# Examples for secondary school students - page 31

1. Golden ratio Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line.
2. Nuts How many we must have at least nuts if we can equally divide it to 10 children, 11 children or 19 children and any nut left?
3. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
4. Three-digit How many three-digit natural numbers is greater than 321 if no digit in number repeated?
5. Prism The volume of tetrahedral prism is 2.43 m3. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
6. Wind drift The plane flies at 860 km/h, passing distance 3000 kilometers with the wind and once again against the wind for 6 h 59 min. What is the wind speed?
7. Angle in RT Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
8. Aircrafts Above the town hall tower flew the plane with constant speed 592 km/h and 15 minutes later the second plane at speed of 675 km/h. How long and how far from the town hall will be aircrafts caught up?
9. Meridian What is the distance (length) the Earth's meridian 23° when the radius of the Earth is 6370 km?
10. Bottles of juice How many 2-liter bottles of juice need to buy if you want to transfer juice to 50 pitchers rotary cone shape with a diameter of 24 cm and base side length of 1.5 dm.
11. Combinatorics The city has 7 fountains. Works only 6. How many options are there that can squirt ?
12. Sequence 2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
13. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
14. Rectangle vs square One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle.
15. Elevator In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the count
16. Garage There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag
17. Vertices of RT Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
18. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
19. Max - cone From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.
20. Hockey Hockey match ended 8:2. How many different matches could be?

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