1) Б. С(3; 0; 0)
2. AO = √(x² + y² + z²) = √(9 + 1 + 25) = √35
3. a(-8; 4; -1), b(2; 3; -6)
1) |a| = √(64 + 16 + 1) = √81 = 9 (A)
2) |b| = √(4 + 9 + 36) = √49 = 7 (Б)
3) |a - b| = |(-10; 1; 5)| = √(100 + 1 + 25) = √126 = 3√14 (Д)
4) a·b = -8·2 + 4·3 + (-1)·(-6) = -16 + 12 + 6 = 2 (В)
4. x₁ = 2x₀ - x₂ = 8 + 2 = 10;
y₁ = 2y₀ - y₂ = -12 - 1 = -13;
z₁ = 2z₀ - z₂ = 22 - 7 = 15
A(10; -13; 15)
5. a·b = 0;
5·7 + n·4 - 3·9 = 0;
35 + 4n - 27 = 0;
4n = -8;
n = -2.
6. A(5; 8; 0), B(-7; 10; 2), C(3; 2; -3)
x₀ = (x₁ + x₂)/2 = (5 - 7)/2 = -2/2 = -1
y₀ = (y₁ + y₂)/2 = (8 + 10)/2 = 18/2 = 9
z₀ = (z₁ + z₂)/2 = (0 + 2)/2 = 2/2 = 1
E(-1; 9; 1)
CE = √(4² + 7² + 4²) = √(16 + 49 + 16) = √81 = 9
7. k = DB₁
DB₁ = √(a² + b² + c²) = √(BC² + BA² + BB₁²) = √(36 + 9 + 25) = √70
2) х1=0 х2=-4
4) х=1
6) х1=9 х2=-1
8) не знаю
10)-9/10
12) х=4
14)х=-2
16) не знаю
Объяснение:
2) 7^х^2+4х-5=1
7^х^2+4х-5=7^0
х^2+4х-5=0 Д= 16+20=36
х1=0 х2=-4
4) 4^5х+1=8^2х+3
(2^2)^5х+1=(2^3)^2х+3
2^10х+2=2^6х+6
10х+2=6х+6
10х-6х=6-2
4х=4
х=1
6) 12^х^2-8х-8=12^1
х^2-8х-8=1
х^2-8х-8-1=0
х^2-8х-9=0 Д=64+36=100
х1=9 х2=-1
10) 36^3х+8 : 6^5= 6^2-4х
(6^2)^3х+8 : 6^5= 6^2-4х
6^6х+16 : 6^5=6^2-4х
6^6х+16-5=6^2-4х
6^6х+11=6^2-4х
6х+11=2-4х
6х+4х=2-11
10х=-9
Х=-9/10
12) 7^2-х * 343^х= 49^2х+5
7^2-х * (7^3)^х=(7^2)^2х+5
7^2-х * 7^3х=7^4х+10
7^2-х+3х=7^4х+10
7^2+2х=7^4х+10
2+2х=4х+10
2х-4х=10-2
-2х=8
х=4
14)
