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Parametric curvesa. Plot the following curves, indicating

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 2RE Chapter 10

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 2RE

Parametric curvesa. Plot the following curves, indicating the positive orientation.b. Eliminate the parameter to obtain an equation in x and y.c. Identify or briefly describe the curve.d. Evaluate dy/dx at the specified point.x = t2 + 4, y = 6 ? t, for ?? < t < ?; evaluate dy/dx at (5, 5).

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Chapter 1 and 2 Notes: Sole proprietorship – a business owned by one person; simple to set u and gives you control. Barber shops, law offices, auto repair shops, small retail stores. Partnership – a business owned by two or more persons associated as partners; because one does not have enough economic resources or because additional partners bring unique skills or resources. Lawyers, doctors, architects, and certified public accountants. Corporation – a business organized as a separate legal entity owned by stockholders; shares of stock are easy to sell, easier for corporations to raise funds (through stockholders). ExxonMobil, General Motors, Citigroup, and Microsoft. Taxes and legal liability:  Sole proprietorship/partnership = more favorable tax treatment, but personally liable.  Corporation = less favorable tax treatment, but not personally liable. Limited liability companies/subchapter S corporations – a hybrid form of the three main types of business organizations, which combine the tax advantages of partnerships with the limited liability of corporations. Accounting – the information system that identifies, records, and communicates the economic events of an organization to interested users (internal or external).  Internal users – mangers who plan, organize, and run a business. Marketing managers, production supervisors, finance directors, and company officers. o What price should Apple charge for an iPad to maximize the company’s net income o Is cash sufficient to pay dividends to Microsoft stockholders o Can General Motors afford to give its employees pay raises this year o Which PepsiCo product line is the most profitable Should any product lines be eliminated  External users – investors (owners), creditors, taxing authorities, customers, labor unions, regulatory agencies. o Is General Electric earning satisfactory income o How does Disney compare in size and profitability with Time Warner o Will United Airlines be able to pay its debts as they come due Sarbanes-Oxley Act (SOX) – regulations passed by Congress to reduce unethical corporate behavior. Solving an ethical dilemma: 1. Recognize an ethical situation and the ethical issues involved. 2. Identify and analyze the principal elements in the situation. 3. Identify the alternatives, and weigh the impact of each alternative on various stakeholders. Three principal types of business activity: 1. Financing: from personal saving and outside sources (borrowing money or issuing shares of stock in exchange for cash) 2. Investing: in equipment to run the business 3. Operating: making a product or providing a service Creditors – people or entities to whom a business owes money. Liabilities – amounts owed to creditors in the form of debt and other obligations.  Accounts payable: the obligations to pay for goods purchased on credit.  Interest payable: on outstanding amounts owed to the bank.  Wages payable: to employees.  Sales taxes/property taxes/income taxes payable: to the government. Common stock – the total amount paid in by stockholders for the shares they purchase. Dividends – payments of cash from a corporation to its stockholders. Assets – resources owned by a business. Property, plant, and equipment, cash, investments, supplies, inventory. Revenue – the increase in assets or decrease in liabilities resulting from the sale of goods or the performance of services in the normal course of business. Sales revenue, service revenue, and interest revenue. Expenses – the cost of assets consumed or services used in the process of generating revenues. Cost of goods sold, selling expenses, marketing expenses, administrative expenses, interest expense, and income taxes. Net income – the amount by which revenues exceed expenses. Net loss – the amount by which expenses exceed revenues. Financial statements: 1. Income statement: to show how successfully your business performed during a period of time.  Income statement - reports a company’s revenues and expenses and resulting net income or loss for a specific period of time. Used to predict future net income. 2. Retained earnings statement: to indicate how much of previous income was distributed to you and the other owners of your business in the form of dividends, and how much was retained in the business to allow for future growth.  Retained earnings – the net income retained in the corporation.  Retained earnings statement – shows the amounts and causes of changes in retained earnings for a specific time period. Used to evaluate dividend payment practices. 3. Balance sheet: to represent a picture at a point in time of what your business owns (its assets) and what it owes (its liabilities).  Balance sheet – reports assets and claims to assets at a specific point in time.  Stockholder’s equity – the owners’ claim to assets. Comprised of common stock and retained earnings.  Basic accounting equation – shows the relationship among the categories on the balance sheet. Assets = liabilities + stockholder’s equity. 4. Statement of cash flows: to show where your business obtained cash during a period of time and how that cash was used.  Statement of cash flows - provides financial information about the cash receipts and cash payments of a business for a specific period of time. Reports the cash effects of a company’s operating, investing, and financing activities. Used to answer: i. Where did cash come from during this period ii. How was cash used during the period iii. What was the change in the cash balance during this period Annual report – a report prepared by corporate management that presents financial information including financial statements, a management discussion and analysis section, notes, and an independent auditor’s report. Management discussion and analysis (MD&A) – a section of the annual report which presents management’s views on the company’s ability to pay near-term obligations, its ability to fund operations and expansion, and its results of operations. Notes to the financial statements – a section of the annual report which clarifies the financial statements and provides additional detail. Auditor’s report – a section of the annual report which is prepared by an independent outside auditor and states the auditor’s opinion as to the fairness of the presentation of the financial position and results of operations and their conformance with generally accepted accounting principles.  