1103163602
Level:
A
The graph of \( f' \) is given in the figure. Find the interval where \( f \) is an increasing function. (The function \( f' \) is the derivative of the function \( f \).)
\( (-1;1) \)
\( (-3;-1) \)
\( (2;4) \)
\( (0;2) \)
A
1103163601
Level:
A
The graph of \( f \) is given in the figure. Choose which of the following graphs is the graph of \( f' \). (The function \( f' \) is the derivative of the function \( f \).)
1103090806
Level:
A
We are given the line segment \( AB \):
\begin{align*}
x&=2+2t, \\
y&=-1+t;\ t\in [0;1],
\end{align*}
and the points \( K=\left[\frac72;-\frac14\right] \), \( L=[-2;-3] \) and \( M=\left[5;\frac12\right] \). Choose a picture where the mutual position of the points \( A \), \( B \), \( K \), \( L \), and \( M \) is indicated correctly.
1103061408
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=|BC|=6\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the planes \( ABC \) and \( AFH \) (see the picture). Round the result to two decimal places.
\( 62.06^{\circ} \)
\( 53.13^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)
1103061407
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( CG \) and \( EC \) (see the picture). Round the result to two decimal places.
\( 42.03^{\circ} \)
\( 47.97^{\circ} \)
\( 45^{\circ} \)
\( 50.04^{\circ} \)
1103061406
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the planes \( ABC \) and \( EFC \) (see the picture). Round the result to two decimal places.
\( 63.43^{\circ} \)
\( 26.57^{\circ} \)
\( 45^{\circ} \)
\( 56.2^{\circ} \)
1103061405
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( AG \) and \( BH \) (see the picture). Round the result to two decimal places.
\( 67.71^{\circ} \)
\( 45^{\circ} \)
\( 37.08^{\circ} \)
\( 49.1^{\circ} \)
1103061404
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( HG \) and \( AH \) (see the picture). Round the result to two decimal places.
\( 90^{\circ} \)
\( 85^{\circ} \)
\( 56.15^{\circ} \)
\( 33.85^{\circ} \)
1103061403
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( CG \) and \( SC \), where \( S \) is the midpoint of the diagonal \( EG \) (see the picture). Round the result to two decimal places.
\( 24.26^{\circ} \)
\( 45^{\circ} \)
\( 35.24^{\circ} \)
\( 63.21^{\circ} \)
1103061402
Level:
A
The rectangular box \( ABCDEFGH \) has sides of lengths \( |AB|=6\,\mathrm{cm} \), \( |BC|=4\,\mathrm{cm} \), \( |AE|=8\,\mathrm{cm} \). Find the angle between the lines \( AC \) and \( SC \), where \( S \) is the midpoint of the diagonal \( EG \) (see the picture). Round the result to two decimal places.
\( 65.74^{\circ} \)
\( 70.28^{\circ} \)
\( 75^{\circ} \)
\( 45^{\circ} \)