ecn 4310 solution to problem

ecn 4310 solution to problem - MATF_Z02.qxd 2/23/09 18:05...

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Getting Started 1 (a) This is shown in Figure SI.1. (b) Type the heading Total Mark in cell D3. Type =B4+C4 into cell D4. Click and drag down to D9. (c) Type the heading Average: in cell C10. Type =(SUM 4:D9))/6 in cell D10 and press Enter. [Note: Excel has lots of built-in functions for performing standard calculations such as this. To ±nd the average you could just type =AVERAGE(D4:D9) in cell D10.] (d) This is shown in Figure SI.2. (e) Just put the cursor over cell C5 and type in the new mark of 42. Pressing the Enter key causes cells D5 and D10 to be automatically updated. The new spreadsheet is shown in Figure SI.3. 2 (a) 14 (b) 11 (c) 5 3 (a) 4; is the solution of the equation 2 x 8 = 0 . (b) Figure SI.4 shows the graph of 2 x 8 plotted between x = 0 and 10. (c) x 2 + 4 x + 4 ; the brackets have been ‘multiplied out’ in the expression ( x + 2) 2 . (d) 7 x + 4 ; like terms in the expression 2 x + 6 + 5 x 2 have been collected together. (e) Figure SI.5 shows the three-dimensional graph of the surface x 3 3 x + xy plotted between 2 and 2 in both the x and y directions. Figure SI.1 Figure SI.3 Figure SI.4 Figure SI.2 Solutions to Problems
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SOLUTIONS TO PROBLEMS 657 Chapter 1 Section 1.1 Practice Problems 1 (a) 30 (b) 2 (c) 5 (d) 5 (e) 36 (f) 1 2 (a) 1 (b) 7 (c) 5 (d) 0 (e) 91 (f) 5 3 (a) 19 (b) 1500 (c) 32 (d) 35 4 (a) x + 9 y (b) 2 y + 4 z (c) Not possible. (d) 8 r 2 + s + rs 3 s 2 (e) 4 f (f) Not possible. (g) 0 5 (a) 5 z 2 z 2 (b) 6 x 6 y + 3 y 6 x =− 3 y (c) x y + z x 2 x + y = z x 2 6 (a) 7( d + 3) (b) 4(4 w 5 q ) (c) 3(3 x y + 3 z ) (d) 5 Q (1 2 Q ) 7 (a) x 2 2 x + 3 x 6 = x 2 + x 6 (b) x 2 xy + yx y 2 = x 2 y 2 (c) x 2 + xy + yx + y 2 = x 2 + 2 xy + y 2 (d) 5 x 2 5 xy + 5 x + 2 yx 2 y 2 + 2 y = 5 x 2 3 xy + 5 x 2 y 2 + 2 y 8 (a) ( x + 8)( x 8) (b) (2 x + 9)(2 x 9) Exercise 1.1 (p. 30) 1 (a) 20 (b) 3 (c) 4 (d) 1 (e) 12 (f) 50 (g) 5 (h) 3 (i) 30 (j) 4 2 (a) 1 (b) 3 (c) 11 (d) 16 (e) 1 (f) 13 (g) 11 (h) 0 (i) 31 (j) 2 3 (a) 3 (b) 2 (c) 18 (d) 15 (e) 41 (f) 3 (g) 18 (h) 6 (i) 25 (j) 6 4 (a) 2 PQ (b) 8 I (c) 3 xy (d) 4 qwz (e) b 2 (f) 3 k 2 5 (a) 19 w (b) 4 x 7 y (c) 9 a + 2 b 2 c (d) x 2 + 2 x (e) 4 c 3 cd (f) 2 st + s 2 + t 2 + 9 6 (a) 10 (b) 18 (c) 2000 (d) 96 (e) 70 7 (a) 1 (b) 5 (c) 6 (d) 6 (e) 30 (f) 44 8 (a) 16 (b) Presented with the calculation, 4 2 , your calculator uses BIDMAS, so squares frst to get 16 and then subtracts From zero to give a fnal answer, 16. To obtain the correct answer you need to use brackets: 9 (a) 9 (b) 21; no 10 (a) 43.96 (b) 1.13 (c) 10.34 (d) 0.17 (e) 27.38 (f) 3.72 (g) 62.70 (h) 2.39 11 (a) 7 x 7 y (b) 15 x 6 y (c) 4 x + 12 (d) 21 x 7 (e) 3 x + 3 y + 3 z (f) 3 x 2 4 x (g) 2 x 5 y + 4 z 12 (a) 5(5 c + 6) (b) 9( x 2) (c) x ( x + 2) (d) 4(4 x 3 y ) (e) 2 x (2 x 3 y ) (f) 5(2 d 3 e + 10) 13 (a) x 2 + 7 x + 10 (b) a 2 + 3 a 4 (c) d 2 5 d 24 (d) 6 s 2 + 23 s + 21 (e) 2 y 2 + 5 y + 3 (f) 10 t 2 11 t 14 (g) 9 n 2 4 (h) a 2 2 ab + b 2 14 (a) 6 x + 2 y (b) 11 x 2 3 x 3 (c) 14 xy + 2 x ; (d) 6 xyz + 2 xy (e) 10 a 2 b (f) 17 x + 22 y (g) 11 3 p (h) x 2 + 10 x 15 (a) ( x + 2)( x 2) (b) ( Q + 7)( Q 7) (c) ( x + y )( x y ) (d) (3 x + 10 y )(3 x 10 y ) 16 (a) 4 x 2 + 8 x 2 (b) 13 x Exercise 1.1* (p. 32) 1 (a) 3 (b) 5 (c) 7 2 (a) 2 7 (9 + 3) 17 (b) 8 (2 + 3) 4 1 (c) 7 (2 6 + 10) = 1 3 (a) 6 (b) 6 (c) 5 (d) 96 (e) 1
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This note was uploaded on 08/22/2011 for the course ECON 3170 taught by Professor Oaisd during the Spring '11 term at Utah State University.

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ecn 4310 solution to problem - MATF_Z02.qxd 2/23/09 18:05...

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