A flat slab of nonconducting material carries a uniform charge per unit volume, $\rho_{\mathrm{E}}$. The slab has thickness $d$ which is small compared to the height and breadth of the slab. Determine the electric field as a function of $x$ (a) inside the slab. Take the origin at the center of the slab.

The steady-state temperature distribution in a onedimensional wall of thermal conductivity k and thickness L is of the form $T=a x^{3}+b x^{2}+c x+d$. Derive expressions for the heat generation rate per unit volume in the wall and the heat fluxes at the two wall faces (x=0, L).

Suppose that the demand and price for strawberries are related by $p=D(q)=5-0.25 q$, where $p$ is the price (in dollars) and $q$ is the quantity demanded (in hundreds of quarts). Find the price at each level of demand. $a.\ 0$ quarts $\quad b.\ 400$ quarts $\quad c.\ 840$ quarts

Find the quantity demanded for the strawberries at each price. $d. \$ 4.50$ $\qquad e.\$ 3.25$ $\qquad f.\$ 2.40$ $g.$ Graph $p=5-0.25 q$. Suppose the price and supply of strawberries are related by $p=S(q)=0.25 q$, where $p$ is the price (in dollars) and $q$ is the quantity supplied (in hundreds of quarts) of strawberries. Find the quantity supplied at each price. $h. \$ 0$ $\qquad i.\$ 2$ $\qquad j.\$ 4.50$ $k.$ Graph $p=0.75 q$ on the same axis used for part $g$. $l.$ Find the equilibrium quantity and the equilibrium price.

A solid nonconducting sphere of radius $r_0$ has a total charge $Q$ which is distributed according to $\rho_{\mathrm{E}}=b r$, where $\rho_{\mathrm{E}}$ is the charge per unit volume, or charge density $\left(\mathrm{C} / \mathrm{m}^3\right)$, and $b$ is a constant. Determine $b$ in terms of $Q.

For the electric dipole shown in the figure, express the magnitude of the resulting electric field as a function of the perpendicular distance $x$ from the center of the dipole axis. Comment on what the magnitude is when $x>0$.

A small but measurable current of $1.2 \times 10^{-10} A$ exists in a copper wire whose diameter is 2.5 mm. The number of charge carriers per unit volume is $8.49 \times 10^{28} m^{-3}$. Assuming the current is uniform, calculate the electron drift speed.

Gifts By Gina tracked the supply and demand of their super-warm parka for a series of monthly prices.

$$\begin{matrix} \text{Month} & \text{Demand} & \text{Supply} & \text{Price}\\ \text{1} & \text{2050} & \text{1225} & \text{\$ 85}\\ \text{2} & \text{1975} & \text{1350} & \text{\$ 90}\\ \text{3} & \text{1810} & \text{1470} & \text{\$ 95}\\ \text{4} & \text{1680} & \text{1620} & \text{\$ 100}\\ \text{5} & \text{1590} & \text{1725} & \text{\$ 105}\\ \text{6} & \text{1430} & \text{1850} & \text{\$ 110}\\ \end{matrix}$$

(a) In which months was there a surplus? (b) In which months was there a shortage? (c) Give an estimate of the equilibrium quantity and price.

The mysterious visitor that appears in the enchanting story The Little Prince was said to come from a planet that “was scarcely any larger than a house!” Assume that the mass per unit volume of the planet is about that of Earth and that the planet does not appreciably spin. Approximate the escape speed from the planet.

The storage shed in Figure $8.66$ is the shape of a half-cylinder of radius $r$ and length $l.$

(b) The shed is filled with sawdust whose density (mass/unit volume) at any point is proportional to the distance of that point from the floor. The constant of proportionality is $k.$ Calculate the total mass of sawdust in the shed.

The following tables give price–demand and price–supply data for the sale of soybeans at a grain market, where $x$ is the number of bushels of soybeans (in thousands of bushels) and $p$ is the price per bushel (in dollars):

Use quadratic regression to model the price–demand data and linear regression to model the price–supply data.

(A) Find the equilibrium quantity (to three decimal places) and equilibrium price (to the nearest cent).

(B) Use a numerical integration routine to find the consumers’ surplus and producers’ surplus at the equilibrium price level.

IS. Density is the amount of mass of an object per unit volume. A piece of iron weighs 45 ounces and has a volume of 10 cubic inches. Given that each ounce has a mass of 28.35 grams, determine the density of iron in grams per cubic inch. ye ,

Table 20P-1 shows supply and demand in the market for sub sandwiches in Wheretown, where the local government wants to raise revenue via a $\$ 1$ tax on all sandwiches, collected from sandwich shops.

a. Graph the initial supply and demand curves, before the tax. Then graph the after-tax supply curve. Before and after the tax: What is the equilibrium quantity? What is the equilibrium price? What price is paid by consumers? What price is received by suppliers?

TABLE 20P-1

Describe the physiological processes occurring in the muscle fibers that account for the gradual onset of muscle fatigue

A solid nonconducting sphere of radius $r_0$ has a total charge $Q$ which is distributed according to $\rho_{\mathrm{E}}=b r$, where $\rho_{\mathrm{E}}$ is the charge per unit volume, or charge density $\left(\mathrm{C} / \mathrm{m}^3\right)$, and $b$ is a constant. Determine (a) $b$ in terms of $Q.