A drilling mud is a slurry pumped into oil wells being drilled. The mud has several functions: It floats rock cuttings to the top of the well where they can easily be removed; lubricates and cools the drill bit; and keeps loose solids and water from leaking into the borehole. A drilling mud is prepared by blending (SG = 4.37) with seawater (SG = 1.03). The seawater has a dissolved salt content of approximately 3.5 wt%. You have been asked to determine the specific gravity of the mud and the wt% barite. You collect a sample of the mud from a blending tank on an oil platform and make the following observations: (i) The mud appears homogeneous, even after standing for 2 days; (ii) the tare mass of the calibrated vessel into which you pour the sample of mud is 118 g; (iii) the volume of the collected sample is 100 mL, and the mass of the collection vessel and sample is 323 g; and (iv) the mass of the vessel and residue remaining after completely evaporating water from the sample is 254 g. a) Estimate the specific gravity of the mud and the wt% barite. b) What is the practical importance of Observation (i)?

Calculate the derivative of the following functions. $y=\theta^{2} \sec 5 \theta$

On $20$ April $2010$, the Deepwater Horizon drilling rig exploded in the Gulf of Mexico, killing $11$ workers and causing an oil spill that became the worst environmental disaster in US history. Following the explosion the Deepwater Horizon sank to the bottom of the Gulf after burning for $36$ hours.

The US Coast Guard quickly became involved with the incident, putting a crisis management plan into place. Environmental experts raised concerns that the Macondo well Deepwater Horizon was drilling could be releasing up to $40000$ barrels of oil per day into the sea. A few days after the disaster, oil from the leaking well began washing ashore in Louisiana; fragile coastal wetlands were inundated with thick, brown mud and beaches were covered in black tar.

BP made a number of vain attempts to cap the leaking well until it finally stopped the leak in July. $\mathrm{BP}$, under considerable political pressure, announced in June that it would place $\$ 20$ billion in a fund to compensate victims of the oil spill and said it would not pay a shareholder dividend in $2010$. By early July $\mathrm{BP}$'s share price had fallen by $50 \%$ since the start of the crisis. The $\mathrm{BP}$ CEO, Tony Hayward, came under pressure because of his perceived mishandling of the crisis. $\mathrm{BP}$ seemed to have no effective contingency plan to deal with the crisis. Tony Hayward was eventually forced to resign.

Evaluate the likely benefits and limitations of $\mathrm{BP}$’s contingency planning when preparing for any future disasters like Deepwater Horizon.

In April 2010, the worst oil spill ever recorded occurred when an explosion and fire on the Deepwater Horizon offshore oil-drilling rig left 11 workers dead and began releasing oil into the Gulf of Mexico. One of the attempts to contain the spill involved pumping drilling mud into the well to balance the pressure of escaping oil against a column of fluid (the mud) having a density significantly higher than those of seawater and oil. In the following problems, you may assume that seawater has a specific gravity of 1.03 and that the subsea wellhead was $5053 \mathrm{ft}$ below the surface of the Gulf.

What would you expect to happen if the barite weight fraction were significantly less than that estimated in Part (c)? Explain your reasoning.

Determine the quadrant in which each angle lies. (a) $87.9^{\circ}$ (b) $-8.5^{\circ}$

A mixture of methanol and propyl acetate contains 25.0 wt% methanol. a) Using a single dimensional equation, determine the g-moles of methanol in 200.0 kg of the mixture. b) The flow rate of propyl acetate in the mixture is to be 100.0 lb-mole/h. What must the mixture flow rate be in $\mathrm{lb}_{\mathrm{m}} / \mathrm{h}$?

A rectangular block of solid carbon (graphite) floats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oil, and the top liquid is water. Of the total block volume, 54.2% is immersed in the oil and the balance is in the water. In a separate experiment, an empty flask is weighed, $35.3 \mathrm{cm}^{3}$ of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was 124.8 g in the first weighing, what would it be in the second weighing? (Suggestion: Recall Archimedes’ principle, and do a force balance on the block.)

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. Tim tried to elude the mosquitoes by...

