# Examples for secondary school students - page 32

- Acceleration

The car accelerates at rate 0.5m/s^{2}. How long travels 400 meters and what will be its speed? - Median

In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb. - Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle. - Committees

How many different committees of 6 people can be formed from a class of 30 students? - Cosine

The point (8, 6) is on the terminal side of angle θ. cos θ = ? - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Area and two angles

Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°. - Garden pool

Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool? - Orchard

Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou - Blackjack TU160

Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At - Trainings

The table contains tennis training schedule for Saturday's younger students during the winter indoor season. Before the start of the summer season is preparing a new training schedule. Tomas Kucera will be able to practice only in the morning, sisters Kova - Divisors

The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers. - Tetrahedral prism - rhomboid base

Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm. - Midpoint of segment

Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B? - Tree

How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground. - Two wine

In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine? - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Exponential equation

Solve exponential equation (in real numbers): 9^{8x-2}=9

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