C

2010006003

Level: 
C
Find the set of values of the parameter \( c\in\mathbb{R} \) for which the line \( 5x-3y-c=0 \) isn't a secant of the ellipse \( 25x^2+16y^2=400 \).
\( (-\infty;-25 ] \cup [ 25;\infty) \)
\( (-25;25) \)
\( \{-25,25\} \)
\( (-\infty;-25) \cup (25;\infty) \)
\( [ 25;\infty) \)

2010005904

Level: 
C
Find a true statement about the ellipse \[ 9 x^{2} + y^{2} + 18x = 0. \]
The tangent to the ellipse can pass through any point on the line \(x = 1\).
The tangent to the ellipse can pass through any point on the line \(y = 1\).
The tangent to the ellipse can pass through the point \([-1;1]\).
The tangent to the ellipse can pass through any point on the line \(y = -1\).

2010005509

Level: 
C
How many numbers do we need to insert between the numbers \( 5 \) and \( 640 \) so that the inserted numbers with the given two numbers are consecutive terms of a geometric sequence? The sum of all numbers inserted must be \( 630 \).
\( 6 \)
\( 4 \)
\( 3 \)
\( 5 \)
\( 7 \)

2010005508

Level: 
C
The half-life of Copper-60 is approximately \( 24 \) minutes. How long will it take before its weight decreases from \( 1\,024\,\mathrm{g} \) to \( 8\,\mathrm{g} \)?
\( 2 \) hours \( 48 \) minutes
\( 3 \) hours \( 9 \) minutes
\( 3 \) hours \( 30 \) minutes
\( 2 \) hours \( 27 \) minutes
\( 3 \) hours \( 51 \) minutes