Matematicas

Z ^

(

x 2 x3 3 x5 x15 ) = ( 5 )3 = 15 yy 4 y y

 3 xy 3  34 x 4 y12 81x 4 y12 = =  2  24 z 8 16 z 8  2z 

4

^

2 3

5

19 19 7 −2 c6 = 2 = c 6 = c6 c

c 2 c5
3

c6

=c3c2
6

c3

 4 3 9  a − ab  ( ab3 )−2 

 a 2 − 3 ab9  =  a −2 b −6  =

−2

(

)

−2

=

(a −
2
1

a 2b 6
3

ab9

)

2

a 2b 6
9  3  3 a 4 − 2a 2 a b 3 + a b 3    a 2b 6
1

2

=

a 4 − 2a 3 b3 + a 3 b 6

7

2



1 − (1 + 0.60) −5 = 1.5077 0.60

(1 + i )12 = (1 + 0.30)2 (1 + i )12 = 1.69 1 + i = 12 1.69 i = 1.04469 − 1 i = 0.04469

(128.35) 2 (25.12)
− 1 3

= 48252.806 = 219.665

27 3 97 = 53.9301 4 28



>

log 3 (27) = L L=3

log 5 (0.008) = L L = −3 5 = 0.008
−3

log8 64 = L log8 8 = L L =1

1 )=L100 1 log10 ( ) = L 10 L = −1 log10 (

log 2 44 = L log 2 16 = L L=4



E

log 2 N = 3 N = 23 = 8

log 5 N = 3 N = 53 = 125

log 4 N =
1 2

1 2

N =4 =2

log 6 N = 5 N = 65 = 7776Z

log10 N = 2 N = 102 = 100

(1.60)− n = 0.100 log10 (1.60) − n = log10 (0.100) −n log10 (1.60) = log10 (0.100) −n = log10 (0.100) log10 (1.60)

(1 + 0.18)n − 1 = 0.35 (1 + 0.18)n = 1 + 0.35(1 + 0.18)n = 1.35 n log10 (1.18) = log10 (1.35) n= log10 (1.35) log10 (1.18)

n = −(−0.4.8990) n = 0.4.8990

n = 1.8131

1 − (1 + 0.04)− n = 0.285 1 − 0.285 = (1.04)− n 0.715 = (1.04) − n log100.715 = log10 (1.04) − n −n = log10 0.715 log10 (1.04)

n = −(−8.5534) n = 8.5534


5, −3, −11,...,

t10 = 5 + (10 − 1)(−8) t10 = −67
S10 = 10 (5 + 9*(−8)) = −335 2

1 5 3 , , ,..., 2 8 4t7 = 1 1 5 + (6) *( ) = 2 8 4

7 1 1 35 s7 = ( + 6( )) = 2 2 8 8

1 1 1 , , − ,..., 4 12 12
t20 = s20 =

1.00,1.05,1.10,...,
t12 = 1.00 + 11(0.05) = 1.55 s12 =

1 1 35 + 19(− ) = − 4 6 12 201 1 175 ( + 19(− )) = − 2 4 6 6

12 (1.00 + 11(0.05)) = 9.3 2



t1 = 8; t5 = 36
tn = t1 + (n − 1)d t5 = 36 36 = 8 + 4d 28 = 4d d =7 t10 = 8 + 9(7) = 71
s10 = 10 (8 + 9(7)) = 355 2

d ,...