Rational functions

2000003701

Level:

Group of mountaineers would climb the top of the mountain at an ascent speed of \(400\,\mathrm{m}\) per day in \(10\) days. However, due to the weather, they have to conquer the peak in \(8\) days. How many more meters per day do they have to cover?

\(100\) meters more

\(80\) meters more

\(120\) meters more

\(90\) meters more

Equation and Centre of Hyperbola

Submitted by ladislav.foltyn on Wed, 03/27/2019 - 13:40

Question:

In the table, mark equations of all hyperbolas with the center given in the first column.

1103129201

Level:

The thin lens equation \( \frac1a+\frac1{a'}=\frac1f \) describes the quantitative relationship between the object distance \( a \), the image distance \( a' \), and the focal length \( f \). Let the focal length of a thin lens be \( 0{.}5\,\mathrm{m} \). Choose the picture that shows the object distance vs. image distance graph, if \( a\in [0.1\,\mathrm{m};0.4\,\mathrm{m}]\cup [0.6\,\mathrm{m};3.0\,\mathrm{m}] \).

1103108604

Level:

The hall’s floor needs a new tiling. All tiles used will be of the same size. The picture shows the graph of the function describing dependence of the number \( p \) of tiles needed in the hall on the area \( S \) of one tile. What is the area of the hall’s floor?

\( 10.5\,\mathrm{m}^2 \)

\( 1\:050\,\mathrm{m}^2 \)

\( 2\:100\,\mathrm{m}^2 \)

\( 42\,\mathrm{m}^2 \)

1003108603

Level:

The fuel consumption of Skoda Fabia \( 1.4 \) MPi/\( 44\,\mathrm{kW} \) stated by the manufacturer varies between \( 5.5\,\mathrm{l} \) / \( 100\,\mathrm{km} \) (out of a town) to \( 9.6\,\mathrm{l} \) / \( 100\,\mathrm{km} \) (in a town). Suppose the car’s fuel tank of capacity \( 45\,\mathrm{l} \) is filled completely. Choose the function describing relation between the distance \( p \) in \( \mathrm{km} \) that the car can travel without tanking on the fuel consumption \( s \).

\( f\colon p=\frac{4\:500}s;\ s\in[5.5;9.6] \)

\( h\colon p=\frac{45}s;\ s\in[5.5;9.6] \)

\( r\colon p=\frac s{0.45};\ s\in[5.5;9.6] \)

\( g\colon p=45\cdot s;\ s\in[5.5;9.6] \)

1103108602

Level:

In a simple electric circuit a voltage source and a variable resistor with resistance \( R \) in the range \( [1\Omega;10\Omega] \) are connected. Suppose the source gives fixed voltage of \( 5\,\mathrm{V} \). From the graphs given below select the one that describes the dependence of the electric current \( I \) on the resistance \( R \) in this circuit. (Note: The relationship between electric currant, voltage and resistance is described by Ohm’s law: \( U=RI \).)

1003108601

Level:

Peter drove from Ostrava to Warsaw. He drove at an average speed of \( 104 \) kilometres per hour and reached Warsaw in \( 4 \) hours. Select the function that describes the dependence of Peter’s driving time \( t \) on the average speed \( v \) of the car. (The driving time \( t \) is given in hours and the average speed \( v \) is given in kilometres per hour.)

\( t=\frac{416}v\text{ ,}\ v\in(0;\infty) \)

\( t=\frac{26}v\text{ ,}\ v\in(0;\infty) \)

\( t=\frac v{26}\text{ ,}\ v\in(0;\infty) \)

\( t=\frac{104}v\text{ ,}\ v\in(0;\infty) \)

1103124503

Level:

The picture shows graphs of functions: \[ \begin{aligned} f(x)&=\frac2x\text{, }x\in\left[\frac12;4\right], \\ g(x)&=\frac{-3}x\text{, }x\in\left[\frac12;4\right], \\ h(x)&=\frac4x\text{, }x\in\left[\frac12;4\right]. \end{aligned} \] Choose the correct statement.