Linear_Transformations

# 09 kilometers herea0andb1609

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Unformatted text preview: each quiz X = old grade X* = new grade X* = x + 5 a = 5, b = 1 ­ We changed the origin ( 0 = 5 ) Examples Examples • If a distance x is measured in miles, the same distance in kilometers is: x* = 1.609(x) – That is 10 miles is the same as 16.09 kilometers. – Here a = 0 and b = 1.609. – This transformation changes the units without changing the origin­ a distance of 0 miles is the same as a distance of 0 kilometers. Example Example • A temperature x measured in degrees Fahrenheit (°F) must be re­expressed in degrees Celsius (°C) to align with every other country in the world. – The transformation is: X* = 5/9( X – 32 ) • What does “a” and “b” equal? • a = ­ 160/9 • b = 5/9 – This changes both the unit size and the origin of the measurements. 0º C is 32º F. Problem #1 Problem #1 • The average salary for an employee at Acme Corporation is \$30,000 per year. This year, management awards the following bonuses to every employee. – A Christmas bonus of \$500 – An incentive bonus equal to 10% of the employee’s salary. • What is the mean bonus received by employees? – (A) \$500 (B) \$3,000 (C) \$3,500 (D) None of the above. (E) There is not enough information to answer this question. Problem #1 Continued Problem #1 Continued • The correct answer is C. To compute the bonus, management applies the following linear transformation to the each employee's salary: – x* = bx + a Y = 0.10 * x + 500 – where x* is the transformed variable (the bonus), x is the original variable (the salary), b is the multiplicative constant 0.10, and a is the additive constant 500. • Since we know that the mean salary is \$30,000, we can compute the mean bonus from the following equation: – Y = bx + a Y = 0.10 * \$30,000 + \$500 = \$3,500 Homework Homework • Textbook pp. 90 – 99 – # 23, 24, 35, 36, 46 • Chapter 3 Project Due Monday, September 12th!! • Unit 1 Test – Thursday, September 15th!...
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