КЛ=10*К+Л, а ЛК=10*Л+К. Тогда КЛ*ЛК=(10*К+Л)*(10*Л+К)=10*К^2+101*К*Л+10*Л^2
1.log(3)45/5+3^2log(3)5=log(3)9+3^log(3)25=2+25=27
2.a)a=log(3)x,a²-2a-3=0,a1+a2=2 Ua1*a2=-3
a1=3,log(3)x=3,x=27
a2=-1,log(3)x=-1,x=1/3
б)lg(x+1,5)=lg1/x < x>0
x+1,5=1/x
x²+1,5x-1=0,x1=1/2 u x=-2 - не удов.усл.
3.2x-5> u 2x-5<4,x>2,5 U x<4,5
4.y`=e^x+x*e^x=e^x(1+x)=0
1+x=0,x=-1
- +
------------------------------------------------------
-1
убыв. min возр.
у(-1)=-1/e
5.x-y=2;x=2+ y
2^2+y*5^2-y=40
4*2^7*25/5^y=40
2^y/5^y=40/100=2/5
(2/5)^y=2/5
y=1,x=2+1=3
Y=5/(x²-9)
D(y)∈(-∞;-3) U (-3;3) U (3;∞)
y(-x)=5/(x²-9) четная
(0;-5/9)-точка пересечения с осями
х=-3 и х=3-вертикальные асиптоты
y`=-2x/(x²-9)²
-2x=0
x=0
+ + _ _
--------(-3)-----------------(0)-------------(3)---------------
возр возр max убыв убыв
Длина единичной окружности: с= 2·π·1 = 2π.
4.2
Дуга АМ =
![\frac{c}{8}=\frac{2 \pi }{8}=\frac{\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B8%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D)
Дуга BD =
![\frac{c}{2}=\frac{2 \pi }{2}=\pi](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B2%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B2%7D%3D%5Cpi)
Дуга CK =
![c*\frac{10}{12}=\frac{5c}{6}=\frac{5*2 \pi }{6}=\frac{5\pi }{3}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B10%7D%7B12%7D%3D%5Cfrac%7B5c%7D%7B6%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B6%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B3%7D)
Дуга MP =
![c*(\frac{1}{8}+\frac{2}{12})=c*(\frac{1}{8}+\frac{1}{6})=\frac{7c}{24}=\frac{7*2 \pi }{24}=\frac{7\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B2%7D%7B12%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B6%7D%29%3D%5Cfrac%7B7c%7D%7B24%7D%3D%5Cfrac%7B7%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B12%7D)
Дуга DM =
![c*\frac{3}{8}=\frac{3*2 \pi }{8}=\frac{3\pi }{4}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B3%2A2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B4%7D)
Дуга MK =
![c*(\frac{1}{8}+\frac{1}{12})=\frac{5c}{24}=\frac{5*2 \pi }{24}=\frac{5\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B12%7D%29%3D%5Cfrac%7B5c%7D%7B24%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B12%7D)
Дуга CP =
![c*\frac{11}{12}=\frac{11*2 \pi }{12}=\frac{11\pi }{6}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B11%7D%7B12%7D%3D%5Cfrac%7B11%2A2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B11%5Cpi+%7D%7B6%7D)
Дуга PC =
![\frac{c}{12}=\frac{2 \pi }{12}=\frac{\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B12%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D)
4.3
Дуга АМ =
![\frac{2}{5}*\frac{c}{4}=\frac{c}{10}=\frac{2 \pi }{10}=\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7Bc%7D%7B10%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B10%7D%3D%5Cfrac%7B%5Cpi+%7D%7B5%7D)
Дуга МB =
![\frac{3}{5}*\frac{c}{4}=\frac{3c}{20}=\frac{3*2\pi }{20}=\frac{3\pi }{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7B3c%7D%7B20%7D%3D%5Cfrac%7B3%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B10%7D)
Дуга DМ =
![c*(\frac{1}{4}+\frac{2}{5}*\frac{1}{4})=c*(\frac{1}{4}+\frac{1}{10})=\frac{7c}{20}=\frac{7*2\pi }{20}=\frac{7\pi }{10}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B10%7D%29%3D%5Cfrac%7B7c%7D%7B20%7D%3D%5Cfrac%7B7%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B10%7D)
Дуга МC =
![c*(\frac{3}{5}*\frac{1}{4}+\frac{1}{4})=c*(\frac{3}{20}+\frac{1}{4})=\frac{8c}{20}=\frac{2c}{5}=\frac{2*2\pi }{5}=\frac{4\pi }{5}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B3%7D%7B20%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3D%5Cfrac%7B8c%7D%7B20%7D%3D%5Cfrac%7B2c%7D%7B5%7D%3D%5Cfrac%7B2%2A2%5Cpi+%7D%7B5%7D%3D%5Cfrac%7B4%5Cpi+%7D%7B5%7D)
1) 10 способов,чтобы выбрать капитана