Page 28 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 1] USEFUL MATH 13

y x 1 2 y z
(j) = (m) = (p) =
x 5 3x + 4 x + 8 x 2 x
1 1
(k) = 8 1 2 8
x + 1 2x − 1 (n) = (q) x =
x 4 − x x
3 5
(l) = x 5 2 18
x − 1 x + 1 (o) = (r) x = x 3
2x − 1 7
1.4. Evaluate the following:
3 −2
2 5
2
3
(a) a a a a (o) a (v) (ab) (a b) −2
(g) −5 a 1/2
4 −2
(b) a a a a 2 3
a (w) 7b 2
2
14 −14
(c) a a (h) a + a 2 (p) b
a −1/2
2
a 6 (i) a − a 2 (q) (a ) 2 3
4 1/2
(d) 2 5 (x) (a b ) b
2 4 1/2
a 2 (j) a + a 3
4 −1/2
(r) (a ) a
a
a 2 (k) a 3/2 1/2 −4 1/3 3
(e) (s) (a ) 3a 2 b 2
a 6 (l) a 1/2 1/2 1/2 (y) 2a
a
a
5
(t) a + a 1/2 b a
5 −2
a a (m) aa 1/3
4
(f) (u) a (ab) −2 2 1/4
a 8 (n) a a 3 a
6 −1/2
(z) (ab)
b 8
1.5. Express the following numbers in powers-of-10 notation:
(a) 720 (d) 0.000062 (g) 49,527 (j) 49,000,000,000
(b) 890,000 (e) 3.6 (h) 0.002943 (k) 0.000000011
(c) 0.02 (f) 0.4 (i) 0.0014 (l) 1.4763
1.6. Express the following numbers in decimal notation:
(a)3 × 10 −4 (f)3.2 × 10 −2
(b)7.5 × 10 3 (g)4.32145 × 10 3
(c) 8.126 × 10 −5 (h)6 × 10 6
(d)1.01 × 10 8 (i) 5.7 × 10 0
(e) 5 × 10 2 (j) 6.9 × 10 −5
1.7. Perform the following additions and subtractions:
2
(a) 3 × 10 + 4 × 10 3 (i) 3.2 × 10 −4 − 5 × 10 −5
4
4
(b) 2 × 10 + 5 × 10 6 (j) 7 × 10 − 2 × 10 5
5
(c) 7 × 10 −2 + 2 × 10 −3 (k) 4.6 × 10 − 3.2 × 10 7
5
(d) 4 × 10 −5 + 5 × 10 −3 (l) 3 × 10 − 2.98 × 10 5
1
(e) 2 × 10 + 2 × 10 −1 (m)4.76 × 10 −3 − 4.81 × 10 −3
3
2
2
(f) 6.32 × 10 + 5 (n) 7 × 10 + 5 × 10 − 9 × 10 2
3
(g) 4 × 10 − 3 × 10 2 (o) 3 × 10 −4 + 6 × 10 −5 − 7 × 10 −3
7
(h) 5 × 10 − 9 × 10 4
1.8. Perform the following multiplications and divisions, using powers-of-10 notation:
(a) (5000)(0.005) (500,000)(18,000)
(c)
5000 9,000,000
(b)
0.005 (30)(80,000,000,000)
(d)
0.0004