 < x < 3.