Are the objects described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? a. A girder is lifted at constant speed by a crane. b. A girder is lowered by a crane. It is slowing down. c. You're straining to hold a 200 lb barbell over your head. d. A jet plane has reached its cruising speed and altitude. e. A rock is falling into the Grand Canyon. f. A box in the back of a truck doesn't slide as the truck stops.

What is the free-fall acceleration at the surface of (a) the moon and (b) Jupiter?

If an object is not moving, does that mean that there are no forces acting on it? Explain.

Use the model we derived for approximating the weight of Sebastes mentella, $\hat{y}=10^{-1.8994} x^{3.0494}$, to determine the sum of the squares of the deviations between the observed weights (in grams) and the predicted values. Did we minimize this quantity in the process of constructing our model? If not, what quantity was minimized?

Let Q represent a mass, in grams, of plutonium $241\left({ }^{241} \mathrm{Pu}\right)$, whose half-life is 14 years. The quantity of plutonium present after t years is given by $Q=100\left(\frac{1}{2}\right)^{t / 14}$.

(a) Determine the initial quantity (when t=0 ).

(b) Determine the quantity present after 10 years.

(c) Use a graphing utility to graph the function over the interval t=0 to t=100.

A company manufactures a product which requires capital and labor to produce. The quantity, Q, of the product manufactured is given by the Cobb-Douglas function $Q=A K^a L^b$, where K is the quantity of capital; L is the quantity of labor used; and A, a, and b are positive constants with $0<a<1$ and $0<b<1$. One unit of capital costs $k and one unit of labor costs$$\ell$. The price of the product is fixed at $p per unit.

Is there a maximum profit in the case a + b = 1? What about$a+b \geq 1$? Explain.

The demand curve for a product is given by $q=$ $120,000-500 p$ and the supply curve is given by $q=$ $1000 p$ for $0 \leq q \leq 120,000$, where price is in dollars. At a price of $\$ 100$, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push prices up or down?

Efficiency wages are wages that A. are below market equilibrium wages. B. are above market equilibrium wages. C. usually result in high turnover of employees. D. usually result in lower levels of output. E. usually necessitate greater amounts of worker supervision.

A population satisfies $d P / d t=0.025 P-0.00005 P^2$.

(a) What are the equilibrium values for $P$ ?

An astronaut takes his bathroom scale to the moon and then stands on it. Is the reading of the scale his weight? Explain.

A direction field for the differential equation $y' = x\cos \pi y$ is shown. Find all the equilibrium solutions.

Compare the quantities in Column A with those in Column B, and choose statement in these statement:

(A) if the quantity in column A is greater.

(B) if the quantity in column B is greater.

(C ) if the two quantities are equal.

(D) if the relationship cannot be determined.

$$\begin{array}{rr} &\text{Column A}&& &&&\text{Column B}\\ &b\quad && (a+b)-c=a &&&c\end{array}$$

Consider the decomposition equilibrium for dinitrogen pentoxide: $2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightleftharpoons 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$ At a certain temperature and a total pressure of 1.00 atm, the $\mathrm{N}_{2} \mathrm{O}_{5}$ is 0.50% decomposed (by moles) at equilibrium. Calculate the mole percent of $\mathrm{N}_{2} \mathrm{O}_{5}$ that will be decomposed at equilibrium if the volume is increased by a factor of 10.0.

A patient takes 150 mg of a drug at the same time every day. It is known that the body eliminates 95% of the drug in 24 hours. (a) What quantity of the drug is in the body after the third tablet? After the n th tablet? (b) What quantity of the drug remains in the body in the long run?