Sфото=20*30=600см
Sрамки=Sфото*0,36=600*0,36
Sрамки=x*y, где 2x=3y =>y=2x/3
Sрамки=2x*x/3=600*0,36
x*x=3*300*0,36=324=18*18
x=18 - ширина рамки
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Первое см. Решение задания
2Sin(2x + π/6) + 1 = √3Sin2x + Cosx
2(Sin2xCosπ/6 + Cos2xSinπ/6) + 1 = √3Sin2x + Cosx
2(Sin2x * √3/2 + Cos2x * 1/2) + 1 = √3Sin2x + Cosx
√3Sin2x + Cos2x + 1 = √3Sin2x + Cosx
Cos2x - Cosx + 1 = 0
2Cos²x - 1 - Cosx + 1 = 0
2Cos²x - Cosx = 0
Cosx(2Cosx - 1) = 0
1) Cosx = 0
x = π/2 + πn , n ∈ Z
2) 2Cosx - 1 = 0
2Cosx = 1
Cosx = 1/2
x= ± arcCos1/2 + 2πn , n ∈ Z
x = ± π/3 + 2πn , n ∈ Z
{4-x>0
{x+5>0
{-x>-4
{x>-5
{x<4
{x>-5
\\\\\\\\\\\\\\\\\\\\\\\\\\\\
--------- -5 ------------- 4 --------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(-5; 4)
Длина интервала: 4- (-5) =4+5=9
Середина интервала: 9: 2=4,5
Ответ: 4) 4,5.