Each line, when completed, should have three words similar in meaning. Enter all missing letters.

in _ _ _ ference $\hspace{1cm}$ _ _ terpo_ _ tion$\hspace{1cm}$_ _ _ _ _ vention

An isolated, charged conducting sphere of radius 12.0 cm creates an electric field of $4.90 \times 104$ N/C at a distance 21.0 cm from its center. What is its surface charge density?

Find $f^{\prime}(0)$ if

$$f(x)=\left\{\begin{array}{ll}{g(x) \sin \frac{1}{x},} & {x \neq 0} \\ {0,} & {x=0}\end{array}\right.$$

and $g(0)=g^{\prime}(0)=0$.

Each line, when completed, should have three words similar in meaning. Enter all missing letters

___reck$\hspace{1cm}$r ze$\hspace{1cm}$ ___ ___ ___ ___is ___

Use the simplex method. Minimize $Z=2 x_{1}+x_{2}$ subject to

$$\begin{aligned} x_{1}+2 x_{2} & \leq 6 \\ x_{1}+x_{2} & \geq 1 \\ x_{1}, x_{2} & \geq 0 \end{aligned}$$

Point charges $q_1=q_2=4.0 \times 10^{-6} \mathrm{C}$ are fixed on the $x$-axis at $x=-3.0 \mathrm{~m}$ and $x=3.0 \mathrm{~m}$. What charge $q$ must be placed at the origin so that the electric field vanishes at $x=0, y=3.0 \mathrm{~m}$ ?

Calculate the determinant of each of the following matrices: *(a)

$$\left[ \begin{array}{rrrr}{5} & {2} & {1} & {0} \\ {-1} & {3} & {5} & {2} \\ {4} & {1} & {0} & {2} \\ {0} & {2} & {3} & {0}\end{array}\right]$$

, (b)

$$\left[ \begin{array}{rrrr}{0} & {5} & {4} & {0} \\ {4} & {1} & {-2} & {7} \\ {-1} & {0} & {3} & {0} \\ {0} & {2} & {1} & {5}\end{array}\right]$$

, (c)

$$\left[ \begin{array}{rrrr}{2} & {1} & {9} & {7} \\ {0} & {-1} & {3} & {8} \\ {0} & {0} & {5} & {2} \\ {0} & {0} & {0} & {6}\end{array}\right]$$

, *(d)

$$\left[ \begin{array}{rrrrr}{0} & {4} & {1} & {3} & {-2} \\ {2} & {2} & {3} & {-1} & {0} \\ {3} & {1} & {2} & {-5} & {1} \\ {1} & {0} & {-4} & {0} & {0} \\ {0} & {3} & {0} & {0} & {2}\end{array}\right]$$

.

Evaluate the series.

$$\sum_{n=2}^8 \ln \frac{n}{n+1}$$

Evaluate the surface integral ∫∫(curl F)*n dA directly for the given F and S. F=[z²,-x²,0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4).

Sketch the given function and represent it as indicated. Graph approximate curves obtained by replacing x with finite limits; also look for Gibbs phenomena.

Find $\mathscr{F}_c\left(e^{-2 x}\right)$ and $\mathscr{F}_s\left(e^{-2 x}\right)$ by formulas involving second derivatives

What is the value of the expression

$$6+(13-1) \div 4+2 ?$$

In a region that does not contain current-carrying wires, the magnetic field is given by:

$$\bold{\vec B}(y,t)=B_0\cdot \cos(k\cdot y-\omega\cdot t)\,\bold{\hat i}$$

If the electric field at that region at $t=0$ is given by:

$$\bold{\vec E}(y,t=0)=\dfrac{k}{\mu_0\cdot \varepsilon_0\cdot \omega}\cdot \cos(k\cdot y)\,\bold{\hat k}$$

What is the electric field $\bold{\vec E}(y,t)$?

Factor by grouping.

$$2 a^2+9 a-18$$

Determine whether n ≥ 0 or n ≤ 0. 40. n + │-n│ = 0