72/( Х + 5 ) + 54/( Х - 5 ) = 9( х^2 - 25 )
72( Х - 5 ) + 54( Х + 5 ) = 9( х^2 - 25 )
72х - 360 + 54х + 270 = 9( х^2 - 25 )
126х - 90 = 9х^2 - 225
9х^2 - 126х - 135 = 0
9( x^2 - 14x - 15 ) = 0
D = 196 + 60 = 256 = 16
X1 = ( 14 + 16 ) : 2 = 15 ( км/час ) собственная скорость баржи
Х2 = ( 14 - 16 ) : 2 = - 1 ( < 0 )
Ответ 15 км/час
1/2х-3/4х при х=2/3
1/2*2/3-3/4*2/3
1/4/3-3/8/3
3/4-9/8
6/8-9/8
<span>-3/8= -0,375</span>
<span>1) f(x)=(-2/3)x³+2x²-x</span>
<span><span> f'(x)=(-2/3)*3x²+2*2x-1 =-2x²+4x-1 </span></span>
<span><span>2) <span>g(x)=(3+2x)/x-2 = 3/x +2 -2 = 3/x</span></span></span>
<span><span><span><span> g'(x)=3*(-1)/x^2 = -3/x^2</span></span></span></span>
<span><span><span><span> g'(1) = -3/1^2 = -3/1 = -3</span></span></span></span>
<span><span><span><span>3) <span> g(x)=3x-5x²+x³ = x(3-5x+x²) = x*(x-x1)*(x-x2)</span></span></span></span></span>
<span><span><span><span><span>x1= (5+D)/2 x2= (5-D)/2 D=13^(1/2)</span></span></span></span></span>
ответ отрезек [х2; x1]
x^2-y=3 x=3-y x=3-y x=3-y [x= √3
x+y=3 (3-y)^2-y=3 9-6y+y^2-3=0 y^2-6y+6=0 { [ y=3- √3
[x=- √3
[y=3+ √3
y^2-6y+6=0
<span>D</span><span> = b</span>2<span> - 4ac = (-6)</span>2<span> - 4∙1∙6 = 12</span>
<span>D</span><span> > 0 ⇒ уравнение имеет 2 корня</span>
<span>y = -b ± √D / 2a</span>
<span>y1</span><span> = (6 - √12) / (2∙1) = 3- √3</span>
<span>y2</span><span> = 3+ √3</span>
2.5X = (X+1)*2
2.5X = 2X + 2
0.5X = 2
X = 4 (км\час) - скорость пешехода по его расчётам
Длина пути (S) = 4*2.5 = 10 (км)
Ответ: 10 км
