B

9000128805

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). Find the angle between the line \(BV \) and the plane \(ABC\). Round to two decimal places.
\(43.31^{\circ }\)
\(59.04^{\circ }\)
\(45^{\circ }\)

9000115605

Level: 
B
Complete the following statement: „The number is divisible by six if and only if ...”
it is divisible by both two and three.
the sum of its digits is divisible by both two and three.
the sum of its digits is even and the last digit of this number is \(3\).
the last digit of this number is \(6\).

9000115606

Level: 
B
Complete the following statement: „The number is divisible by eight if and only if ...”
the number constituted from the last three digits is divisible by eight.
the sum of its digits is divisible by eight.
it is divisible by both two and four.
the number constituted from the last two digits is divisible by eight.

9000115607

Level: 
B
Complete the following statement: „The number is divisible by nine if and only if ...”
the sum of its digits is divisible by nine.
the number constituted from the last two digits is divisible by nine.
the sum of its digits is odd.
the last digit of this number is \(9\).

9000115608

Level: 
B
Complete the following statement: „The number is divisible by ten if and only if ...”
the last digit of this number is \(0\).
the sum of its digits is divisible by ten.
the number constituted from the last two digits is divisible by five.
the last digit of this number is even.

9000117401

Level: 
B
Find the intersection of the planes \(\rho \) and \(\sigma \). \[\begin{aligned} \rho \colon 2x - 5y + 4z - 10 = 0,\qquad \sigma \colon x - y - z - 2 = 0 & & \end{aligned}\]
\(\begin{aligned}[t] p\colon x& = 3t, & \\y & = -2 + 2t, \\z & = t;\ t\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] q\colon x& = 2s - 10,& \\y & = 5s - 10, \\z & = s;\ s\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] a\colon x& = 2u - 4,& \\y & = 2u - 4, \\z & = u;\ u\in \mathbb{R} \\ \end{aligned}\)
\(\begin{aligned}[t] b\colon x& = 3v + 1,& \\y & = v - 2, \\z & = v;\ v\in \mathbb{R} \\ \end{aligned}\)

9000117408

Level: 
B
In the following list find the plane perpendicular to the plane \(\rho \). \[\begin{aligned} \rho \colon 2x - 3y + 7z - 2 = 0 & & \end{aligned}\]
\(\omega \colon x + 3y + z + 7 = 0\)
\(\tau \colon - 2x + 3y - 7z + 2 = 0\)
\(\nu \colon - 2x - 3y + 7z + 2 = 0\)
\(\sigma \colon 7x - 3y + 2z - 2 = 0\)

9000117409

Level: 
B
Find the plane parallel to \(\rho \) passing through the point \(M\). \[\begin{aligned} \rho \colon x - 2y + 5z - 3 = 0,\qquad M = [3;-1;1] & & \end{aligned}\]
\(\tau \colon x - 2y + 5z - 10 = 0\)
\(\sigma \colon 3x - y + z - 3 = 0\)
\(\nu \colon x - 2y + 5z + 1 = 0\)
\(\omega \colon 3x - y + z - 11 = 0\)

9000115610

Level: 
B
Complete the following statement: „A number is divisible by fifteen if and only if ...”
it is divisible by both three and five.
the sum of its digits is divisible by both three and five.
the sum of its digits is odd and divisible by five.
the last digit of this number is either \(5\) or \(0\).