# Examples for secondary school students - page 29

- Variations 3rd class

From how many elements we can create 13,800 variations 3rd class without repeating? - Rotary cylinder

The rotating cylinder has a surface area 69.08 cm^{2}. The area of the shell is 62.8 cm^{2}. What is the diameter of the cylinder? - Chord - TS

The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2}. What were the original dimensions of the hall? - Rectangle - sides

What is the perimeter of a rectangle with area 266 cm^{2}if length of the shorter side is 5 cm shorter than the length of the longer side? - Copiers

The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier? - Eight blocks

Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four - Fraction

Fraction ? write as fraction a/b, a, b is integers numerator/denominator. - Alloy

The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to. - Angles and sides of the triangle

Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ? - Logarithmic equation

Solve equation: log_{33}(3x + 21) = 0 - See harmonics

It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases. - Arc

Convert to arc measures (radians): 924 ° Result write as a multiple of π - Hiker and cyclist

At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker? - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - Distance

Wha is the distance between the origin and the point (18; 22)? - Exponential equation

In the set R solve the equation: ? - To the cinema

Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in. - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - Pot

Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.

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