Page 321 - Theory and Problems of BEGINNING CHEMISTRY

310 SCIENTIFIC CALCULATIONS [APP.

A.41. Solve for m:

10.0g (0.693)(1.88 years)
ln =
m 2.79 years
Ans. m = 6.27 g
A.42. Solve for t:
13.1 years 72.3g

t = ln
0.693 8.11 g
Ans. t = 41.4 years
A.43. Solve for m 0 :

m 0 (0.693)(4.22 years)
ln =
1.50 g 6.71 years
Ans. m 0 = 2.32 g
A.44. Determine the values of a, b, and c in each of the following quadratic equations after you put the equation in the
2
form ax + bx + c = 0. Then calculate two values for each x.
2
2
2
2
(a) x + x − 6 = 0 (d)4x − 21x + 20 = 0 (g) x + 4 = 5x (j) x − 6x =−8
2
2
2
(b) x − 5x + 4 = 0 (e) x − 6x + 8 = 0 (h) x =−(4x + 4)
2
2
2
(c) x + 4x + 4 = 0 ( f ) x = 6 − x (i) 4x = 21x − 20
Ans.
a b c x a b c x
(a)1 1 −6 −3 and 2 (d)4 −21 20 1.25 and 4
(b)1 −5 4 1 and 4 (e)1 −6 8 2 and 4
(c)1 4 4 −2 and −2
The equations of parts f to j may be rearranged to give the same equations as in parts a to e, respectively, and so the
answers are the same.
A.45. What answer is displayed on the calculator after each of the following sequences of keystrokes?

(a) ( 2 . 3 EXP +/− 1 1 − 7 . 2 EXP +/− 1 0 ) ÷ 3
(b) 2 . 3 EXP +/− 1 1 − 7 . 2 EXP +/− 1 0 ÷ 3
(c) 5 . 0 EXP 8 log

(d) 21/x
(e) 2 + 6 = 1/x × 1 6 =
( f ) 1 4 INV log
(or 2ndF )
(g) 2 0 ln
(h) 3 x 2 STO x 2 × RCL =

Ans. (a) −2.323 333 33 − 10 (e) 2
(b) −2.17 − 10 ( f )1 14
(c) 8.698 970 004 (g)2.995 732 274
6
(d)0.5 (h) 729 (3 power)