Auditor – an accounting professional who conducts an independent examination of a company’s financial statements.  Certified public accountant (CPA) – accountants who meet certain criteria. Only CPAs may perform audits. Classified balance sheet – a balance sheet that groups together similar assets and similar liabilities, using a number of standard classifications and sections.  Assets:  Liabilities and Stockholder’s o Current Equity: assets o Long-term investments o Property, o Current liabilities plant, and equipment o Long-term liabilities o Stockholder’s equity o Intangible assets Current assets – assets that a company expects to convert to cash or use up within one year or its operating cycle, whichever is longer. Cash, investments, receivables, inventories, and prepaid expenses. Companies list current assets in the order in which they expect to convert them into cash. Operating cycle – the average time required to go from cash to cash in producing revenue—to purchase inventory, sell it on account, and then collect cash from customers. Long-term investments – investments in stocks and bonds of other corporations that are held for more than one year, long-term assets such as land or buildings that a company is not currently using in its operating activities, and long-term notes receivable. Property, plant, and equipment – assets with relatively long useful lives that are currently used in operating the business. Land, buildings, equipment, delivery vehicles, and furniture. Depreciation – the allocation of the cost of an asset to a number of years. Accumulated depreciation – shows the total amount of depreciation that the company has expensed thus far in the asset’s life. Intangible assets – assets that do not have physical substance and yet often are very valuable. Goodwill, patents, copyrights, and trademarks/trade names that give the company exclusive right of use for a specified period of time. Current liabilities – obligations that the company is to pay within the next year or operating cycle, whichever is longer. Accounts payable, salaries and wages payable, notes payable, interest payable, and income taxes payable. Long-term liabilities – obligations that a company expects to pay after one year. Bonds payable, mortgages payable, long-term notes payable, lease liabilities, and pension liabilities. Stockholder’s equity – common stock and retained earnings.  Common stock – the investments of assets into the business by the stockholders.  Retained earnings – the income retained for use in the business. Ratio analysis – expresses the relationship among selected items of financial statement data. Ratio – expresses the mathematical relationship between one quantity and another. Comparisons to shed light on company performance: 1. Intracompany comparisons: covering two years for the same company. 2. Industry-average comparisons: based on average ratios for particular industries. 3. Intercompany comparisons: based on comparisons with a competitor in the same industry. Profitability ratios – measure the income or operating success of a company for a given period of time. Earnings per share.  Earnings per share (EPS) – measure the net income earned on each share of common stock. EPS = (Net income – preferred dividends) / (weighted average common shares outstanding) Liquidity ratios – measure short-term ability of the company to pay its maturing obligations and to meet unexpected needs for cash. Current ratios.  Current ratio – current ratio = current assets / current liabilities. Liquidity – a company’s ability to pay obligations expected to become due within the next year or operating cycle. Working capital.  Working capital – the difference between the amounts of current assets and current liabilities. Working capital = current asset – current liabilities. Solvency ratios - measure the ability of the company to survive over a long period of time. Solvency – the ability of a company to pay interest as it comes due and to repay the balance of a debt due at its maturity. Debt to assets ratio.  Debt to assets ratio – measures the percentage of total financing provided by creditors rather than stockholders. Debt to assets ratio = total liabilities (current and long-term) / total assets. Free cash flow – describes the net cash provided by operating activities after adjusting for capital expenditures and dividends paid. Free cash flow = net cash provided by operating activities – capital expenditures – cash dividends. Generally accepted accounting principles (GAAP) – a set of accounting standards that have authoritative support. Securities and Exchange Commission (SEC) – the agency of the U.S. government that oversees U.S. financial markets and accounting standard-setting bodies. Financial Accounting Standards Board (FASB) – the primary accounting standard- setting body in the United States. International Accounting Standards Board (IASB) – issues standards called International Financial reporting Standards. International Financial Reporting Standards (IFRS) – accounting standards, issued by the IASB, that have been adopted by many countries outside of the United States. Public Company Accounting Oversight Board (PCAOB) – determines auditing standards and reviews the performance of auditing firms. FASB and IASB fundamental and enhancing qualities:  Fundamental: 1. Relevance 2. Faithful representation  Enhancing: 1. Comparability – when different companies use the same accounting principles. Consistency – a company uses the same accounting principles and methods from year to year. 2. Verifiability – if independent observers, using the same methods, obtain similar results. 3. Timeliness – available to decision-makers before it loses its capacity to influence decisions. 4. Understandability – it is presented in a clear and concise fashion, so that reasonable informed users of that information can interpret it and comprehend its meaning. GAAP generally uses one of two measurement principles: 1. Historical cost principle – dictates that companies record assets at their cost. 2. Fair value principle – indicates that assets and liabilities should be reported at fair value (the price received to sell an asset or settle a liability). Full disclosure principle – requires that companies disclose all circumstances and events that would make a difference to financial statement users. Cost of restraint – constraint that weighs the cost that companies will incur to provide the information against the benefit that financial statement users will gain from having the information available.

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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Parametric curvesa. Plot the following curves, indicating