Define each boldface word. Then, use each word in a paragraph of your own. this woman has a discrepancy in her life, empirical research does exist, the material realm of their lives.

Suppose that we have two $100-\mu \mathrm{F}$ capacitors. One is charged to an initial voltage of 50 V, and the other is charged to 100 V. If they are placed in series with the positive terminal of the first connected to the negative terminal of the second, determine the equivalent capacitance and its initial voltage. Now compute the total energy stored in the two capacitors. Compute the energy stored in the equivalent capacitance. Why is it less than the total energy stored in the original capacitors?

Annual sales of music compact discs (CDs) have declined since 2000. Sales were 942.5 million in 2000 and 384. 7 million in 2008.Use the formula to predict music CD sales in 2012.

Let $T$ be a linear operator on a finite-dimensional vector space $V,$ and suppose there exists an ordered basis $\beta$ for $V$ such that $[T]_{\beta}$ is an upper triangular matrix. $\\$ (a) Prove that the characteristic polynomial for T splits.$$ (b) State and prove an analogous result for matrices.

Systematically list the possible sexes of a 4 -child family. Hence determine the probability that a randomly selected 4 -child family has two children of each sex.

Which muscles move the thigh, legs, and foot?

Find the coefficient of $x^{3}$ in the expansion of $(x+5)^{6}$.

Review your work in Question 4. a. List the example(s) in which you could draw more than one parabola. How many points were you given for the example(s) you listed? b. List the example(s) in which you could draw only one parabola. How many points were you given for the example(s) you listed? c. List the example(s) in which you could not draw a parabola. What did you notice that was different from the examples in which you were able to draw one or more parabolas?

In each equation, label the acids, bases, and conjugate pairs:

$$\mathrm { HCl } + \mathrm { H } _ { 2 } \mathrm { O } \rightleftharpoons \mathrm { Cl } ^ { - } + \mathrm { H } _ { 3 } \mathrm { O } ^ { + }$$

For the quadratic function $f ( x ) = 2 ( x + 1 ) ^ { 2 } – 5$ a. Identify the vertex and tell if it is a maximum or minimum point on the graph. b. What is the value of the function at that minimum or maximum point?

A new car straight line depreciates according to the equation $y=-1,875 x+20,625$. a. What is the original price of the car? b. How many years will it take for this car to fully straight line depreciate?

Determine the roots of the indicial equation of the given differential equation. Also obtain the general form of two linearly independent solutions to the differential equation on an interval (0, R). Finally, if

$$r _ { 1 } - r _ { 2 }$$

equals a positive integer, obtain the recurrence relation and determine whether the constant A in

$$y _ { 2 } ( x ) = A y _ { 1 } ( x ) \ln x + x ^ { r _ { 2 } } \sum _ { n = 0 } ^ { \infty } b _ { n } x ^ { n }$$

is zero or nonzero.

$$x ^ { 2 } \left( x ^ { 2 } + 1 \right) y ^ { \prime \prime } + 7 x e ^ { x } y ^ { \prime } + 9 ( 1 + \tan x ) y = 0.$$

Two satellites are in circular orbits around a planet that has radius $9.00 \times 10^{6} \mathrm{m}$. One satellite has mass 68.0 kg, orbital radius $7.00 \times 10^{7} m$, and orbital speed 4800 m/s. The second satellite has mass 84.0 kg and orbital radius $3.00 \times 10^{7} \mathrm{m}$. What is the orbital speed of this second satellite?

Solve the following differential equation by series and also by elementary method and verify that your solutions agree

$$xy^{^{\prime }}=xy+y$$