10
: 1) ; 2) ; 3) CD ; 4) , CD .
(-2;2) B (10;-7) (8;7)
:
.
=√(2-(-7))²+(10-(-2))² = √(81+144)=√225= 15
.
Y=kX+b.
k =dY/dX = - 9/12 = -3/4
b = Ay - k*Ax = 2 -(-3/4)*(-2) = 0.5
Y(AB) = -3/4*X + 0.5
4. CD .
CD -
k = - 1/k(AB) = - 1 /(-3/4) = 4/3.
(8;7).
b = Cy - k*Cx = 7 - 4/3*8 = - 3, 2/3
CD - Y(CD) = 4/3*X 3, 2/3
D AB CD.
4*Y+3*X = 2 - AB
3*Y - 4*X = -11 - D.
- det D = -25, detY= 25, detX= 50.
Dx = 2 Dy= - 1.
CD - .
CD = √(8² + 6²)= √100 = 10 - - -
5. O CD.
- AD -
Ox = (Cx+Dx)/2 = (8+2)/2 = 5
Oy = *Cy+Dy)/2) = (7+(-1))/2 = 3.
. (5;3) R=5.
(x-5)² + (y-3)² = 25
20
:
;
:
30
. , .
:
1. . .
:
(xn)' = n xn-1
(x)' = 1
:
.
75 x2 = 0
:x1 = 0
(-∞;0) | (0; +∞) |
f'(x) > 0 | f'(x) > 0 |
3. . .
. .
:x1 = 0
(-∞;0) | (0; +∞) |
f''(x) < 0 | f''(x) > 0 |
40
:
:
50
, , .
= sinx , =0, = , =0.
, y=f(x) Ox,
a=0, b= , f(x)=sinx, ,
60
,
|
|
, (0) = 1.
y'-y=exp(2*x)
:
-y+y' = e2 x
. :
-y+y'= 0
1. , :
y' = y
, :
ln(y) = x
y = ex
:
y(x) = C(x)(ex), y'(x) = C(x)'(ex) + C(x)(ex)'
C(x) ex+C(x)' ex-y=e2 x
C(x)' ex = e2 x
C(x)' = ex
, :
y(x)=C(x)y, :
y(x) = C(x)y = (C+ex) ex
y = C ex+e2 x
: y(0) = 1
y(0) = C+1 = 1
:
c1 = 0
, :
y(0) = e2 x
70
.
:
:
x=(-b√D)/2a, D=b²-4ac
, : k1 = 3.
C1, C2 − .
80
. ,
:
2 , , 6*6=36.
8 2 , .
4+4 =8;
3+5 =8;
5+3=8;
2+6 =8;
6+2 =8.
, ( 8 ), 5. 36. 5/36=0,138888888. 0, 139 ( )
90
X Y Y X.
x | ||||||||||
y |
:
Rx,y | = |
| , (1.4) : |
Mx | = |
|
| xk, | My | = |
|
| yk, | Mxy | = |
|
| (1,5)xkyk |
Sx2 | = |
|
| xk2 - Mx2, | Sy2 | = |
|
| yk2 - My2 (1,6) |
(1.4), xk2, yk2 xkyk 1.
1
k | xk | yk | k 2 | yk 2 | kyk |
484.00000 | 625.00000 | 550.00000 | |||
529.00000 | 900.00000 | 690.00000 | |||
576.00000 | 900.00000 | 720.00000 | |||
625.00000 | 900.00000 | 750.00000 | |||
625.00000 | 1225.00000 | 875.00000 | |||
529.00000 | 625.00000 | 575.00000 | |||
324.00000 | 625.00000 | 450.00000 | |||
441.00000 | 400.00000 | 420.00000 | |||
361.00000 | 100.00000 | 190.00000 | |||
400.00000 | 100.00000 | 200.00000 |
Mx
xk
x1 + x2 + + x10 = 22.00000 + 23.00000 +... + 20.00000 = 220.000000
|
|
220.00000 / 10 = 22.00000
Mx = 22.000000
My.
yk
y1 + y2 + + y10 = 25.00000 + 30.00000 +... + 10.00000 = 240.000000
240.00000 / 10 = 24.00000
My = 24.000000
Mxy.
6- 1
550.00000 + 690.00000 +... + 200.00000 = 5420.000000
5420.00000 / 10 = 542.00000
Mxy = 542.000000
Sx2
4- 1
484.00000 + 529.00000 +... + 400.00000 = 4894.000000
4894.00000 / 10 = 489.40000
Mx Sx2
Sx2 = 489.40000 - 22.000002 = 489.40000 -484.00000 = 5.40000
Sy2
5- 1
625.00000 + 900.00000 +... + 100.00000 = 6400.000000
6400.00000 / 10 = 640.00000
My Sy2
Sy2 = 640.00000 - 24.000002 = 640.00000 -576.00000 = 64.00000
Sx2 Sy2.
Sx2Sy2 = 5.40000 64.00000 = 345.600000
, SxSy.
SxSy = 18.59032
R = (542.00000 - 22.00000 24.00000) / 18.59032 = (542.00000
528.00000) / 18.59032 = 0.75308
: Rx,y = 0.753080
4. .
, ( ) X Y. , X , Y ,
Y = a + bX (2.1), :
b = | Rx,y |
| = | Rx,y |
|
a = My - bMx
b . a b .
Y X :
σy/x = σy |
| = Sy |
| - , |
δy/x = |
| 100% - |
σy/x , Y , () X.
| . |
Sy2 / Sx2 = 64.00000 / 5.40000 = 11.85185
| . |
- :
Sy / Sx = 3.44265
b
b = 0.75308 3.44265 = 2.59259
a
a = 24.00000 - 2.59259 22.00000 = -33.03704
.
Sy2 :
Sy = |
| = 8.00000; | ||||
Rx,y :
R2x,y = 0.753082 = 0.56713
( )
σy/x = 8.00000 |
| = 5.26343 |
δy/x = (5.26343 / 24.00000)100% = 21.93096%
: | : Y = 2.59259 X -33.03704 (2.6) |
: σy/x = 5.26343; δy/x = 21.93096% |