Graph the function f(x)=x cot x using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits. a. $\lim _{x \rightarrow \pi^{+}} f(x)$, b. $\lim _{x \rightarrow \pi^{-}} f(x)$, c. $\lim _{x \rightarrow-\pi^{+}} f(x)$, (d) $\lim _{x \rightarrow-\pi^{-}} f(x)$

Use long division to divide. $\left(5 x-1+10 x^{3}-2 x^{2}\right) \div\left(2 x^{2}+1\right)$

Sketch the graph of $f(x)=x^{3}$ and the graph of the function g. Describe the transformation from f to g. $g(x)=-x^{3}+4$

Bergamo Bay’s computer system generated the following trial balance on December 31, 2017. The company’s manager knows something is wrong with the trial balance because it does not show any balance for Work in Process Inventory but does show a balance for the Factory Overhead account. In addition, the accrued factory payroll (Factory Wages Payable) has not been recorded.

$$\begin{matrix} & \text{Debit} & \text{Credit}\\ \text{Cash} \ldots\ldots\ldots& \text{\$170,000}\\ \text{Accounts receivable} \ldots\ldots\ldots& \text{75,000}\\ \text{Raw materials inventory} \ldots\ldots\ldots& \text{80,000}\\ \text{Work in process inventory}\ldots\ldots\ldots & \text{0}\\ \text{Finished goods inventory}\ldots\ldots\ldots & \text{15,000}\\ \text{Prepaid rent} \ldots\ldots\ldots& \text{3,000}\\ \text{Accounts payable} \ldots\ldots\ldots& \quad & \text{\$ 17,000}\\ \text{Notes payable} \ldots\ldots\ldots& \quad & \text{25,000}\\ \text{Common stock}\ldots\ldots\ldots & \quad & \text{50,000}\\ \text{Retained earnings} \ldots\ldots\ldots& \quad & \text{271,000}\\ \text{Sales} \ldots\ldots\ldots& \quad & \text{373,000}\\ \text{Cost of goods sold} \ldots\ldots\ldots & \text{218,000}\\ \text{Factory overhead} \ldots\ldots\ldots& \text{115,000}\\ \text{Operating expenses} \ldots\ldots\ldots& \text{60,000}\\ \text{Totals} \ldots\ldots\ldots & \text{\$736,000} & \text{\$736,000}\\ \end{matrix}$$

After examining various files, the manager identifies the following six source documents that need to be processed to bring the accounting records up to date.

$$\begin{matrix} \text{Materials requisition 21-3010:} & \text{\$10,200 direct materials to Job 402}\\ \text{Materials requisition 21-3011:} & \text{\$18,600 direct materials to Job 404}\\ \text{Materials requisition 21-3012:} & \text{\$5,600 indirect materials}\\ \text{Labor time ticket 6052:} & \text{\$36,000 direct labor to Job 402}\\ \text{Labor time ticket 6053:} & \text{\$23,800 direct labor to Job 404}\\ \text{Labor time ticket 6054:} & \text{\$8,200 indirect labor}\\ \end{matrix}$$

Jobs 402 and 404 are the only units in process at year-end. The predetermined overhead rate is 200% of direct labor cost. 1. Use information on the six source documents to prepare journal entries to assign the following costs. a. Direct materials costs to Work in Process Inventory. b. Direct labor costs to Work in Process Inventory. c. Overhead costs to Work in Process Inventory. d. Indirect materials costs to the Factory Overhead account. e. Indirect labor costs to the Factory Overhead account. 2. Determine the revised balance of the Factory Overhead account after making the entries in part 1. Determine whether there is any under- or over-applied overhead for the year. Prepare the adjusting entry to allocate any over- or under-applied overhead to Cost of Goods Sold, assuming the amount is not material. 3. Prepare a revised trial balance. 4. Prepare an income statement for 2017 and a balance sheet as of December 31, 2017. 5. Assume that the $5,600 on materials requisition 21-3012 should have been direct materials charged to Job 404. Without providing specific calculations, describe the impact of this error on the income statement for 2017 and the balance sheet at December 31, 2017.

Calculate the expected value of X for the given probability distribution.

$$\begin{matrix} \text{x} & \text{-5} & \text{-1} & \text{0} & \text{2} & \text{5} & \text{10}\\ \text{P(X=x)} & \text{.2} & \text{.3} & \text{.2} & \text{.1} & \text{.2} & \text{0}\\ \end{matrix}$$

Find the zeros (if any) of the rational function. Use a graphing utility to verify your answer. $f(x)=\frac{x^{2}+4 x-21}{x^{2}-4 x+3}$