You are a merchant during the era of the Umayyads. You travel the empire buying and selling goods. Write a diary entry describing one of your travels.

A firm’s income tax return shows income taxes for 2009 of $35,000. The firm reports deferred tax assets before any valuation allowance of$24,600 at the beginning of 2009 and $27,200 at the end of 2009. It reports deferred tax liabilities of$18,900 at the beginning of 2009 and $16,300 at the end of 2009.

• a. Assume for this part that the valuation allowance on the deferred tax assets totaled$6,400 at the beginning of 2009 and $7,200 at the end of 2009. Compute the amount of income tax expense for 2009.
• b. Assume for this part that the valuation allowance on the deferred tax assets totaled$6,400 at the beginning of 2009 and $4,800 at the end of 2009. Compute the amount of income tax expense for 2009.

An object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in centimeters. Find: the time required for one cycle.

$$d = 20 \cos \frac { \pi } { 4 } t$$

Two coils wound on a common core have $L_1 = 1 H, L_2 = 2 H,$ and M = 0.5 H. The currents are $i_1 = 1 A$ and $i_2 = 0.5 A .$ If both currents enter dotted terminals, find the flux linkages of both coils. Repeat if $i_1$ enters a dotted terminal and $i_2$ leaves a dotted terminal.

Use computer to find fundimental set of solutions for the system $\mathbf{y}^{\prime}=A \mathbf{y}$, where is A the given matrix.

$$A=\left( \begin{array}{ccc}{0} & {-2} & {2} \\ {12} & {-6} & {8} \\ {9} & {-1} & {3}\end{array}\right)$$

In a mystery story, no detail is unimportant. Mystery authors often use two types of details: those that will help readers solve the mystery and those that will lead readers astray. Because details are so important to the plot of a mystery, they must be included carefully and at specific points in the action. Details revealed too early could give away the ending; details revealed too late may cause frustration or loss of interest in the reader.

Cite two details in this story that contribute to the mystery's solution. Where in the story are these two details introduced?

Find a formula for the nth partial sum of the series and use it to determine if the series converges or diverges. If a series converges, find its sum.

$$\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 } { n ^ { 2 } } - \frac { 3 } { ( n + 1 ) ^ { 2 } } \right)$$

Identify examples of new ideas in the form of scientific discoveries or innovations that appeared during the 1500 s and 1600 s. Use a diagram like the one below to identify the ideas and the changes they produced.

For each given $p$-series, identify $p$ and determine whether the series converges.

$$\sum_{k=1}^{\infty} k^{-2 / 3}$$

The time T in seconds for a pendulum to complete one back-and-forth swing is given by

$$T = 2 \pi \sqrt { \frac { L } { 9.8 } }$$

where L is the length of the pendulum in meters. A clockmaker needs a pendulum that will complete 120 back-and-forth swings in one minute. To the nearest hundredth of a meter, how long should the pendulum be?

A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 12° with the horizontal. The flagpole’s shadow is 16 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is 20° Write an equation that can be used to find the height of the flagpole.

using known Taylor series, find the first four nonzero terms of the Taylor series about $0$ for the function.

$$e^{-x}$$

The previous exercise illustrates that one of the nuances of “conditional” convergence is that the sum of a series that converges conditionally depends on the order that the terms of the series are summed. Absolutely convergent series are more dependable, however. It can be proved that any series that is constructed from an absolutely convergent series by rearranging the terms will also be absolutely convergent and has the same sum as the original series. Use this fact together with parts (a) and (b) of the theorems above in this exercise.

Use the series for $\pi^2/6$ given in the preceding exercise to show that

$$\frac{\pi^2}{12}=1-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+\cdots$$

(Count occurrence of numbers) Write a program that reads the integers between 1 and 50 and counts the occurrences of each. Assume the input ends with 0. Here is a sample run of the program:

Enter the integers between 1 and 50: 2 5 6 5 4 3 23 43 2 0
2 occurs 2 times
3 occurs 1 time
4 occurs 1 time
5 occurs 2 times
6 occurs 1 time
23 occurs 1 time
43 occurs 1 time

Note if a number occurs more than one time, the plural word “times” is used in the output

(Count occurrence of numbers) Rewrite the above exercise using streams.