B

9000100001

Level: 
B
The function \(f(x) = 3 - 2x\) is graphed in the picture. Consider the region between the graph of the function on the interval \([ 0,\, 1.5] \) and the axes. Determine the solid of revolution obtained by revolving this region about \(y\)-axis
A cone with the base of radius \(1.5\).
A cone with the base of radius \(3\).
A pyramid of the height \(1.5\).
A pyramid of the height \(3\).

9000100003

Level: 
B
The function \(f(x) = x^{2} + 2\) is graphed in the picture. Consider the region between the graph of the function on the interval \([ 0,\, 1] \), both axes and the line \(x = 1\). Find the formula for the volume of the solid of revolution obtained by revolving this region about \(y\)-axis.
\(V =\pi \int _{ 0}^{3}1\, \mathrm{d}y -\pi \int _{2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 0}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y -\pi \int _{0}^{3}1\, \mathrm{d}y\)
\(V =\pi \int _{ 2}^{3}(\sqrt{y - 2})^{2}\, \mathrm{d}y\)

9000088807

Level: 
B
Suppose we are given the following equality of two fractions with nonzero denominators. From the given expressions, choose the one that by substituting to the starred position makes the equality true. \[ \frac{3 - 2x} {x - 2} = \frac{3(4x^{2} - 12x + 9)} {*} \]
\((3x - 6)(3 - 2x)\)
\((x - 2)(2x - 3)\)
\((x - 2)(9 - 4x)\)
\((3x - 6)(2x - 3)\)

9000086601

Level: 
B
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition \[ \neg (a \vee b) \] is true.
Both statements are false.
Both statements are true.
The statement \(a\) is true, \(b\) is false.
The statement \(a\) is false, \(b\) is true.