ANSWERS TO SUPPLEMENTARY PROBLEMS in Visual Studio .NET

Creation QR Code JIS X 0510 in Visual Studio .NET ANSWERS TO SUPPLEMENTARY PROBLEMS

Fig. A-9

11 1105 , . 2 8

7 1 5 214 12.20 (a) 3, ; (b) y = x + 63; (c) (3, 0) and , 5 . 3 15 9 3 12.22 (a) Yes; (b) yes; (c) no; (d) no. 10 ; (b) no. 3 1 12.24 . 2 x( x 1)2

12.23 (a)

13.6 (a) (x 100 + 2x 50 3)(56x 7 + 20) + (7x 8 + 20x + 5)(100x 99 + 100x 49 ); (b) x 2 + 8x + 3 (x + 4)(2x) (x 2 3) = ; 2 (x + 4) (x + 4)2

2x 7 + 35x 4 + 3x 3 6x 2 7 (x 3 + 7)(5x 4 1) (x 5 x + 2)(3x 2 ) = ; (x 3 + 7)2 (x 3 + 7)2

2 12 3 12 15 (d) 6 ; (e) 24x 2 2x + 2 4 ; ( f ) 9x 2 + 1 4 + 5 . x x x x x 3 5 7 1 13.7 (a) y = x + ; (b) y = x . 4 4 4 4 13.10 (b) At x = 0 and x = 4. 1 13.8 . 4 13.9 At all points except x = 3. 13.12 8.

13.11 (a) x = 0; (b) x = 2; (c) x = 1;

14.7 (a) max = 13 (at x = 2), min = 7 (at x = 3); (b) max = 1 (at x = 1), min = (c) max = 3 (at x = 1), min = 7 129 at x = ; 8 4

31 1 at x = ; (d) max = 1 (at x = 0), min = 11 (at x = 1); 27 3 1 1 (e) max = 99 (at x = 4), min = 9 (at x = 2); ( f ) max = (at x = 3), min = (at x = 4); 5 4 5 3 1 (g) max = (at x = 4), min = (at x = 2); (h) max = (at x = 1), min = 1 (at x = 1); 4 4 3 14 2 1 (i) max = (at x = 2), min = at x = . 3 27 3 14.8 75 yd east-west by 50 yd north-south. 14.9 60 yd parallel to stream, 30 yd perpendicular to stream. 14.10 50 mi/h. 14.11 $200. 14.12 x = 350, at $65 per radio.

14.13 (a) Side of base = 5 ft, height = 5 ft; (b) side of base = 5 2 ft, height = 5/ 2 ft. 14.14 Length = 105 ft, width (parallel to divider) = 60 ft. 14.15 175.

14.16 (a) x = 50, y = 50; (b) x = 100, y = 0 or x = 0, y = 100; (c) x = 50, y = 50. 14.17 l = 314 m, w = 628/ 200 m. 14.18 (a) The entire wire for the circle; (b) 4L L for the circle, for the square. +4 +4 14.21 r = 2 ft, h = 5 ft. 3

14.19 The whole wire for the square. 2a 2a 14.22 h = , r = . 3 3 14.24 (a)

14.23 The equilateral triangle of side p/3.

3 25 , 231 ; (b) ( 5, 0). 16 16

14.25 East-west dimension = 80 ft, north-south dimension = 48 ft. 14.26 (a) 21 x 100 m; (b) 20 400 m2 (when x = 100 m). 14.27 15 tons.

ANS.]

15.7 (a) ( f g)(x) = 6 2 , (g f )(x) = ; (b) x 6 + 2x 3 5, (x 2 + 2x 5)3 ; (c) 49, 3; (d) x 6 , x 6 ; (e) x, x; 3x + 1 x+1 ( f ) x 2 4, x 2 4.

1 1 15.8 (a) All x; (b) x = ; (c) x = ; (d) x = 0; (e) x = 2. 4 3 15.9 (a) f (x) = x 3 x 2 + 2, g(x) = x 7 ; (b) f (x) = 8 x, g(x) = x 4 ; (c) f (x) = 1 + x 2 , g(x) = (d) f (x) = x 2 4, g(x) = x 1 . 15.10 (a) 4(x 3 2x 2 + 7x 3)3 (3x 2 4x + 7); (b) 15(7 + 3x)4 ; (c) 4(2x 3) 3 ; (d) 18x(3x 2 + 5) 4 ; (e) (4x 2 3)(x + 5)2 (28x 2 + 80x 9); ( f ) 15 (x + 2)2 20x(x 2 2) 4(1 6x) 3 ; (g) ; (h) ; (i) 4 2 (x 3) (2x 2 + 1)3 (3x 2 x + 5)2 x2 1 + x3 . x;

15.11 (a)

3 1/4 1 x(2 9x 3 ) 1 x(21x 8) 3 x ; (b) ; (c) 2 ; (d) ; (e) ; 2 2 x + 2( x 1)3 (1 3x 3 )2/3 (x + 1)3/2 4(7x 3 4x 2 + 2)3/4 2 + 3x ; (i) ; (h) 3 2 x3 3 4x 2 + 3 4 4 16x 1 (4 + x) (4 + x) ;

1 ( f ) 6x 1/4 + x 3/4 + x 4/3 ; (g) 3 ( j) 2(1 + x 2 x 3 ) . (1 2x)2 (1 + x 3 )1/3 8 3 x+ . 50 25

15.12 y =

5 15.13 y = x + 10. 3 3x 2 + 20x 12 8(x + 2) x+2 2 4= ; (g f ) (x) = . x 2 (x 2)2 (x 2)3