9000151305
Level:
B
Find the angle \(\varphi \)
between the lines \(x + y + 1 = 0\)
and \(x - y - 1 = 0\).
\(90^{\circ }\)
\(0^{\circ }\)
\(30^{\circ }\)
\(60^{\circ }\)
B
9000150107
Level:
B
Evaluate the following integral on the interval \((3;+\infty)\).
\[
\int \frac{x^{3} - 27}
{x - 3} \, \mathrm{d}x
\]
\(\frac{x^{3}}
{3} + \frac{3x^{2}}
{2} + 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}}
{3} -\frac{3x^{2}}
{2} + 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}}
{3} -\frac{3x^{2}}
{2} - 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}}
{3} + \frac{3x^{2}}
{2} - 9x + c,\ c\in \mathbb{R}\)
9000153606
Level:
B
Give a verbal description to the angle shown in the picture.
The angle between the edge on triangular face and the base edge from the same face.
The angle between the triangular face and a base edge not in this face.
The angle between two triangular faces having a common edge.
The angle between a triangular face and square base.
9000153603
Level:
B
Give a verbal description to the angle shown in the picture.
The angle between two opposite triangular faces.
The angle between a triangular face and the base.
The angle between two edges in the same triangular face.
The angle between two triangular faces having a common edge.
9000153601
Level:
B
Give a verbal description to the angle shown in the picture.
The angle between the triangular face and the base.
The angle between the edge and the base.
The angle between two triangular faces.
The angle between the edge of a triangular face and the base edge.
9000153604
Level:
B
Give a verbal description to the angle shown in the picture.
The angle between two edges in a common triangular face.
The angle between two opposite triangular faces.
The angle between two opposite edges.
The angle between two triangular faces having common edge.
9000153602
Level:
B
Give a verbal description to the angle shown in the picture.
The angle between the edge and the base.
The angle between the triangular face and the square base.
The angle between two opposite edges.
The angle between the edge on a face and the base edge.
9000149707
Level:
B
Find the center of the following hyperbola.
\[
5x^{2} - 6y^{2} - 30x + 12y + 9 = 0
\]
\([3;1]\)
\([3;-1]\)
\([-3;1]\)
\([-3;-1]\)
9000149710
Level:
B
Find the vertex of the following parabola.
\[
x^{2} - 6x - 12y - 3 = 0
\]
\([3;-1]\)
\([3;1]\)
\([-3;1]\)
\([-3;-1]\)
9000149709
Level:
B
Find the vertex of the following parabola.
\[
y^{2} - 12x + 4y + 64 = 0
\]
\([5;-2]\)
\([5;2]\)
\([-5;2]\)
\([-5;-2]\)