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Math100_Asgn1_Ans

# Math100_Asgn1_Ans - Macao Polytechnic Institute School of...

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Macao Polytechnic Institute School of Business Commerce Programme 1 st Semester, Year 2008/09 Math100-21621 / 31711, Mathematics Answer to Assignment (I) 1. (a) Find the equation of the line passing through point (2, -2) and perpendicular to the line –3 y + 7 x = 20. (b) Solve the inequality |2z – 3| < 5. Give your answer in interval notation, and indicate the answer geometrically on the real-number line. (c) Solve the equation for x , 2 3 x x - = 1 9 x . Ans : (a) Rearrange the line equation: y = 7 3 x 20 3 , i.e. m 1 = 7 3 . The line passing through (2, –2), and perpendicular to m 1 : 2 2 y x + - = – 3 7 . Simplify to get: 7 y + 3 x = –8. (b) The solution to |2z – 3| < 5 is, –5 < (2z – 3) < 5. –2 < 2z < 8, –1 < z < 4. Or, z (–1, 4). (c) log 3 ( 2 3 x x - ) = log 3 ( 2 1 3 x ), x x 2 = –2 x , x 2 – 3 x = 0, x = 0 or 3. 2. Trend Equation The projected annual sales (in dollars) of a new product is given by the equation S = 150,000 + 3000 t , where t is the time in years from 2001. Such an equation is called a trend equation (o ). Find the projected annual sales for 2006. Is S a function of t ? Ans : Let 2001 correspond to t = 1, not 0. The year 2006 corresponds to t = 6. Projected annual sales for 2006, S = 150000 + 3000(6) = 168000. 3. Suppose a and b are linearly related so that a = 1 when b = 2 and a = 5 when b = 3. Find a general linear form of an equation that relates a and b . Also, find a when b = 5. Ans

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Math100_Asgn1_Ans - Macao Polytechnic Institute School of...

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