A football player runs directly down the field for 35 m. He then turns right, at an angle of $25^{\circ}$ from his original direction, and runs an additional 15 m before being tackled. What is his displacement from his original position? Given: Unknown:

Which of the following is not an outcome of complement activation?

A) Production of histamine

B) Bacterial cell lysis

C) Opsonization

D) Inflammation

E) All of the above are outcomes of complement activation

Write down what you think are the three main general properties that distinguish metals from non-metals.

Cloud Shoes manufactures recovery sandals and is planning on producing 12,000 units in March and 11,500 in April. Each sandal requires 1.2 yards if material, which costs $3.00 per yard. The company’s policy is to have enough material on hand to equal 15% of next month’s production needs and to maintain a finished goods inventory equal to 20% of the next month’s production needs. What is the budgeted cost of purchases for March?

Complete the given requirements.

a. Displacement Problem: Suppose that as a rocket rises from its launch pad its upward velocity, $v$, in feet per second, is given as a function of time, 1 , in seconds, by

$$v=150 t^{05}$$

Find the displacement, $y$, of the rocket from $t=0$ to $t=9$ by sketching the graph of $v$; showing a representative strip of width dt and a sample point $(t, v)$, writing the differentual $d y$, and integrating. Confirm the property of the sum of two integrals with the same integrand by finding the displacement from $t=0$ to $t=4$ and from $t=4$ to $t=9$.

b. Figure 5 -11c shows the region in Quadrant I bounded below by the graph of $y=\ln x$ and above by the line $y=\ln 4$. Slice a narrow strip in the region parallel to the $x$-axis. Find the differential of area, $d A$, in terms of a sample point $(x, y)$ on the graph of $y=\ln x$. Transform $d \mathrm{~A}$ so it is in terms of $y$ and $d y$ and then integrate algebraically to find the area of the region exactly, in terms of $e$ and In if necessary.

Determine the phase of the following substances and find the values of the unknown quantities.a. Nitrogen: P = 2000 kP a, 120 K, v = ?, Z = ? b. Nitrogen: 120 K, v = 0.0050 m3/kg, Z = ? c. Air: T = 100$^{\circ} \mathrm{C}$, v = 0.500 m3/kg, P = ? d. R-410a: T = 25$^{\circ} \mathrm{C}$, v = 0.01 m3/kg, P = ?, h = ?

Why, in general, is a sigma bond between two atoms stronger than a pi bond between the same two atoms?

Writing The general equation giving the height of an oscillating object attached to a spring is

$$y=A \sin \sqrt{\frac{k}{m}} t+B \cos \sqrt{\frac{k}{m}} t$$

where $k$ is the spring constant and $m$ is the mass of the object.

Show that the maximum displacement of the object is $\sqrt{A^2+B^2}$.

The following table gives the cost and revenue, in dollars, for different production levels, $q$.

(a) At approximately what production level is profit maximized?

$$\begin{array}{c|c|c|c|c|c|c} \hline q & 0 & 100 & 200 & 300 & 400 & 500 \\ \hline R(q) & 0 & 500 & 1000 & 1500 & 2000 & 2500 \\ \hline C(q) & 700 & 900 & 1000 & 1100 & 1300 & 1900 \\ \hline \end{array}$$

A food particle from your breakfast takes a circuitous path through your digestive system. Suppose its motion over a period of time can be represented by the four displacement vectors depicted in FIGURE 3-49. Let the vectors have magnitudes $A=8.0 \mathrm{~cm}, B=$ $16 \mathrm{~cm}, C=23 \mathrm{~cm}$, and $D=5.6 \mathrm{~cm}$. (a) What is the total displacement of the food particle? Give its direction relative to the direction of vector $\overrightarrow{\mathbf{A}}$. (b) If the average speed of the particle is $0.010 \mathrm{~mm} / \mathrm{s}$, what is its average velocity over the time interval of the four displacements?

Suppose that $f(t)$ is the displacement of a moving object from a fixed plane. Explain why the difference quotient,

$$\frac{f(b)-f(a)}{b-a}$$

is the average velocity from t = a t = b. How Is the instantaneous velocity at t = a related to this average velocity? The definition of derivative should help you answer this question.

The table shows the daily crude oil production $y$ (in thousands of barrels) in Saudi Arabia for each year $x$ from 1995 through 2001.

$$\begin{array}{|c|c|} \hline \text { Year, } \boldsymbol{x} & \text { Oil production, } \boldsymbol{y} \\ \hline 1995 & 8231 \\ 1996 & 8218 \\ 1997 & 8362 \\ 1998 & 8389 \\ 1999 & 7833 \\ 2000 & 8404 \\ 2001 & 8031 \\ \hline \end{array}$$

Sketch a scatter plot of the data.

The production of oil (in millions of barrels per day) extracted from oil sands in Canada is projected to be

$$P(t) = \dfrac{4.76}{1 + 4.11e^{-0.22t}}\qquad 0 \le t \le 15$$

where $t$ is measured in years, with $t = 0$ corresponding to the beginning of $2005$. What will the total oil production of oil from oil sands be over the years from the beginning of $2005$ until the beginning of $2020 (t = 15)$?

Using the diagrams of unit cells shown below, count the number of atoms at each type of position (corner, edge, face, internal) and each atom's fraction in the unit cell to determine the formulas $\left(\mathrm{M}_m \mathrm{X}_n\right)$ of the compounds represented. Open circles represent cations, and closed circles represent anions.