1.
а) 3^(-5) : 3^(-7) -2^(-2)*2^4 +((2/3)^(-1))^3 =3² -2² +(3/2)³ =67/ 8.
б) ((3¹⁰)*(32)) (^1/5) -∛48/(∛2*∛3) = ((3¹⁰)*(2⁵)) (^1/5) -∛48/(∛(2*3) =
3²*2 - ∛(48/6) =18 -2 =16.
в) 25^(3/2)*25^(-1) + (5³)^(2/3): 5³ -48^(2/3):6^(2/3) =5³/25 +5²/5³ -(48/6)^(2/3) =
5 +1/5 - (2³)^(2/3) = 5 +1/5 -2² = 1,2.
------------
2. 8600 =0,86*10⁴ ; 0,0076 =0,76*10^(-2) .
---
0,86*10⁴ *0,76*10^(-2) =0,86*0,76*10² =0,6536*10².
0,86*10⁴ : 0,76*10^(-2) = (0,86/ 0,76) *10⁶ ≈ 0,1132*10⁷ .
------------
3.
а) 3x ^(-9)*2x⁵/ x^(-4) =6x^(-4)/x^(-4) = 6 . * * * x≠0 * * *
б) (x ^(-1) +y^(-1))*(1/xy)^(-2) =(1/x+1/y) * (xy)² = xy(x+y).
------------
4. a ^(5/3) / (∛a²) *a^(1/4)) = a / a^(1/4) =a ^(3/4) , если a=81 то :
=81^(3/4) =(3⁴)^(3/4) =3³ =27.
------------
5. 0,76^(2/3) =∛0,76² >∛ 0,67² = 0,67^(2/3) ;
( 3,09)^(-1/3) =1/∛(3,09) < 1/∛(3,08) =( 3,08)^(-1/3) .
<span>
</span>
1) pi/2 < a < pi, поэтому sin a > 0, cos a < 0
cos a = -√6/4; cos^2 a = 6/16
sin^2 a = 1 - cos^2 a = 1 - 6/16 = 10/16; sin a = √10/4
tg a = sin a / cos a = (√10/4) : (-√6/4) = -√10/√6 = -√5/√3 = -√15/3
2) 0 < a < pi/2, поэтому sin a > 0, cos a > 0
sin a = √2/3; sin^2 a = 2/9
cos^2 a = 1 - sin^2 a = 1 - 2/9 = 7/9; cos a = √7/3
tg a = sin a / cos a = (√2/3) : (√7/3) = √2/√7 = √14/7
3) 3pi/2 < a < 2pi, поэтому sin a < 0, cos a > 0
cos a = 15/17; cos^2 a = 225/289
sin^2 a = 1 - cos^2 a = 1 - 225/289 = 64/289; sin a = -8/17
tg a = sin a / cos a = (-8/17) : (15/17) = -8/15
Х+у=59
х-у=35
2х=59+35
2x=94
x=94:2=47
y=59-47=12
47+12=59
<span>47-12=35</span>
Что??!_____________________________
-3х²-6х+с=0
х1+х2=-(-6/-3)=-2
х1-х2=5
Прибавим
2х1=3⇒х1=1,5
х2=-2-х1=-2-1,5=-3,5
с/-3=х1*х2⇒с=-3х1*х2=-3*1,5*(-3,5)=15,75