B

9000039302

Level: 
B
Find \(N\), the number of the turns, as a function of the other variables in the formula for the magnetic induction of a solenoid. \[ B =\mu \frac{NI} {l} \]
\(N = \frac{Bl} {\mu I} \)
\(N = \frac{Bl\mu } {I} \)
\(N = B -\mu \frac{I} {l} \)
\(N = \frac{Bl} {\mu } - I\)

9000045708

Level: 
B
Given a regular hexagon with the side \(a\), find the radius \(\rho \) of the circle inscribed to this hexagon.
\(\rho = \frac{a} {2\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 30^{\circ }\)
\(\rho = \frac{2a} {\mathop{\mathrm{tg}}\nolimits 30^{\circ }}\)
\(\rho = 2a\cdot \mathop{\mathrm{tg}}\nolimits 60^{\circ }\)

9000046405

Level: 
B
A circle is circumscribed to the regular octagon. The perimeter of the octagon is \(16\, \mathrm{cm}\). Find the radius of the circle and round the result to two decimal places. (The regular octagon is a polygon which has eight sides of equal length. The perimeter of the octagon is the sum of the length of all eight sides.) Circle circumscribed to the regular octagon.
\(2.61\, \mathrm{cm}\)
\(1.08\, \mathrm{cm}\)
\(1.41\, \mathrm{cm}\)

9000039304

Level: 
B
Find the focus length \(f\) as a function of the other variables from the following equation relating this distance with object and image distances \(a\) and \(a'\). \[ \frac{1} {f} = \frac{1} {a} + \frac{1} {a'} \]
\(f = \frac{aa'} {a+a'}\)
\(f = \frac{a-a'} {a+a'}\)
\(f = a + a'\)
\(f = \frac{a} {a'}\)

9000037409

Level: 
B
Find the polar form of the complex number \[z=\frac{1} {\cos \frac{7\pi } {6} +\mathrm{i}\sin \frac{7\pi } {6} }. \]
\(\cos \frac{5\pi } {6} + \mathrm{i}\sin \frac{5\pi } {6}\)
\(\cos \left (-\frac{5\pi } {6}\right ) + \mathrm{i}\sin \left (-\frac{5\pi } {6}\right )\)
\(\cos \frac{\pi }{6} + \mathrm{i}\sin \frac{\pi }{6}\)
\(\cos \left (-\frac{\pi }{6}\right ) + \mathrm{i}\sin \left (-\frac{\pi }{6}\right )\)

9000038906

Level: 
B
Consider the function \(f\colon y =\mathop{\mathrm{tg}}\nolimits x\). In the following list identify the nonnegative function.
None of the given functions is nonnegative.
\(A\cdot f(x)\), where \(A\in (-\infty ,0)\)
\(A\cdot f(x)\), where \(A\in (0,+\infty )\)
\(f(B\cdot x)\), where \(B\in (0,+\infty )\)
\(f(x + C)\), where \(C\in (-\infty ,0)\)

9000038907

Level: 
B
Consider the function \(f(x) =\mathop{\mathrm{cotg}}\nolimits x\) with domain restricted to the interval \(\mathop{\mathrm{Dom}}(f) = (0,\pi )\). In the following list identify the function with domain \(\left (0, \frac{\pi } {3}\right )\).
\(f(3\cdot x)\)
\(f(x - 3)\)
\(f(x + 3)\)
\(f\left (\frac{x} {3} \right )\)
\(3\cdot f(x)\)