C

1103025404

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the side \( a \) of the length \( 3\,\mathrm{cm} \) and the height \( v \) of the length \( 8\,\mathrm{cm} \). Find the distance between the planes \( AEE' \) and \( BDD' \).
\( 3 \)
\( \sqrt3 \)
\( 2\sqrt3 \)
\( \frac{\sqrt3}2 \)

1103025403

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the side \( a \) of the length \( 3\,\mathrm{cm} \) and the height \( v \) of the length \( 8\,\mathrm{cm} \). Find the distance between the lines \( FA' \) and \( CD' \).
\( 3\sqrt3 \)
\( 6 \)
\( 6\sqrt3 \)
\( \frac32\sqrt3 \)

1103025402

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the side \( a \) of the length \( 3\,\mathrm{cm} \) and the height \( v \) of the length \( 8\,\mathrm{cm} \). Find the angle between the plane \( ABD' \) and the base plane \( ABC \). Round the result to two decimal places.
\( 57^{\circ} \)
\( 53.13^{\circ} \)
\( 33^{\circ} \)
\( 72.01^{\circ} \)

1103025401

Level: 
C
A regular hexagonal prism \( ABCDEFA'B'C'D'E'F' \) has the side \( a \) of the length \( 3\,\mathrm{cm} \) and the height \( v \) of the length \( 8\,\mathrm{cm} \). Find the angle between the lines \( AD' \) and \( BD' \). Round the result to two decimal places.
\( 17.46^{\circ} \)
\( 72.54^{\circ} \)
\( 16.70^{\circ} \)
\( 20.57^{\circ} \)

1103020106

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which inequality is it?
\( y > \frac32x+\frac{13}2 \)
\( y \geq \frac32x+\frac{13}2 \)
\( y < \frac32x+\frac{13}2\)
\( y \leq \frac32x+\frac{13}2\)