A square loop of wire with sides of length L and carrying a conventional current I lies in the yz plane with its center at the origin. What is the approximate equation for the magnitude of the magnetic field at a location x that is much greater than L, in terms of the magnetic moment of the loop?

(b) List all of the following statements that are correct: (1) At the location of the compass, the magnetic field due to the magnet is equal in magnitude to the magnetic field due to the coil. (2) It isn’t necessary to take the magnetic field of the magnet into account, since the coil is in between the magnet and the compass. (3) Because not all parts of the magnet are the same distance from the compass, treating the magnet as a dipole located at the center of the magnet is an approximation. (4) The magnetic dipole moment of the coil is equal to the magnetic dipole moment of the compass. (5) At the location of the compass, the net magnetic field is equal to the magnetic field of the Earth.

Let $R^{3}$ have the Euclidean inner product, and suppose that u=(1, 1, -1) and v=(6, 7, -15). Find a value of k for which ||ku+v||=13.

Dr. Alscott has examined two sets of data from his research. In the first set, the standard deviation was very small, while in the second set there was a much larger standard deviation. Based on this information, what conclusion can be drawn from these two sets? a. The median was greater than the mean in the second set. b. The mean was greater than the median in the second set. c. The standard deviation in both sets reveled a positive correlation between the, data. d. Most data points were closer to the mean in the first set than in the second. e. Most data points were closer to the mean in the second set than in the first.

Compare and contrast asexual and sexual reproduction, identifying and explaining as many differences as possible.

State the size of each matrix.

$$\left[\begin{array}{l}{1} \\ {2} \\ {3} \\ {4}\end{array}\right]$$

Does Earth's surface give off light at night? If so, what type? If not, why not?

Sixty people are in the marching band. If one fourth of them play trumpet, how many do not play trumpet? Draw a picture to illustrate the problem.

Determine the second-order Taylor formula for the given function about the given point $(x_0, y_0)$.
$f (x, y) = 1/(x^2 + y^2 + 1)$, where $x_0 = 0, y_0 = 0$

Find an equation for the line in the form $ax+by=c$, where $a,b,$ and $c$ are integers with no factor common to all three and $a\ge 0$. The line with $x$-intercept and perpendicular to $2x−y=4$

Prove the given statement about subsets A and B of $\mathbb{R}^n$, or provide the required example in $\mathbb{R}^2$. $[(\text { aff } A) \cup(\text { aff } B)] \subset \operatorname{aff}(A \cup B)$.

Show that

$$\lim\left(\frac{1}{n}-\frac{1}{n+1}\right)=0.$$

In your Evidence Notebook, draw a model of the structure of a water molecule and explain how this structure relates to some of the unique properties of water.

Describe what you have to do in each class in order to get a good grade. Use complete sentences.

(la clase español) ________________________ (la clase de matemáticas) _____________________ (la clase de ciencias) ___________________________ (la clase de inglés) ______________________________