12*5=60 (м2) - площадь одного куска
10*60=600 (м2) - можно обклеить
1.(x-6)²=(x-3)²
x²-12x+36=x²-6x+9
x²-12x+36-<span>x</span>²<span>+6x-9=0
-6x+27=0
-6x= -27
x=4.5
2. </span><span>-2x</span>²<span> - 2x + 5= -x</span>²<span> - x - (1+x</span>²<span>)
</span><span>-2x</span>²<span> - 2x + 5+x</span>²<span>+x+1+x</span>²<span>=0
</span>-x+6=0
x=6
РЕШЕНИЕ
1) (11,9 - 1 4/5)*(1 1/3) = (11,9 - 1,8)* 4/3 = 0,1* 4/3 = 4/30 = 2/15 - ОТВЕТ
2) 16 1/2 : (11 + 9 1/6) = 33/2 : 20 1/6 = 33/2 : 121/6 = (33*6)/(121*2) = 198/242 = 9/11 - ОТВЕТ
2<em>0-6=14 пейзажей выставили в галлерее</em>
<em>1</em>4-6=8
ответ на 8 больше выставили пейзажей чем портретов
Ответ:
Пошаговое объяснение:
Найдем точки пересечения параболы <em>y = x²</em> - x и прямой <em>y = 3x</em>
![\[\left\{\begin{gathered}y={x^2}-x\hfill\\y=3x\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}{x^2}-x=3x\hfill\\y=3x\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}{x^2}-4x=0\hfill\\y=3x\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}x(x-4)=0\hfill\\ y=3x\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}{x_1}=0,{x_2}=4\hfill\\{y_1}=0,{y_2}=12\hfill\\\end{gathered}\right.\]](https://tex.z-dn.net/?f=%5C%5B%5Cleft%5C%7B%5Cbegin%7Bgathered%7Dy%3D%7Bx%5E2%7D-x%5Chfill%5C%5Cy%3D3x%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5CLeftrightarrow%5Cleft%5C%7B%5Cbegin%7Bgathered%7D%7Bx%5E2%7D-x%3D3x%5Chfill%5C%5Cy%3D3x%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5CLeftrightarrow%5Cleft%5C%7B%5Cbegin%7Bgathered%7D%7Bx%5E2%7D-4x%3D0%5Chfill%5C%5Cy%3D3x%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5CLeftrightarrow%5Cleft%5C%7B%5Cbegin%7Bgathered%7Dx%28x-4%29%3D0%5Chfill%5C%5C%20y%3D3x%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5CLeftrightarrow%5Cleft%5C%7B%5Cbegin%7Bgathered%7D%7Bx_1%7D%3D0%2C%7Bx_2%7D%3D4%5Chfill%5C%5C%7By_1%7D%3D0%2C%7By_2%7D%3D12%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5C%5D)
Парабола и прямая пересекаются в точках (0; 0) и (4; 12)
Для того, чтобы получить площадь фигуры ограниченной линиями, необходимо вычислить определенный интеграл вида:
![\displaystyle\[\int\limits_a^b{\left({f(x)-g(x)}\right)}dx\]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5B%5Cint%5Climits_a%5Eb%7B%5Cleft%28%7Bf%28x%29-g%28x%29%7D%5Cright%29%7Ddx%5C%5D)
где a = x₁, b = x₂
![\[\begin{gathered}f(x)=3x\hfill\\g(x)={x^2}-x\hfill\\\end{gathered}\]](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Bgathered%7Df%28x%29%3D3x%5Chfill%5C%5Cg%28x%29%3D%7Bx%5E2%7D-x%5Chfill%5C%5C%5Cend%7Bgathered%7D%5C%5D)
![\displaystyle \[\int\limits_0^4{3xdx-\int\limits_0^4{({x^2}-x)dx}}=24-\frac{{40}}{3}=\boxed{\frac{{32}}{3}}\]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%5B%5Cint%5Climits_0%5E4%7B3xdx-%5Cint%5Climits_0%5E4%7B%28%7Bx%5E2%7D-x%29dx%7D%7D%3D24-%5Cfrac%7B%7B40%7D%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7B%7B32%7D%7D%7B3%7D%7D%5C%5D)
![\displaystyle \[\int\limits_0^4{3xdx=3\cdot\frac{{{x^2}}}{2}\mathop|\limits_0^4=}3\cdot\frac{{{4^2}}}{2}-3\cdot\frac{{{0^2}}}{2}=3\cdot8-0=24\]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%5B%5Cint%5Climits_0%5E4%7B3xdx%3D3%5Ccdot%5Cfrac%7B%7B%7Bx%5E2%7D%7D%7D%7B2%7D%5Cmathop%7C%5Climits_0%5E4%3D%7D3%5Ccdot%5Cfrac%7B%7B%7B4%5E2%7D%7D%7D%7B2%7D-3%5Ccdot%5Cfrac%7B%7B%7B0%5E2%7D%7D%7D%7B2%7D%3D3%5Ccdot8-0%3D24%5C%5D)
![\displaystyle \[\int\limits_0^4{({x^2}-x)dx=\left({\frac{{{x^3}}}{3}-\frac{{{x^2}}}{2}}\right)}\mathop|\limits_0^4=\left({\frac{{{4^3}}}{3}-\frac{{{0^3}}}{3}}\right)-\left({\frac{{{4^2}}}{2}-\frac{{{0^2}}}{2}}\right)=\frac{{64}}{3}-\frac{{16}}{2}=\frac{{40}}{3}\]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5C%5B%5Cint%5Climits_0%5E4%7B%28%7Bx%5E2%7D-x%29dx%3D%5Cleft%28%7B%5Cfrac%7B%7B%7Bx%5E3%7D%7D%7D%7B3%7D-%5Cfrac%7B%7B%7Bx%5E2%7D%7D%7D%7B2%7D%7D%5Cright%29%7D%5Cmathop%7C%5Climits_0%5E4%3D%5Cleft%28%7B%5Cfrac%7B%7B%7B4%5E3%7D%7D%7D%7B3%7D-%5Cfrac%7B%7B%7B0%5E3%7D%7D%7D%7B3%7D%7D%5Cright%29-%5Cleft%28%7B%5Cfrac%7B%7B%7B4%5E2%7D%7D%7D%7B2%7D-%5Cfrac%7B%7B%7B0%5E2%7D%7D%7D%7B2%7D%7D%5Cright%29%3D%5Cfrac%7B%7B64%7D%7D%7B3%7D-%5Cfrac%7B%7B16%7D%7D%7B2%7D%3D%5Cfrac%7B%7B40%7D%7D%7B3%7D%5C%5D)
