A conducting strip of infinite length lies in the xy plane with its length oriented along the x axis, and where $-b / 2<y<b / 2$ defines its width along y. Current $I_{1}$ flows down the strip in the positive x direction and is uniformly distributed over the width. Above the strip and parallel to it at z = d is an infinitely long current filament that carries current $I_{2}$ in the positive x direction. Find the force of attraction between the two currents per unit length in x. Assume $d<<b.$

A box of candies contains 6 caramels and 4 butter-creams, all appearing identical. What's the probability that a person who starts eating them one at a time wont get a caramel until the third candy?

State the Midpoint Rule.

For the following exercises, find the indicated term of each binomial without fully expanding the binomial. The tenth term of $(x-1)^{12}$

Describe three changes in environment that will uncoil or otherwise denature a protein.

A positive point charge q of mass m injected with a velocity $\text{u}_0 = \text{a}_{\text{y}}\text{u}_0$ into the y > 0 region where a uniform magnetic field $\text{B} = \text{a}_{\text{x}}\text{B}_0$ exists. Obtain the equation of motion of the charge, and describe the path that the charge follows.

Find the intervals of concavity and the inflection points.

$$f(x)=\frac{1}{2} x^{4}-4 x^{2}+3$$

For the following exercises, write a recursive formula for each sequence. $-2.5,-5,-10,-20,-40, \ldots$

For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. At a market, the three most popular vegetables make up 53% of vegetable sales. Corn has 4% higher sales than broccoli, which has 5% more sales than onions. What percentage does each vegetable have in the market share?

Use the sets A=(-11, 3] B=[0, 8] $C=[-9, \infty)$ Compute the set. $(A \cup B) \backslash C$

For the following exercises, write the equation of the ellipse in standard form. Then identify the center, vertices, and foci. $\frac{x^{2}}{25}+\frac{y^{2}}{64}=1$

Let the universal set be $\mathbb{Z}$ and let A={−4, −2, 0, 1, 2, 3, 5, 7, 9} B={−3, −2, −1, 2, 4, 6, 8, 9, 10} Compute the set. $B \backslash A$

In the following exercises, show that matrix A is the inverse of matrix B.

$$A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right], B=\left[\begin{array}{rr} -2 & 1 \\ \frac{3}{2} & -\frac{1}{2} \end{array}\right]$$

Sketch the graph of the function. g(x) = ||x| - 1|