3^(-18) / 3^(-20)=3^(-18+20)=3^2=9. Ответ: цифра 1.
умножаем первое уравнение на 2, а второе на -3 и получаем:
6х+8у=0 и -6х-9у=-3
складываем два уравнения и получаем:
-у=-3 и 6х+8у=0
умножаем первое уравнение на -1 и получаем:
у=3 и 6х+8*3=0
у=3 и 6х=-24
у=3 и х=-4
а) Loq(4) sinπ/12 +1/3Loq³(4) sin13π/6+ Loq(4) sin7π/12 =
Loq(4) sinπ/12 +1/3Loq³(4) sin(2π+π/6)+ Loq(4) sin(π/2+π/12) =
Loq(4) sinπ/12 +1/3Loq³(4) sinπ/6+ Loq(4) cosπ/12 =
Loq(4) sinπ/12 +Loq(4) sinπ/6+ Loq(4) cosπ/12 =
Loq(4) sinπ/12 *cosπ/12 *sinπ/6) =Loq(4) (1/2)sinπ/6 *sinπ/6)=
Loq(4) (1/2)³ = Loq(2²) (2)^(-3) = -3/2 = -1,5.
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б) (1/2)Loq(8) (cosπ/8 -sinπ/8)² - Loq(8) (cosπ/8 +sinπ/8) ^(-1) =
|| т.к. cosπ/8 -sinπ/8 >0||
=((1/2)*2)Loq(8) (cosπ/8 -sinπ/8) - (-1)Loq(8) (cosπ/8 +sinπ/8)=
Loq(8) (cosπ/8 -sinπ/8) + Loq(8) (cosπ/8 +sinπ/8) =
Loq(8) (cosπ/8 -sinπ/8)*(cosπ/8 +sinπ/8) =Loq(8) (cos²π/8 -sin²π/8)=
Loq(8) cos2*(π/8) = Loq(8) cosπ/4 =Loq(8) 1/√2 = Loq(2³) 2^(-1/2) =
(-1/2)/3 = - 1/6.
5x+6+x-3=5+x-4
5x=-2
x=-2/5
2) y<=5-x
y>=-1
y<=x+5
S=36/25*(5*10)/2=36
1)y<2-|x|
x>=0 y<2-x
x<0 y<2+x
y>|x-1|
x>=1 y>x-1
x<1 y>1-x
x-1=2-x x=1,5 y=0.5
A(0;2) B(3/2;1/2) AB=(3/2;-3/2) |ab|=3/2sqrt(2)
C(1;0) bc=(1/2;1/2) |bc|=1/2sqrt(2)
S=|ab|*|bc|=3/2*sqrt(2)*1/2*sqrt(2)=3/2