B

9000035003

Level: 
B
The tree of the height \(12\, \mathrm{m}\) is observed from the place horizontal with the base of the tree. The angle of elevation is \(10^{\circ }\). Find the distance of the observer from the base and round to the nearest meters.
\(68\, \mathrm{m}\)
\(2\, \mathrm{m}\)
\(12\, \mathrm{m}\)
\(48\, \mathrm{m}\)

9000035008

Level: 
B
Sun shines to the road at the angle \(53^{\circ }22'\). An electric column near the road casts the shadow of the length \(4.5\, \mathrm{m}\). Find the height of the column and round your answer to the nearest meters.
\(6\, \mathrm{m}\)
\(3\, \mathrm{m}\)
\(4\, \mathrm{m}\)
\(5\, \mathrm{m}\)

9000035009

Level: 
B
Two forces act on the body at one point. The force \(F_{1} = 760\, \mathrm{N}\) acts horizontally from left to the right and the force \(F_{2} = 28.8\, \mathrm{N}\) acts vertically from the top to the bottom. Find the angle between the horizontal direction and the direction of the resulting force and round your answer to the nearest degrees and minutes.
\(2^{\circ }10'\)
\(3^{\circ }10'\)
\(2^{\circ }20'\)
\(3^{\circ }20'\)

9000034305

Level: 
B
Solve the following equation in the set of complex numbers. \[ x^{4} + 16 = 0 \]
\(x_{1, 2} = \sqrt{2}(1\pm \mathrm{i}),\ x_{3, 4} = -\sqrt{2}(1\pm \mathrm{i})\)
\(x_{1, 2} = 1\pm \mathrm{i},\ x_{3, 4} = -1\pm \mathrm{i}\)
\(x_{1, 2} = 2(1\pm \mathrm{i}),\ x_{3, 4} = -2(1\pm \mathrm{i})\)
\(x_{1, 2} = \frac{\sqrt{2}} {2} (1\pm \mathrm{i}),\ x_{3, 4} = -\frac{\sqrt{2}} {2} (1\pm \mathrm{i})\)

9000034704

Level: 
B
Solve the inequality \[ ax - 2 > 0 \] with a real unknown \(x\) and a nonpositive real parameter \(a < 0\).
\(\left (-\infty ; \frac{2} {a}\right )\)
\(\left (-\infty ;-\frac{2} {a}\right )\)
\(\left (\frac{2} {a};\infty \right )\)
\(\left (-\frac{2} {a};\infty \right )\)

9000034306

Level: 
B
Solve the following equation in the set of complex numbers. \[ x^{6} - 64 = 0 \]
\(x_{1, 2} =\pm 2,\ x_{3, 4} = 1\pm \mathrm{i}\sqrt{3},\ x_{5, 6} = -1\pm \mathrm{i}\sqrt{3}\)
\(x_{1, 2} =\pm 2,\ x_{3, 4} = \frac{1} {2}\pm \mathrm{i}\frac{\sqrt{3}} {2} ,\ x_{5, 6} = -\frac{1} {2}\pm \mathrm{i}\frac{\sqrt{3}} {2} \)
\(x_{1, 2} =\pm 4,\ x_{3, 4} = 1\pm \mathrm{i}\sqrt{3},\ x_{5, 6} = -1\pm \mathrm{i}\sqrt{3}\)
\(x_{1, 2} =\pm 8,\ x_{3, 4} = 2\pm 2\mathrm{i}\sqrt{3},\ x_{5, 6} = -2\pm 2\mathrm{i}\sqrt{3}\)

9000034705

Level: 
B
Solve the inequality \[ 2x + b > 0 \] with a real unknown \(x\) and a real parameter \(b\in \mathbb{R}\).
\(\left (-\frac{b} {2};\infty \right )\)
\(\left (\frac{b} {2};\infty \right )\)
\(\left (-\infty ; \frac{b} {2}\right )\)
\(\left (-\infty ;-\frac{b} {2}\right )\)

9000034807

Level: 
B
Find the polar form of the complex number \(z = 2\mathrm{i}\).
\(2\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)
\(\sqrt{2}\left (\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\right )\)
\(\cos \frac{\pi }{2} + \mathrm{i}\sin \frac{\pi }{2}\)
\(2\left (\cos 0 + \mathrm{i}\sin 0\right )\)