The demand function for a product is modeled by p=20-0.02x, $0 \leq x \leq 1000$ where p is the price (in dollars) and x is the number of units. (a) Determine when the demand is elastic, inelastic, and of unit elasticity. (b) Use the result of part (a) to describe the behavior of the revenue function.

What criteria serve to demonstrate that a culture of a previously undescribed microorganism is pure?

Edgar is training to be on the cross-country team at his high school. Edgar has training runs that are two different lengths. One trail is 4 miles, and he usually completes it in 0.5 hours (30 minutes). If he runs the 10-mile trail, it usually takes him 1.25 hours (75 minutes). a. Graph points for the length and time of Edgar's run on a graph. Does it make sense to connect the points? Where could you add a point to show how far he has traveled after 0 minutes? b. Helena is a long-distance runner. Once a week, she does a 17-mile training run that usually takes her 2 hours. Does she run slower or faster than Edgar? How do you know?

On graph paper, graph $\Delta A B C$ if A is at (-2, -3), B is at (-2, 5), and C is at (3, 0). a. What is the length of the base of $\Delta A B C ?$ Label side AB with its length in grid units. b. What is the height of $\Delta A B C ?$ Draw this length on your graph and label it. c. What is the area of $\Delta A B C ?$ Show how you got your answer. d. If you formed a parallelogram with the triangle on your graph using a copy of $\Delta A B C,$ where would the fourth vertex be? Is there more than one possible answer?

The lifetime of an exited state of a nucleus is usually about $10^{-12} \sec$. What is the uncertainty in energy of the $\gamma$-ray photon emitted?

A rock is dropped from a height of $88.2 \mathrm{m}$ and falls toward Earth in a straight line. In t seconds the rock falls $4.9 t^{2} \mathrm{m}$. (a) What is the average velocity of the rock for the first 2 s? (b) How long does it take for the rock to hit the ground? (c) What is the average velocity of the rock during its fall? (d) What is the velocity v of the rock when it hits the ground?

Use substitution to find each indefinite integral. $\int\left(x^{2}-1\right) e^{x^{3}-3 x} d x$

What are the major differences between insertion sequences and transposons?

Rectilinear Motion As an object in rectilinear motion moves, its signed distance s (in meters) from the origin after t seconds is given by the position function $s=f(t)=2 t^{3}+4$. Find the velocity v at $t_{0}=0$. At $t_{0}=3$. At any time $t_{0}$.

Did Bohr postulate the quantization of energy? What did he postulate?

As an object in rectilinear motion moves, its signed distance s from the origin at time t is given by the position function $s=s(t)=3 t^{2}-\frac{1}{t}$, where s is in centimeters and t is in seconds. Find the velocity v of the object at $t_{0}=1$ and $t_{0}=4$.

Use direction fields and isoclines to make a qualitative sketch of the solutions, determine the equilibrium values (when they exist), and classify them as stable or unstable. Consider the parameters a and b to be positive in each case. $y^{\prime}=e^{y}-1$

What are the functions of the Sec and Tat systems and why are they necessary? How do these systems know which proteins to act upon?

Find all points where the functions have any relative extrema. Identify any saddle points. f(x, y)=3xy+6y-5x