![1) \ a) \ 10x^2y(-3xy^2)^3 = 10x^2y(-27x^3y^6) =\\ -270x^5y^7\\ b) (x+4y)^2 - (4y-x)(x+4y) = \\ (x+4y)((x+4y) - (4y-x)) =\\ (x+4y)*2x = 2x^2 + 8xy \\](https://tex.z-dn.net/?f=1%29+%5C+a%29+%5C+10x%5E2y%28-3xy%5E2%29%5E3+%3D+10x%5E2y%28-27x%5E3y%5E6%29+%3D%5C%5C+-270x%5E5y%5E7%5C%5C+b%29+%28x%2B4y%29%5E2+-+%284y-x%29%28x%2B4y%29+%3D+%5C%5C+%28x%2B4y%29%28%28x%2B4y%29+-+%284y-x%29%29+%3D%5C%5C+%28x%2B4y%29%2A2x+%3D+2x%5E2+%2B+8xy+%5C%5C)
2) ![a) \ ab^3 - 9a^3b = ab(b^2 - 9a^2) \\ b) -25a+10a^2-a^2 = -25a+9a^2 = \\ a(9a - 25)](https://tex.z-dn.net/?f=a%29+%5C+ab%5E3+-+9a%5E3b+%3D+ab%28b%5E2+-+9a%5E2%29+%5C%5C+b%29+-25a%2B10a%5E2-a%5E2+%3D+-25a%2B9a%5E2+%3D+%5C%5C+a%289a+-+25%29)
3) ![(5x-4)/4 - (x +2)/3 = 2 \\ (5x-4)/4 - (x +2)/3 = 2 | * 12 \\ (5x-4)*3 - (x +2)*4 = 24 \\ 15x - 12 - 4x - 8 = 24 \\ 11x = 44 \\ x = 4](https://tex.z-dn.net/?f=%285x-4%29%2F4+-+%28x+%2B2%29%2F3+%3D+2+%5C%5C+%285x-4%29%2F4+-+%28x+%2B2%29%2F3+%3D+2+%7C+%2A+12+%5C%5C+%285x-4%29%2A3+-+%28x+%2B2%29%2A4+%3D+24+%5C%5C+15x+-+12+-+4x+-+8+%3D+24+%5C%5C+11x+%3D+44+%5C%5C+x+%3D+4)
4) 2*x = 6*m + 8*u
x - количество деталей в заказе.
m - количество деталей, которое производит мастер в час
u - количество деталей, которое производит ученик в час
x = 6*m
x = 8*u
7 = m + u
2*x = 6*m + 6*u + 2*u
2*x = 6*7 + 2*u
(6*7 + 2*u)/2 = 8*u
3*7 + u = 8*u
u = 3 детали в час
7 = m + 3
m = 4 детали в час
Ответ: <em>x = 24 детали.</em>
<span>Sin^2(3pi/2-y)+sin^2(3pi+y)+2tg(5pi/2-y)×tg (3pi+y)
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Решение
Вычислить Sin²(3π/2-y)+sin²(3π+y)+2tg(5π/2-y)*tg (3π+y) .
<span>---</span>
Применяя формулы приведения ,получаем :
Sin²(3π/2-y)+sin²(3π+y)+2tg(5π/2-y)*tg (3π+y)= (cos²y +sin²y)+ 2ctqy*tqy =1 +2*`1 =3.
ответ : 3.
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sin (3π<span>/2-y)) = -cosy
</span>sin(3π +y ) =sin( (2π+(π +y ) )=sin(π<span> +y </span><span>) = </span> -siny
tg(5π/2-y) =tg((2π +(π<span>/2-y) )</span> =tq(π/2-y) =ctqy
tq(3π +y ) =tq( (2π+(π +y ) ) =tq(π<span> +y ) =tqy</span>
log₆144--log₆4-11=log₆(36*4)-log₆4-11=log₆(36 * 4) - log₆4-11=log₆6²+log₆4-log₆4-11=2-11= - 9
(у-5)² : 2у + 12у² - 36 : 2у - 10 = у² - 10у + 25/2у + 12у² - 18у - 10 = 13у² - 31/2у - 10