=2*(-3)²-0,5*4+6=2*9-2+6=18-2+6=22
тетрадь x рублей, альбом x+40;
5x+x+40=356;
6x=316;
x=52,(6)
альбом 52,(6)+40=92,(6).
тетрадь + альбом = 52,(6)+92,(6)=145р33к.
6x²+bx-7=0, x=1/3
6(1/3)²+b/3-7=0
6/9+b/3-7=0
2/3+b/3-7=0
2+b-21=0
b-19=0
b=19
D=361+168=529, √D=√529=23
x1=(-19+23)/12=4/12=1/3
x2=(-19-23)/2=-42/2=-21
Otvet: b=19
![\frac{ x^{2} - y^{2} }{ x^{2} +2xy+ y^{2} }= \frac{(x-y)(x+y)}{(x+y) ^{2} }= \frac{x-y}{x+y}\\\\ \frac{23,5-6,5}{23,5+6,5} = \frac{17}{30}\\\\\\ \frac{2x}{4x+3} \geq \frac{1}{2} \\\\ \frac{2x}{4x+3}- \frac{1}{2} \geq 0\\\\ \frac{4x-4x-3}{2(4x+3)} \geq 0\\\\ -\frac{3}{2(4x+3)} \geq 0\\\\ \frac{1}{4x+3} \leq 0\\\\4x+3 \leq 0\\\\4x \leq -3\\\\x \leq -0,75](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B2%7D+-+y%5E%7B2%7D+%7D%7B+x%5E%7B2%7D+%2B2xy%2B+y%5E%7B2%7D+%7D%3D+%5Cfrac%7B%28x-y%29%28x%2By%29%7D%7B%28x%2By%29+%5E%7B2%7D+%7D%3D+%5Cfrac%7Bx-y%7D%7Bx%2By%7D%5C%5C%5C%5C+%5Cfrac%7B23%2C5-6%2C5%7D%7B23%2C5%2B6%2C5%7D+%3D++%5Cfrac%7B17%7D%7B30%7D%5C%5C%5C%5C%5C%5C+%5Cfrac%7B2x%7D%7B4x%2B3%7D+%5Cgeq++%5Cfrac%7B1%7D%7B2%7D+%5C%5C%5C%5C+%5Cfrac%7B2x%7D%7B4x%2B3%7D-+%5Cfrac%7B1%7D%7B2%7D+%5Cgeq+0%5C%5C%5C%5C+%5Cfrac%7B4x-4x-3%7D%7B2%284x%2B3%29%7D+%5Cgeq+0%5C%5C%5C%5C+-%5Cfrac%7B3%7D%7B2%284x%2B3%29%7D++%5Cgeq+0%5C%5C%5C%5C+%5Cfrac%7B1%7D%7B4x%2B3%7D+%5Cleq+0%5C%5C%5C%5C4x%2B3+%5Cleq+0%5C%5C%5C%5C4x+%5Cleq+-3%5C%5C%5C%5Cx+%5Cleq+-0%2C75++++++++++)
ОДЗ: 4x + 3 ≠ 0 ⇒ x ≠ - 0,75
Ответ: (- ∞ ; - 0,75)
Находим первую производную функции:
y' = -30cos(x)+33
Приравниваем ее к нулю:
-30cos(x)+33 = 0
cos(x)=33/30
cos(x)=1.1
Корней нет, так как принимает свои значения [-1;1]
Вычисляем значения функции на отрезке
f(π/2) ≈ 50.8363
f(0) = 29
Ответ: fmin<span> = 29, f</span>max<span> = 50.84</span>