Radical equations and inequalities

1003177803

Level: 
C
Choose the domain of the expression. \[ \frac1{\sqrt{|3x-9|-\sqrt2}} \]
\( \left(-\infty;3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3+\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(-3+\frac{\sqrt2}3;\infty\right) \)

9000024805

Level: 
C
A falling body dropped at a velocity \(60\, \mathrm{m}\mathrm{s}^{-1}\). Find the initial height \(h\), if the relation between the velocity and the initial height \(h\) is \(v = \sqrt{2hg}\). Use \(g = 10\, \mathrm{m}\mathrm{s}^{-2}\) for acceleration of gravity.
The initial height is between \(150\, \mathrm{m}\) and \(200\, \mathrm{m}\).
The initial height is smaller than \(100\, \mathrm{m}\).
The initial height is between \(100\, \mathrm{m}\) and \(150\, \mathrm{m}\).
The initial height is bigger than \(200\, \mathrm{m}\).

9000024807

Level: 
C
A body hangs on a string of the length \(l_{1}\). The length \(l\) of the spring defines the period \(T\) of motion by the relation \[ T = 2\pi \sqrt{ \frac{l} {g}}, \] where \(g\) is a standard acceleration of gravity. We have to adjust the length of the string such that the period doubles. Find the new length of the string.
We elongate the string by \(3\cdot l_{1}\), i.e. \(l_{2} = l_{1} + 3l_{1}\).
The length doubles, i.e. \(l_{2} = 2l_{1}\).
The new length will be half of the original length, i.e. \(l_{2} = \frac{1} {2}l_1\).
We shorten the string by \(3\cdot l_{1}\), i.e. \(l_{2} = l_{1} - 3l_{1}\).