The number $10$ is divided into two parts such that the sum of double of the first part and the square of the second part is minimum. The two parts are respectively:

The equation $x \log x = 3 - x$:

If the extreme value of the function $f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x}$ in the interval $[0, \frac{\pi}{2}]$ is $m$ and it exists at $x = k$,then $\cos k =$

If $\frac{dy}{dx} = (x - 1)^3 (x - 2)^4$,then $y$ has:

Let $\sqrt{3}$ be the radius and $\frac{\pi}{3}$ be the semi-vertical angle of a given cone. Then the height of the right circular cylinder of maximum volume that can be inscribed in the given cone is

$A$ wire of length $36 \text{ m}$ is cut into two pieces. One piece is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum,and the circumference of the circle is $k \text{ m}$,then $\left(\frac{4}{\pi}+1\right) k$ is equal to ..... .