Explanation Definition used: Descartes’ Rule of Signs: 1. The number of positive of a polynomial equation f ( x ) = 0 cannot be greater than the number of changes in sign in f ( x ) in moving from one term to the next in f ( x ) . 2. The number of negative cannot be greater than the number of sign changes in f ( − x ) . Calculation: It is given that the equation is 2 x 4 − 15 x 2 − 7 x + 3 = 0 . Here, f ( x ) = 2 x 4 − 15 x 2 − 7 x + 3 . Move from left to right, obtain the number of sign changes. As there are 2 sign changes, the number of positive roots is 2. Change the function f ( x ) to f ( − x ) as follows

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 15.3, Problem 22E

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Chapter 15.3, Problem 21E

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2) Find the general solution to the differential equation d²x dt² 2 dax = dt

Last Chance Mine (LCM) purchased a coal deposit for $2,918,300. It estimated it would extract 18,950 tons of coal from the deposit. LCM mined the coal and sold it, reporting gross receipts of $1.24 million, $13 million, and $11 million for years 1 through 3, respectively. During years 1-3, LCM reported net income (loss) from the coal deposit activity in the amount of ($11,400), $550,000, and $502,500, respectively. In years 1-3, LCM extracted 19,950 tons of coal as follows: (1) Tons of Coal 18,950 Depletion (2) Basis (2)(1) Rate $2,918,300 $154.00 Tons Extracted per Year Year 1 4,500 Year 2 8,850 Year 3 6,600 Note: Leave no answer blank. Enter zero if applicable. Enter your answers in dollars and not in millions of dollars. a. What is LCM's cost depletion for years 1, 2, and 3? Cost Depletion Year 1 Year 2 Year 3

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Chapter 15 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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