317;318;320

a) S = ½•12√2•4•√3/2 = 6√2•4•√3/2
6√2•2√3 = 12√6
b) S = ½•3•18√2•√2/2 = 3•9√2•2√2 = 54/2 = 27
g) S = ½•14•7•77/100
7•7•77/100 = 3773/100 = 37,73

60 = ½•15•x•1/2
60 = 1/4•15•x
60 = 15/4x
16 = x
x=16

S = ½•2•2•1/2 = 1

193;194

193.

√16=4√

√25=5

4/5=2/x

x=2,5

194.

4/25=8/x

x=50

167

167

DE/EC=AD/CF=AE/EF=2/1

AD/CF=2/1

AD=7; CF=3,5

AE=10; EF=5

AD/CF=EF/EF=DE/EC=5/2

DE/EC=5/2

DE=8/5

EC=4

149;150;151

149

AB=5սմ

CD=80մմ=8սմ

MN=1դմ=10սմ

EF=?

AB/EF=CD/MN

5/x=8/10

8x=50

x=6,25սմ

BC/CD=AC/OC

150

KP/DO=MN/AL

80/100=40/x

4000=80x

x=50

151

BC/CD=AC/OC

BC/10=(2 x OC)/OC

BC/10=2

BC=20

P=2×10+2×20=60

72;73;74;75;76;77;78

72

→p = →xy+→zx+→yz

→p = →xy+→yz+→zx = xx = 0

→q = (→xy-→xz)+ →yz

→q = →xy+→yz+→zx = xx = 0

→r = (→zy-→xy)-zx

→r = →zy+→yz+→xz

→r = →xz+→zy+→yx = xx = 0

73

→xy = -a-b+c+d

74

→a = →AB

→b = →AC

a) →-a

b) AC+CB = AB

b+CB = a

CB = a-b

g) →CB+→BA = →-b

75

→a = →AM

→b = →AN

→BM = →-a

→NC = →b

→MN

AB+MN = AN

→a+→MN = →b

b-a

→BN

MB+BN = MN

→a+BN = b-a

BN = b-2a

76

→x = →AB1

→y = →AB

→B1C = x

→BB1 = BA+AB1 = -y+x = BB1

→BA = -y

→BC = BB1+B1C = -y+x+x = -y+2x = BC

77

a) →a = →AB

→b = →BC

AC = a+b

b) CA = a+b

AC = -a-b

g) AC = a-b

78

a) →a = →AB

→b = →AD

DC+CB = a-b

b) BO+OC = b

d) →BA-→DA = -a+b

66;67;68;69

b) |→AB+→AC|

BK = q/2

x²+(a/2)² = a²

x²+a²/4 = a²

x² = a²-a²/4

x² = a²(3/4)

x = ∓√a²3/4 = √a²3/√4 = √a²√3/2 = |a|√3/2 = a√3/2

AD = 2x = 2•a√3/2 = a√3

56;57;58;59

52;53;54;55

․

45;46;47;48;49

40;41;42;43;44

40

4x+3y-6 = 0 և 2x+y-4 = 0

{4x+3y-6 = 0

{2x+y-4 = 0

{4x+12-6x-6 = 0

{y = 4-2x

{-2x+6 = 0

{y = 4-2x

{x = 3

{y = -2

(3;-2)

41

M(2;5)

y = 5

x = 2

42

A(-8;-6)

B(-3;-1)

x+8/5 = y+6/5

x+8 = y+6

y = x+8-6

y = x+2

y₀ = 7

M(5;7)

43

x+5 = y-0/2

2x+10 = 5y

x-5/-5 = y/2

2x-10 = -5y

x-5/-5 = y/-2

-2x+10 = -5y

x+5/5 = y/-2

-2x-5 = 5y

44

a) (1;-2) R = 5

b) (0;-7) R = 1

g) x²+8x = (x+8/2)²-(8/2)² = (x+4)²-4² = (x+4)²-16

y²-4y = (y-4/2)²-(4/2)² = (y-2)²-2² = (y-2)²-4

(x+4)²-16+(y-2)²-4+40 = 0

(x+4)²•(y-2)² = -20

Պատ՝ չի լինում։

d) (a-b)² = a²-2ab+b²

(x²+y²-2x+4y)-20 = 0

(x²-2x+1)-1+(y²+3•2•y+y)-y-20 = 0

(x-1)²-1+(y+2)²-24 = 0

(x-1)²+(y+2)² = 25

(1;-2) R = 5