Page 30 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 1] USEFUL MATH 15

Answers to Supplementary Problems

1.1. (a) a + b + c − d (e) 4b + 9 (i) 3a + 13b − 4c
(b) a − b − c + d (f) −2b − 9 (j) 10b + 10c
(c) a + 2b − 8 (g) −2a + 5b
(d) a − 2b + 8 (h) −3b

1.2. (a) 4.5 (c) −3 (e) −6.5 (g)10 (i) 10
(b) 0.8 (d) −1 (f) −7.5 (h)0
1.3. (a) 2 (g) 72/y 2 (m)0
(b) 8 (h) −y(1 + z)/(1 − z) (n) 32/9
(c) −3 (i) 4y/z (o) 5 3
√
(d) 2 (j) 5y (p) y/z
(e) 2 (k) 2 (q) 2
2
(f) (z + 3y)/(3 − y) (l) 4 (r) 3
1.4. (a) a 7 (h) 2a 2 (o) a 1/2 (v) b/a
6
(b) a 2 (i) 0 (p) a 3/2 (w) 7a /b
2
(c) 1 (j) a + a 5 (q) a 2 (x) (b/a) 8
(d) a 4 (k) a 2 (r) a −2 (y) 18b 4
(e) a −4 (l) a 3/2 (s) a −4/3 (z) a 7/2 b
5
(f) a −5 (m) a 4/3 (t) a + a 1/2
2
(g) a 6 (n) a 11/2 (u) a /b 2
1.5. (a)7.2 × 10 2 (d)6.2 × 10 −5 (g)4.9527 × 10 4 (j) 4.9 × 10 10
(b)8.9 × 10 5 (e) 3.6 × 10 0 (h)2.943 × 10 −3 (k) 1.1 × 10 −8
(c) 2 × 10 −2 (f)4 × 10 −1 (i) 1.4 × 10 −3 (l) 1.4763 × 10 0

1.6. (a) 0.0003 (d) 101,000,000 (g) 4321.45 (j) 0.000069
(b) 7500 (e) 500 (h) 6,000,000
(c) 0.00008126 (f) 0.032 (i) 5.7
1.7. (a) 4.3 × 10 3 (e) 2.02 × 10 1 (i) 2.7 × 10 −4 (m) −5 × 10 −5
(b) 5.02 × 10 6 (f) 6.37 × 10 2 (j) −1.3 × 10 5 (n) 6.6 × 10 3
(c) 7.2 × 10 −2 (g) 3.7 × 10 3 (k) −3.154 × 10 7 (o) −6.64 × 10 −3
(d) 5.04 × 10 −3 (h) 4.991 × 10 7 (l) 2 × 10 3
1.8. (a)2.5 × 10 1 (d)6 × 10 15 (g)2 × 10 −8 (j) 5 × 10 −6
(b)10 6 (e) 9 × 10 −4 (h)2.5 × 10 −5
(c) 10 3 (f)8.3 × 10 −12 (i) 6 × 10 −6

1.9. (a)6.4 × 10 28 (c) 2.5 × 10 −15 (e) 9 × 10 −16 (g)3.7 × 10 10
(b)4 × 10 14 (d)3.2 × 10 −9 (f)4 × 10 −24

1.10. (a) 2 × 10 3 (d) 2 × 10 −2 (g) 3.4 × 10 4 (j) 1.6 × 10 −2 (m)1.6 × 10 −3
(b) 6.3 × 10 3 (e) 6.3 × 10 −3 (h) 7.4 × 10 4 (k) 7.4 × 10 −3
(c) 2 × 10 4 (f) 1.6 × 10 4 (i) 1.6 × 10 5 (l) 3.4 × 10 −3