# Examples for secondary school students - page 38

- Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Profits

Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn? - Geometric progression 2

There is geometric sequence with a_{1}=5.7 and quotient q=-2.5. Calculate a_{17}. - Tower model

Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi - Geometric sequence

In the geometric sequence is a_{4}= 20 a_{9}= -160. Calculate the first member a_{1}and quotient q. - Center of gravity

The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A_{1}[14; -2; 5] m_{1}= 10.2 kg A_{2}[-2; -16; 7] m_{2}= 13.6 kg A_{3} - Parabola

Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax^{2}+bx+c) - Decimal to fraction

Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures. - Three vectors

The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces. - Two months

Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies? - MATES

In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is? - Ratio of two unknown numbers

Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given? - Trapezoid 15

Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4 - Segment in a triangle

In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB. - Power

Number ?. Find the value of x. - Arc-sector

arc length = 17 cm area of sector = 55 cm^{2}arc angle = ? the radius of the sector = ? - Traffic laws

Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa - Unknown number

Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies: • Difference first and second prime number is half the difference between the third and second prime numbers. • The produ - Rhombus

One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m^{3}to have painted/bricked walls with least amount of material.

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