3 - 4(x + 1) < 8 + 5x
3 - 4x - 4 < 8 + 5x
-9x < 9
x > -1
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![\frac{2x-1}{3x+4}=\frac{x+7}{x-1}\\(2x-1)(x-1)=(x+7)(3x+4);3x+4\neq0;x-1\neq0\\2x^2-3x+1=3x^2+25x+28;x\neq-4/3;x\neq1\\x^2+28x+27=0;x\neq-4/3;x\neq1\\x_1=-27;x_2=-1](https://tex.z-dn.net/?f=%5Cfrac%7B2x-1%7D%7B3x%2B4%7D%3D%5Cfrac%7Bx%2B7%7D%7Bx-1%7D%5C%5C%282x-1%29%28x-1%29%3D%28x%2B7%29%283x%2B4%29%3B3x%2B4%5Cneq0%3Bx-1%5Cneq0%5C%5C2x%5E2-3x%2B1%3D3x%5E2%2B25x%2B28%3Bx%5Cneq-4%2F3%3Bx%5Cneq1%5C%5Cx%5E2%2B28x%2B27%3D0%3Bx%5Cneq-4%2F3%3Bx%5Cneq1%5C%5Cx_1%3D-27%3Bx_2%3D-1)
<span>а) 1+sin a = 2cos²(45°- a/2)
1+sina=2*(1+cos(90-a))/2=1+sina</span>
<span>1+sina=</span><span><span>1+sina
</span>формула cos²a=(1-cos2a)/2
b) 2sin²(45°- a) + sin 2a = 1
2(1-cos(90-2a))/2+sin2a=1-sin2a+sin2a=1
1=1
c) 1 - sin a = 2 sin²(45°- a/2)
1-sina=2(1-cosa)/2=1-sina
1-sina=1-sina
</span>
1.
S=a*b
153=9*17
a=9
b=17
2.
P=2*(a+b)
P=2*26=52
52/8=6,5. То есть 7 упаковок, пол упаковки останется
3) f(x) = (6x -1)⁻⁵
f'(x) = -5(6x -1)⁻⁶ * (6x -1)' = -30/(6x -1)⁶
f'(x₀) = f'(1/3) = -30/(6*1/3 -1)⁶ = -30
4) f(x) = √(3x² +4)
f'(x) = 1/2√(3x² +4) * (3x² +4)' = 6x/2√(3x² +4) = 3x/√(3x² +4)
5) f(x) = x⁵ - 3 1/3 x³ +5x
f'(x) = 5x⁴-10x² +5
f'(x₀) = f'(-1) = 5 -10 +5 = 0
Много мазни,но думаю будет понятно.