Đáp án:
191) $D.\,100\pi a^3\sqrt3$
192) $B.\, x =2$
193) $D.\, x = -2;\, x =2$
194) $D.\, 25$
Giải thích các bước giải:
191) Khối trụ tròn xoay có đường sinh đúng bằng chiều cao
$\to h = 4a\sqrt3$
$\to V = \pi r^2h = \pi.(5a)^2.4a\sqrt3 = 100\pi a^3\sqrt3$
192) $y= \sqrt{4x - x^2}$
$\to y = \sqrt{-(x-2)^2 + 4}$
$\to y \leq \sqrt{0 + 4} = 2$
Dấu $=$ xảy ra $\Leftrightarrow x - 2 = 0 \Leftrightarrow x = 2$
193) $9.3^{\displaystyle{2x}} -82.3^{\displaystyle{x}} + 9 =0$
$\Leftrightarrow \left[\begin{array}{l}3^{\displaystyle{x}} =\dfrac{1}{9}\\3^{\displaystyle{x}} = 9\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}3^{\displaystyle{x}} =3^{-2}\\3^{\displaystyle{x}} = 3^2\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x = -2\\x = 2\end{array}\right.$
194) $E = a^{\displaystyle{4\log_{a^2}5}}\qquad (a >0; a \ne 1)$
$\Leftrightarrow E = a^{\displaystyle{4\cdot\dfrac{1}{2}\log_{a}5}}$
$\Leftrightarrow E = a^{\displaystyle{2\log_{a}5}}$
$\Leftrightarrow E = a^{\displaystyle{\log_{a}5^2}}$
$\Leftrightarrow E = a^{\displaystyle{\log_{a}25}}$
$\Leftrightarrow E = 25$
