![1)~ MK=\{-1-(-2);3-(-4)\}=\{1;7\}\\ PM=\{-2-4;-4-4\}=\{-6;-8\}\\ \\ 2)~ |MK|=\sqrt{1^2+7^2}=\sqrt{50}=5\sqrt{2}\\ |PM|=\sqrt{(-6)^2+(-8)^2}=10](https://tex.z-dn.net/?f=1%29~+MK%3D%5C%7B-1-%28-2%29%3B3-%28-4%29%5C%7D%3D%5C%7B1%3B7%5C%7D%5C%5C+PM%3D%5C%7B-2-4%3B-4-4%5C%7D%3D%5C%7B-6%3B-8%5C%7D%5C%5C+%5C%5C+2%29~+%7CMK%7C%3D%5Csqrt%7B1%5E2%2B7%5E2%7D%3D%5Csqrt%7B50%7D%3D5%5Csqrt%7B2%7D%5C%5C+%7CPM%7C%3D%5Csqrt%7B%28-6%29%5E2%2B%28-8%29%5E2%7D%3D10)
![EF=2MK-3KP=\{2\cdot1+3\cdot6;2\cdot7+3\cdot8\}=\{20;38\}](https://tex.z-dn.net/?f=EF%3D2MK-3KP%3D%5C%7B2%5Ccdot1%2B3%5Ccdot6%3B2%5Ccdot7%2B3%5Ccdot8%5C%7D%3D%5C%7B20%3B38%5C%7D)
4) Скалярное произведение двух векторов:
MK * PM = 1*(-6) + 7*(-8) = - 62
![\cos\angle (MK,PM)=\dfrac{MK\cdot PM}{|MK|\cdot |PM|}=\dfrac{-62}{5\sqrt{2}\cdot10}=-0.62\sqrt{2}](https://tex.z-dn.net/?f=%5Ccos%5Cangle+%28MK%2CPM%29%3D%5Cdfrac%7BMK%5Ccdot+PM%7D%7B%7CMK%7C%5Ccdot+%7CPM%7C%7D%3D%5Cdfrac%7B-62%7D%7B5%5Csqrt%7B2%7D%5Ccdot10%7D%3D-0.62%5Csqrt%7B2%7D)
AC=BD. AO=OC
AC=12.5*2=25=bd
ТРЕУГABC: ABC=90. AC=25
AB^2+BC^2=25^2
(3х)^2+(4x)^2=25^2
x=5
ab=15. bc=20
db^2=bc^2+cd^2
cd^2=225
cd=15
1) 3a(a-b)+b(20-b)= 3a^2 - 3ab + 20b - b^2 = 3a^2 -b^2 -3ab + 29b
2) -4x^3 (x^2 -3x+2)= -4x^5 + 12x^4 - 8x^3
3) (5c-4)^2 = 5c^2 - 4^2 = 5c^2 - 16
4) 2x^2 - 0,5x+6 при x=4
2•4^2 - 0,5•4+6
2,4²=5,76
число в квадрате должно находиться между 5,76 и 6
например, 2,41
2,41²=5,8081
или 2,43²=5,9049
Ответ: 2,41 2,43