Calculate the inductance, $L$, for the following long coils: (Note: $1\text{ m}=100\text{ cm}$ and $1\text{ m}^2=10,000\text{ cm}^2$.) a. air core, $20$ turns, area $3.14\text{ cm}^2$, length $25\text{ cm}$. b. same coil as step a with ferrite core having a $\mu_\text{r}$ of $5000$. c. air core, $200$ turns, area $3.14\text{ cm}^2$, length $25\text{ cm}$. d. air core, $20$ turns, area $3.14\text{ cm}^2$, length $50\text{ cm}$. e. iron core with $\mu_\text{r}$ of $2000$, $100$ turns, area $5\text{ cm}^2$, length $10\text{ cm}$.

Determine whether the natural numbers are closed under the given operation. Subtraction

Identify the following as characteristic of a solution, a colloid, or a suspension:

a. Particles of this mixture remain inside a semipermeable membrane but pass through filters.

b. The particles of solute in this solution are very large and visible.

Describe an experimental method for determining whether a solid is an electrolyte or a nonelectrolyte

A rock is thrown into the river below from a bridge It takes $2.40 \mathrm{~s}$ for the rock to hit the water. (a) Calculate the speed (in $\mathrm{m} / \mathrm{s}$ ) of the rock as it hits the water. (b) How high (in metres) is the bridge above the water?

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.Statement:

$$If f(x) = x^n, where n is odd, then f^-1 exists.$$

A torque $T$ is applied to the 20 -mm-diameter steel rod $A B$. Assuming the steel to be elastoplastic with $G=77.2 \mathrm{GPa}$ and $\tau_Y=145 \mathrm{MPa}$, determine $(a)$ the forque $T$ when the angle of twist at $A$ is $25^{\circ}$. (b) the corresponding diameter of the elastic core of the shaft.

Two networks are represented by the following impedance matrices

$$\mathbf{z}_{1}=\left[\begin{array}{ll}{4.7} & {0.5} \\ {0.87} & {1.8}\end{array}\right] \mathbf{k} \Omega \text { and } \mathbf{z}_{2}=\left[\begin{array}{cc}{1.1} & {2.2} \\ {0.89} & {1.8}\end{array}\right] \mathbf{k} \Omega,$$

respectively. (a) Determine the t matrix which characterizes the cascaded network resulting from connecting network 2 to the output of network 1. (b) Reverse the order of the networks and compute the new t matrix which results.

Evaluate the integral and interpret it as the area of a region. Sketch the region.

$$\int_{-1}^1\left|x^3-x\right| d x$$

A safe containing $1,000,000 is locked with a combination lock. You pay one dollar for one guess at the six-digit combination. If you open the lock, you get to keep the million dollars. What is your expectation?

Sketch the region bounded above by y=8/(x^2+4) and bounded below by 4y=x^2. What is the area of this region?

A projectile (mass $M$ ) is launched at an angle $\theta$ with an initial speed $v_0$. Considering the torque and angular momentum about the launch point, explicitly show that $d L / d t=\tau$. Ignore the effects of air resistance. (The equations for projectile motion are found in Chapter 3.)

Determine whether the real numbers are closed under the given operation. Division

List the three important properties of a myosin head. What is a cross-bridge?