2.
. .
, , :
:
. n n
.
, , . , = (4, 2, 5, 0, -2) ; , 5, -2.
,
(1.1),
(1.2)
(1.1) -, (1.2)--.
.
n - , :
n
=
, , :
=(0, 0, , 0).
:
.
: = .
k
.
. n , , n .
.
() .
.
1. 0,5 , 5 , 3 , 2 1,5 12, 11, 15, 30, 80 . . =(0,5; 5; 3; 2; 1,5) = (12; 11; 15; 30; 80), , , :
() = 0,5∙12+5∙11+3∙15+2∙30+1,5∙80=286 .
2. 300 000 . : 50 000 12%, 50 000 15%, 100 000 10% 100 000 20%.
= (50 000, 50 000, 100 000, 100 000), = (0,12; 0,15; 0,10; 0,20).
, :
() = 50 000∙0,12+50 000∙0,15+100 000∙0,10+100 000∙0,20 = 43 500 .
:
1. () = ().
2. (k ) =k ).
3. ( + ) =() + ().
4. () ≥ 0; () = 0 , - .
1. a = {1; 2} b = {4; 8}.
: a b = 1 4 + 2 8 = 4 + 16 = 20.
|
|
2. a b, |a| = 3, |b| = 6, 60˚.
: a b = |a| |b| cos α = 3 6 cos 60˚ = 9.
3. p = a + 3b q = 5a - 3 b, |a| = 3, |b| = 2, a b 60˚.
:
p q = (a + 3b) (5a - 3b) = 5 a a - 3 a b + 15 b a - 9 b b =
= 5 |a|2 + 12 a b - 9 |b|2 = 5 32 + 12 3 2 cos 60˚ - 9 22 = 45 +36 -36 = 45.